Analysis of Augmented Randomised Complete Block Design in Single and Multiple Environments Using Mixed Models
Source:R/augmentedRCBD.mix.R
augmentedRCBD.mix.RdThe function augmentedRCBD.mix implements analysis of variance of an
augmented randomised block design (Federer, 1956; Federer, 1961) and the
generation as well as comparison of the adjusted means of the
treatments/genotypes using mixed-effect models. The analysis can be performed
for cases where the design is in a single environment or is across multiple
environments such as locations and/or seasons with either 1) test treatments
are replicated across environments (scenario = "I") or 2) test
treatments are not replicated across environments (scenario = "II").
Arguments
- block
Vector of blocks (as a factor).
- treatment
Vector of treatments/genotypes (as a factor).
- env
Vector of environments (as a factor).
- y
Numeric vector of response variable (Trait).
- checks
Character vector of the checks present in
treatmentlevels.- env.random
logical. If
TRUE,envis considered as a random effect. Default isFALSE.- check.random
logical. If
TRUE,checktreatments are considered as random effects. Default isFALSE.- test.random
logical. If
TRUE,testtreatments are considered as random effects. Default isTRUE.- drop.nonsig.interaction
logical. If
TRUE, "test treatment \(\times\) environment" interaction effect is dropped from the model if found to be non-significant.- scenario
Either
1or2(see Details).- scenario.violation.threshold
Threshold proportion of number of accessions violating
scenariorequirements to trigger an error. Default of0.1.- df_method
Degrees-of-freedom method for estimation of BLUE means.
- console
If
TRUE, output will be printed to console. Default isTRUE. Default isTRUE.
Details
The model to be fitted as well as the method for estimation of treatment
means is determined by the arguments scenario, env.random,
check.random, test.random, drop.nonsig.interaction.
- 1. Single Environment: Random Effects - check, test
- Model:
y ~ (1|block) + (1|treatment)- Mean Estimate:
Check and Test treatments (BLUP)
- 2. Single Environment: Fixed Effects - check; Random Effects - test
- Model:
y ~ check + (1|block) + (1|treatment:test)- Mean Estimate:
Check treatment (BLUE) and Test treatment (BLUP)
- 3. Single Environment: Fixed Effects - check, test
- Model:
y ~ treatment + (1|block)- Mean Estimate:
Check and Test treatments (BLUE)
- 4. Multiple Environments - Scenario I: Random Effects - env, check, test; Test treatment \(\times\) Environment Interaction - FALSE
- Model:
y ~ (1|env) + (1|treatment) + (1|env:block) + (1|env:treatment:check)- Mean Estimate:
Check and Test treatments (BLUP)
- 5. Multiple Environments - Scenario I: Random Effects - env, check, test; Test treatment \(\times\) Environment Interaction - TRUE
- Model:
y ~ (1|env) + (1|treatment) + (1|env:block) + (1|env:treatment)- Mean Estimate:
Check and Test treatments (BLUP)
- 6. Multiple Environments - Scenario I: Fixed Effects - check; Random Effects - env, test; Test treatment \(\times\) Environment Interaction - FALSE
- Model:
y ~ check + (1|env) + (1|env:block) + (1|env:check) + (1|treatment:test)- Mean Estimate:
Check treatment (BLUE) and Test treatment (BLUP)
- 7. Multiple Environments - Scenario I: Fixed Effects - check; Random Effects - env, test; Test treatment \(\times\) Environment Interaction - TRUE
- Model:
y ~ check + (1|env) + (1|env:block) + (1|env:treatment) + (1|treatment:test)- Mean Estimate:
Check treatment (BLUE) and Test treatment (BLUP)
- 8. Multiple Environments - Scenario I: Fixed Effects - check, test; Random Effects - env; Test treatment \(\times\) Environment Interaction - FALSE
- Model:
y ~ treatment + (1|env) + (1|env:block2) + (1|env:check)- Mean Estimate:
Check and Test treatments (BLUE)
- 9. Multiple Environments - Scenario I: Fixed Effects - check, test; Random Effects - env; Test treatment \(\times\) Environment Interaction - TRUE
- Model:
y ~ treatment + (1|env) + (1|env:block2) + (1|env:treatment)- Mean Estimate:
Check and Test treatments (BLUE)
- 10. Multiple Environments - Scenario I: Fixed Effects - env; Random Effects - check, test; Test treatment \(\times\) Environment Interaction - FALSE
- Model:
y ~ env + (1|treatment) + (1|env:block) + (1|env:treatment:check)- Mean Estimate:
Check and Test treatments (BLUP)
- 11. Multiple Environments - Scenario I: Fixed Effects - env; Random Effects - check, test; Test treatment \(\times\) Environment Interaction - TRUE
- Model:
y ~ env + (1|treatment) + (1|env:block) + (1|env:treatment)- Mean Estimate:
Check and Test treatments (BLUP)
- 12. Multiple Environments - Scenario I: Fixed Effects - env, check; Random Effects - test; Test treatment \(\times\) Environment Interaction - FALSE
- Model:
y ~ env + check + env:check + (1|env:block) + (1|treatment:test)- Mean Estimate:
Check treatment (BLUE) and Test treatment (BLUP)
- 13. Multiple Environments - Scenario I: Fixed Effects - env, check; Random Effects - test; Test treatment \(\times\) Environment Interaction - TRUE
- Model:
y ~ env + check + env:check + (1|env:block) + (1|treatment:test) + (1|env:treatment:test)- Mean Estimate:
Check treatment (BLUE) and Test treatment (BLUP)
- 14. Multiple Environments - Scenario I: Fixed Effects - env, check, test; Test treatment \(\times\) Environment Interaction - FALSE
- Model:
y ~ env + treatment + env:check + (1|env:block)- Mean Estimate:
Check and Test treatments (BLUE)
- 15. Multiple Environments - Scenario I: Fixed Effects - env, check, test; Test treatment \(\times\) Environment Interaction - TRUE
- Model:
y ~ env + treatment + env:treatment + (1|env:block)- Mean Estimate:
Check and Test treatments (BLUE)
- 16. Multiple Environments - Scenario II: Random Effects - env, check, test; Test treatment \(\times\) Environment Interaction - FALSE
- Model:
y ~ (1|env) + (1|treatment) + (1|env:block) + (1|env:treatment:check)- Mean Estimate:
Check treatment (BLUP) and Test treatment (BLUP within Environment)
- 17. Multiple Environments - Scenario II: Fixed Effects - check; Random Effects - env, test; Test treatment \(\times\) Environment Interaction - FALSE
- Model:
y ~ check + (1|env) + (1|env:block) + (1|env:check) + (1|treatment:test)- Mean Estimate:
Check treatment (BLUE) and Test treatment (BLUP within Environment)
- 18. Multiple Environments - Scenario II: Fixed Effects - check, test; Random Effects - env; Test treatment \(\times\) Environment Interaction - FALSE
- Model:
y ~ treatment + (1|env) + (1|env:block2) + (1|env:check)- Mean Estimate:
Check treatment (BLUE) and Test treatment (BLUE within Environment)
- 19. Multiple Environments - Scenario II: Fixed Effects - env; Random Effects - check, test; Test treatment \(\times\) Environment Interaction - FALSE
- Model:
y ~ env + (1|treatment) + (1|env:block) + (1|env:treatment:check)- Mean Estimate:
Check treatment (BLUP) and Test treatment (BLUP within Environment)
- 20. Multiple Environments - Scenario II: Fixed Effects - env, check; Random Effects - test; Test treatment \(\times\) Environment Interaction - FALSE
- Model:
y ~ env + check + env:check + (1|env:block) + (1|treatment:test)- Mean Estimate:
Check treatment (BLUE) and Test treatment (BLUP within Environment)
- 21. Multiple Environments - Scenario II: Fixed Effects - env, check, test; Test treatment \(\times\) Environment Interaction - FALSE
- Model:
y ~ env + treatment + env:check + (1|env:block)- Mean Estimate:
Check treatment (BLUE) and Test treatment (BLUE within Environment)
Note
Making checks random but tests fixed breaks the nesting/partition logic and creates a non-identifiable treatment variance decomposition. So this combination is not implemented in this function.
Examples
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Single Environment: Random Effects - check, test
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Example data
blk <- c(rep(1,7),rep(2,6),rep(3,7))
trt <- c(1, 2, 3, 4, 7, 11, 12, 1, 2, 3, 4, 5, 9, 1, 2, 3, 4, 8, 6, 10)
y1 <- c(92, 79, 87, 81, 96, 89, 82, 79, 81, 81, 91, 79, 78, 83, 77, 78, 78,
70, 75, 74)
y2 <- c(258, 224, 238, 278, 347, 300, 289, 260, 220, 237, 227, 281, 311,
250, 240, 268, 287, 226, 395, 450)
data <- data.frame(blk, trt, y1, y2)
# Convert block and treatment to factors
data$blk <- as.factor(data$blk)
data$trt <- as.factor(data$trt)
# 01. Random Effects - check, test
out1 <- augmentedRCBD.mix(block = data$blk, treatment = data$trt,
y = y1, checks = c("1", "2", "3", "4"),
check.random = TRUE, test.random = TRUE,
console = TRUE)
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#>
#> Augmented Design Details
#> ========================
#> NULL
#>
#> Model Formula
#> =========================
#> y ~ (1 | treatment) + (1 | block)
#> Model Details
#> =========================
#> Linear mixed model fit by REML. t-tests use Satterthwaite's method [
#> lmerModLmerTest]
#> Formula: frmla_int
#> Data: model.frame(mod_final)
#> Control: lmerControl(optimizer = "bobyqa")
#>
#> REML criterion at convergence: 122.8
#>
#> Scaled residuals:
#> Min 1Q Median 3Q Max
#> -1.39758 -0.63355 -0.09756 0.32441 1.98295
#>
#> Random effects:
#> Groups Name Variance Std.Dev.
#> treatment (Intercept) 0.00 0.000
#> block (Intercept) 22.17 4.709
#> Residual 26.27 5.125
#> Number of obs: 20, groups: treatment, 12; block, 3
#>
#> Fixed effects:
#> Estimate Std. Error df t value Pr(>|t|)
#> (Intercept) 81.500 2.951 2.031 27.61 0.00121 **
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> optimizer (bobyqa) convergence code: 0 (OK)
#> boundary (singular) fit: see help('isSingular')
#>
#>
#> Model Diagnostics
#> =========================
#> conv_opt conv_lme4
#> 1 0 boundary (singular) fit: see help('isSingular')
#> opt_message opt_warnings singular treatment block Residual
#> 1 Normal exit from bobyqa TRUE 0 22.17234 26.26546
#> AIC BIC
#> 1 130.7885 134.7715
#>
#> ANOVA, Fixed Effects
#> =========================
#> NULL
#>
#> LRT, Random Effects
#> =========================
#> ANOVA-like table for random-effects: Single term deletions
#>
#> Model:
#> y ~ 1 + (1 | treatment) + (1 | block)
#> npar logLik AIC LRT Df Pr(>Chisq)
#> <none> 4 -61.394 130.79
#> (1 | treatment) 3 -61.394 128.79 0.0000 1 1.00000
#> (1 | block) 3 -64.072 134.14 5.3557 1 0.02065 *
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Model Formula
#> =========================
#> treatment mean SE df type
#> 1 1 81.5 0 NA BLUP
#> 2 2 81.5 0 NA BLUP
#> 3 3 81.5 0 NA BLUP
#> 4 4 81.5 0 NA BLUP
#> 5 5 81.5 0 NA BLUP
#> 6 6 81.5 0 NA BLUP
#> 7 7 81.5 0 NA BLUP
#> 8 8 81.5 0 NA BLUP
#> 9 9 81.5 0 NA BLUP
#> 10 10 81.5 0 NA BLUP
#> 11 11 81.5 0 NA BLUP
#> 12 12 81.5 0 NA BLUP
# 02. Fixed Effects - check; Random Effects - test
out2 <- augmentedRCBD.mix(block = data$blk, treatment = data$trt,
y = y1, checks = c("1", "2", "3", "4"),
check.random = FALSE, test.random = TRUE,
console = TRUE)
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#>
#> Augmented Design Details
#> ========================
#> NULL
#>
#> Model Formula
#> =========================
#> y ~ check + (1 | block) + (1 | treatment:test)
#> Model Details
#> =========================
#> Linear mixed model fit by REML. t-tests use Satterthwaite's method [
#> lmerModLmerTest]
#> Formula: frmla_int
#> Data: model.frame(mod_final)
#> Control: lmerControl(optimizer = "bobyqa")
#>
#> REML criterion at convergence: 106.2
#>
#> Scaled residuals:
#> Min 1Q Median 3Q Max
#> -1.2205 -0.3482 -0.2066 0.4002 1.6731
#>
#> Random effects:
#> Groups Name Variance Std.Dev.
#> treatment:test (Intercept) 10.52 3.243
#> block (Intercept) 17.69 4.206
#> Residual 24.84 4.984
#> Number of obs: 20, groups: treatment:test, 12; block, 3
#>
#> Fixed effects:
#> Estimate Std. Error df t value Pr(>|t|)
#> (Intercept) 81.8763 3.0135 3.0523 27.170 9.66e-05 ***
#> check1 2.7904 3.8030 0.9570 0.734 0.601
#> check2 -2.8763 3.8030 0.9570 -0.756 0.592
#> check3 0.1237 3.8030 0.9570 0.033 0.979
#> check4 1.4570 3.8030 0.9570 0.383 0.769
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Correlation of Fixed Effects:
#> (Intr) check1 check2 check3
#> check1 0.050
#> check2 0.050 -0.300
#> check3 0.050 -0.300 -0.300
#> check4 0.050 -0.300 -0.300 -0.300
#>
#> Model Diagnostics
#> =========================
#> conv_opt conv_lme4 opt_message opt_warnings singular
#> 1 0 Normal exit from bobyqa FALSE
#> treatment.test block Residual AIC BIC
#> 1 10.51697 17.68735 24.8361 122.1983 130.1642
#>
#> ANOVA, Fixed Effects
#> =========================
#> Type III Analysis of Variance Table with Satterthwaite's method
#> Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
#> check 32.778 8.1946 4 2 0.3299 0.842
#>
#> LRT, Random Effects
#> =========================
#> ANOVA-like table for random-effects: Single term deletions
#>
#> Model:
#> y ~ check + (1 | block) + (1 | treatment:test)
#> npar logLik AIC LRT Df Pr(>Chisq)
#> <none> 8 -53.099 122.20
#> (1 | block) 7 -54.569 123.14 2.94061 1 0.08638 .
#> (1 | treatment:test) 7 -53.164 120.33 0.13036 1 0.71806
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Model Formula
#> =========================
#> treatment mean SE df type
#> 1 1 84.66667 4.969050 2.152436 BLUE
#> 2 2 79.00000 4.969050 2.152436 BLUE
#> 3 3 82.00000 4.969050 2.152436 BLUE
#> 4 4 83.33333 4.969050 2.152436 BLUE
#> 5 5 79.95499 2.786081 NA BLUP
#> 6 6 79.91155 2.779019 NA BLUP
#> 7 7 83.91242 2.779019 NA BLUP
#> 8 8 78.42413 2.779019 NA BLUP
#> 9 9 79.65750 2.786081 NA BLUP
#> 10 10 79.61407 2.779019 NA BLUP
#> 11 11 81.83003 2.779019 NA BLUP
#> 12 12 79.74765 2.779019 NA BLUP
# 03. Random Effects - Fixed Effects - check, test
out3 <- augmentedRCBD.mix(block = data$blk, treatment = data$trt,
y = y1, checks = c("1", "2", "3", "4"),
check.random = FALSE, test.random = FALSE,
console = TRUE)
#>
#> Augmented Design Details
#> ========================
#> NULL
#>
#> Model Formula
#> =========================
#> y ~ treatment + (1 | block)
#> Model Details
#> =========================
#> Linear mixed model fit by REML. t-tests use Satterthwaite's method [
#> lmerModLmerTest]
#> Formula: frmla_int
#> Data: model.frame(mod_final)
#>
#> REML criterion at convergence: 58.9
#>
#> Scaled residuals:
#> Min 1Q Median 3Q Max
#> -1.1234 -0.2299 0.0000 0.0000 1.4439
#>
#> Random effects:
#> Groups Name Variance Std.Dev.
#> block (Intercept) 1.944 1.394
#> Residual 26.972 5.193
#> Number of obs: 20, groups: block, 3
#>
#> Fixed effects:
#> Estimate Std. Error df t value Pr(>|t|)
#> (Intercept) 81.014 1.550 1.341 52.258 0.0035 **
#> treatment1 3.653 3.041 6.031 1.201 0.2747
#> treatment2 -2.014 3.041 6.031 -0.662 0.5323
#> treatment3 0.986 3.041 6.031 0.324 0.7567
#> treatment4 2.319 3.041 6.031 0.763 0.4744
#> treatment5 -2.182 5.040 7.677 -0.433 0.6770
#> treatment6 -5.287 5.015 7.413 -1.054 0.3250
#> treatment7 14.427 5.015 7.413 2.876 0.0224 *
#> treatment8 -10.287 5.015 7.413 -2.051 0.0772 .
#> treatment9 -3.182 5.040 7.677 -0.631 0.5462
#> treatment10 -6.287 5.015 7.413 -1.253 0.2481
#> treatment11 7.426 5.015 7.413 1.481 0.1799
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Correlation of Fixed Effects:
#> (Intr) trtmn1 trtmn2 trtmn3 trtmn4 trtmn5 trtmn6 trtmn7 trtmn8
#> treatment1 -0.213
#> treatment2 -0.213 0.028
#> treatment3 -0.213 0.028 0.028
#> treatment4 -0.213 0.028 0.028 0.028
#> treatment5 0.052 -0.076 -0.076 -0.076 -0.076
#> treatment6 0.069 -0.084 -0.084 -0.084 -0.084 -0.127
#> treatment7 0.069 -0.084 -0.084 -0.084 -0.084 -0.127 -0.132
#> treatment8 0.069 -0.084 -0.084 -0.084 -0.084 -0.127 -0.072 -0.132
#> treatment9 0.052 -0.076 -0.076 -0.076 -0.076 -0.062 -0.127 -0.127 -0.127
#> treatment10 0.069 -0.084 -0.084 -0.084 -0.084 -0.127 -0.072 -0.132 -0.072
#> treatment11 0.069 -0.084 -0.084 -0.084 -0.084 -0.127 -0.132 -0.072 -0.132
#> trtmn9 trtm10
#> treatment1
#> treatment2
#> treatment3
#> treatment4
#> treatment5
#> treatment6
#> treatment7
#> treatment8
#> treatment9
#> treatment10 -0.127
#> treatment11 -0.127 -0.132
#>
#> Model Diagnostics
#> =========================
#> conv_opt conv_lme4
#> 1 0
#> opt_message
#> 1 NLOPT_XTOL_REACHED: Optimization stopped because xtol_rel or xtol_abs (above) was reached.
#> opt_warnings singular block Residual AIC BIC
#> 1 FALSE 1.944444 26.97222 86.93248 100.8727
#>
#> ANOVA, Fixed Effects
#> =========================
#> Type III Analysis of Variance Table with Satterthwaite's method
#> Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
#> treatment 470.46 42.769 11 6.3919 1.5857 0.2883
#>
#> LRT, Random Effects
#> =========================
#> ANOVA-like table for random-effects: Single term deletions
#>
#> Model:
#> y ~ treatment + (1 | block)
#> npar logLik AIC LRT Df Pr(>Chisq)
#> <none> 14 -29.466 86.932
#> (1 | block) 13 -29.491 84.983 0.050141 1 0.8228
#>
#> Model Formula
#> =========================
#> treatment mean SE df type
#> 1 1 84.66667 3.104656 7.892933 BLUE
#> 2 2 79.00000 3.104656 7.892933 BLUE
#> 3 3 82.00000 3.104656 7.892933 BLUE
#> 4 4 83.33333 3.104656 7.892933 BLUE
#> 5 5 78.83213 6.158823 7.969123 BLUE
#> 6 6 75.72742 6.158823 7.969123 BLUE
#> 7 7 95.44045 6.158823 7.969123 BLUE
#> 8 8 70.72742 6.158823 7.969123 BLUE
#> 9 9 77.83213 6.158823 7.969123 BLUE
#> 10 10 74.72742 6.158823 7.969123 BLUE
#> 11 11 88.44045 6.158823 7.969123 BLUE
#> 12 12 81.44045 6.158823 7.969123 BLUE
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Multiple Environments - Scenario 1:
# Test treatments are replicated across all environments
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Example data
blk1 <- c(1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3,
4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6,
7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9)
trt1 <- c(1, 2, 3, 4, 7, 11, 12, 1, 2, 3, 4, 5, 9, 1, 2, 3, 4, 8, 6, 10,
1, 2, 3, 4, 8, 11, 5, 1, 2, 3, 4, 12, 9, 1, 2, 3, 4, 7, 6, 10,
1, 2, 3, 4, 7, 9, 12, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 8, 11, 10)
y1 <- c(92, 79, 87, 81, 96, 89, 82, 79, 81, 81, 91, 79, 78, 83, 77,
78, 78, 70, 75, 74, 90, 80, 85, 78, 95, 86, 81, 78, 78, 76, 88,
76, 79, 80, 76, 75, 74, 77, 75, 72, 91, 81, 86, 80, 94, 87, 83,
78, 79, 77, 90, 74, 76, 82, 83, 86, 76, 73, 74, 69)
env1 <- c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3)
data1 <- data.frame(env1, blk1, trt1, y1)
chks1 <- c(1, 2, 3, 4)
# Convert block, treatment and environment to factors
data1$blk1 <- as.factor(data1$blk1)
data1$trt1 <- as.factor(data1$trt1)
data1$env1 <- as.factor(data1$env1)
# Contingency tables of factors
table(data1$env1, data1$trt1)
#>
#> 1 2 3 4 5 6 7 8 9 10 11 12
#> 1 3 3 3 3 1 1 1 1 1 1 1 1
#> 2 3 3 3 3 1 1 1 1 1 1 1 1
#> 3 3 3 3 3 1 1 1 1 1 1 1 1
table(data1$env1, data1$blk1)
#>
#> 1 2 3 4 5 6 7 8 9
#> 1 7 6 7 0 0 0 0 0 0
#> 2 0 0 0 7 6 7 0 0 0
#> 3 0 0 0 0 0 0 7 6 7
table(data1$blk1, data1$trt1)
#>
#> 1 2 3 4 5 6 7 8 9 10 11 12
#> 1 1 1 1 1 0 0 1 0 0 0 1 1
#> 2 1 1 1 1 1 0 0 0 1 0 0 0
#> 3 1 1 1 1 0 1 0 1 0 1 0 0
#> 4 1 1 1 1 1 0 0 1 0 0 1 0
#> 5 1 1 1 1 0 0 0 0 1 0 0 1
#> 6 1 1 1 1 0 1 1 0 0 1 0 0
#> 7 1 1 1 1 0 0 1 0 1 0 0 1
#> 8 1 1 1 1 1 1 0 0 0 0 0 0
#> 9 1 1 1 1 0 0 0 1 0 1 1 0
# 04. Random Effects - env, check, test;
# With dropping of non-significant env:test interaction
out4 <- augmentedRCBD.mix(env = data1$env1, block = data1$blk1,
treatment = data1$trt1,
y = data1$y1, checks = c("1", "2", "3", "4"),
env.random = TRUE,
check.random = TRUE, test.random = TRUE,
drop.nonsig.interaction = TRUE,
scenario = "I", console = TRUE)
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#>
#> Augmented Design Details
#> ========================
#> NULL
#>
#> Model Formula
#> =========================
#> y ~ (1 | env) + (1 | treatment) + (1 | env:block2) + (1 | env:treatment:check)
#> Model Details
#> =========================
#> Linear mixed model fit by REML. t-tests use Satterthwaite's method [
#> lmerModLmerTest]
#> Formula: frmla_wo_int
#> Data: model.frame(mod_final)
#> Control: lmerControl(optimizer = "bobyqa")
#>
#> REML criterion at convergence: 375.9
#>
#> Scaled residuals:
#> Min 1Q Median 3Q Max
#> -1.5350 -0.6249 -0.1477 0.4048 2.2955
#>
#> Random effects:
#> Groups Name Variance Std.Dev.
#> env:treatment:check (Intercept) 0.000 0.000
#> treatment (Intercept) 3.305 1.818
#> env:block2 (Intercept) 13.438 3.666
#> env (Intercept) 0.000 0.000
#> Residual 23.625 4.861
#> Number of obs: 60, groups:
#> env:treatment:check, 36; treatment, 12; env:block2, 9; env, 3
#>
#> Fixed effects:
#> Estimate Std. Error df t value Pr(>|t|)
#> (Intercept) 80.559 1.488 10.011 54.12 1.09e-13 ***
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> optimizer (bobyqa) convergence code: 0 (OK)
#> boundary (singular) fit: see help('isSingular')
#>
#>
#> Model Diagnostics
#> =========================
#> conv_opt conv_lme4
#> 1 0 boundary (singular) fit: see help('isSingular')
#> opt_message opt_warnings singular env.treatment.check treatment
#> 1 Normal exit from bobyqa TRUE 0 3.304911
#> env.block2 env Residual AIC BIC
#> 1 13.43794 0 23.625 387.8948 400.4608
#>
#> ANOVA, Fixed Effects
#> =========================
#> NULL
#>
#> LRT, Random Effects
#> =========================
#> ANOVA-like table for random-effects: Single term deletions
#>
#> Model:
#> y ~ 1 + (1 | env) + (1 | treatment) + (1 | env:block2) + (1 | env:treatment:check)
#> npar logLik AIC LRT Df Pr(>Chisq)
#> <none> 6 -187.95 387.89
#> (1 | env) 5 -187.95 385.89 0.0000 1 0.9999998
#> (1 | treatment) 5 -188.43 386.85 0.9602 1 0.3271461
#> (1 | env:block2) 5 -193.89 397.77 11.8762 1 0.0005685 ***
#> (1 | env:treatment:check) 5 -187.95 385.89 0.0000 1 1.0000000
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Model Formula
#> =========================
#> treatment mean SE df type
#> 1 1 82.29086 1.270503 NA BLUP
#> 2 2 79.87577 1.270503 NA BLUP
#> 3 3 80.92850 1.270503 NA BLUP
#> 4 4 81.23813 1.270503 NA BLUP
#> 5 5 79.52941 1.559247 NA BLUP
#> 6 6 79.87221 1.558127 NA BLUP
#> 7 7 82.64335 1.556813 NA BLUP
#> 8 8 80.42125 1.557021 NA BLUP
#> 9 9 80.45872 1.559491 NA BLUP
#> 10 10 78.90556 1.557019 NA BLUP
#> 11 11 80.75118 1.556806 NA BLUP
#> 12 12 79.78956 1.558369 NA BLUP
# 05. Random Effects - env, check, test;
# Without dropping of non-significant env:test interaction
out5 <- augmentedRCBD.mix(env = data1$env1, block = data1$blk1,
treatment = data1$trt1,
y = data1$y1, checks = c("1", "2", "3", "4"),
env.random = TRUE,
check.random = TRUE, test.random = TRUE,
drop.nonsig.interaction = FALSE,
scenario = "I", console = TRUE)
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#>
#> Augmented Design Details
#> ========================
#> NULL
#>
#> Model Formula
#> =========================
#> y ~ (1 | env) + (1 | treatment) + (1 | env:block2) + (1 | env:treatment)
#> Model Details
#> =========================
#> Linear mixed model fit by REML. t-tests use Satterthwaite's method [
#> lmerModLmerTest]
#> Formula: frmla_int
#> Data: model.frame(mod_final)
#> Control: lmerControl(optimizer = "bobyqa")
#>
#> REML criterion at convergence: 375.9
#>
#> Scaled residuals:
#> Min 1Q Median 3Q Max
#> -1.5350 -0.6249 -0.1477 0.4048 2.2955
#>
#> Random effects:
#> Groups Name Variance Std.Dev.
#> env:treatment (Intercept) 0.000 0.000
#> treatment (Intercept) 3.305 1.818
#> env:block2 (Intercept) 13.438 3.666
#> env (Intercept) 0.000 0.000
#> Residual 23.625 4.861
#> Number of obs: 60, groups:
#> env:treatment, 36; treatment, 12; env:block2, 9; env, 3
#>
#> Fixed effects:
#> Estimate Std. Error df t value Pr(>|t|)
#> (Intercept) 80.559 1.488 10.011 54.12 1.09e-13 ***
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> optimizer (bobyqa) convergence code: 0 (OK)
#> boundary (singular) fit: see help('isSingular')
#>
#>
#> Model Diagnostics
#> =========================
#> conv_opt conv_lme4
#> 1 0 boundary (singular) fit: see help('isSingular')
#> opt_message opt_warnings singular env.treatment treatment
#> 1 Normal exit from bobyqa TRUE 0 3.304911
#> env.block2 env Residual AIC BIC
#> 1 13.43794 0 23.625 387.8948 400.4608
#>
#> ANOVA, Fixed Effects
#> =========================
#> NULL
#>
#> LRT, Random Effects
#> =========================
#> ANOVA-like table for random-effects: Single term deletions
#>
#> Model:
#> y ~ 1 + (1 | env) + (1 | treatment) + (1 | env:block2) + (1 | env:treatment)
#> npar logLik AIC LRT Df Pr(>Chisq)
#> <none> 6 -187.95 387.89
#> (1 | env) 5 -187.95 385.89 0.0000 1 0.9999998
#> (1 | treatment) 5 -188.43 386.85 0.9602 1 0.3271461
#> (1 | env:block2) 5 -193.89 397.77 11.8762 1 0.0005685 ***
#> (1 | env:treatment) 5 -187.95 385.89 0.0000 1 1.0000000
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Model Formula
#> =========================
#> treatment mean SE df type
#> 1 1 82.29086 1.270503 NA BLUP
#> 2 2 79.87577 1.270503 NA BLUP
#> 3 3 80.92850 1.270503 NA BLUP
#> 4 4 81.23813 1.270503 NA BLUP
#> 5 5 79.52941 1.559247 NA BLUP
#> 6 6 79.87221 1.558127 NA BLUP
#> 7 7 82.64335 1.556813 NA BLUP
#> 8 8 80.42125 1.557021 NA BLUP
#> 9 9 80.45872 1.559491 NA BLUP
#> 10 10 78.90556 1.557019 NA BLUP
#> 11 11 80.75118 1.556806 NA BLUP
#> 12 12 79.78956 1.558369 NA BLUP
# 06. Fixed Effects - check; Random Effects - env, test;
# With dropping of non-significant env:test interaction
out6 <- augmentedRCBD.mix(env = data1$env1, block = data1$blk1,
treatment = data1$trt1,
y = data1$y1, checks = c("1", "2", "3", "4"),
env.random = TRUE,
check.random = FALSE, test.random = TRUE,
drop.nonsig.interaction = TRUE,
scenario = "I", console = TRUE)
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#>
#> Augmented Design Details
#> ========================
#> NULL
#>
#> Model Formula
#> =========================
#> y ~ check + (1 | env) + (1 | env:block2) + (1 | env:check) + (1 | treatment:test)
#> Model Details
#> =========================
#> Linear mixed model fit by REML. t-tests use Satterthwaite's method [
#> lmerModLmerTest]
#> Formula: frmla_wo_int
#> Data: model.frame(mod_final)
#> Control: lmerControl(optimizer = "bobyqa")
#>
#> REML criterion at convergence: 360.8
#>
#> Scaled residuals:
#> Min 1Q Median 3Q Max
#> -1.50439 -0.63853 -0.03649 0.35541 2.43950
#>
#> Random effects:
#> Groups Name Variance Std.Dev.
#> env:check (Intercept) 0.000 0.000
#> treatment:test (Intercept) 7.712 2.777
#> env:block2 (Intercept) 12.826 3.581
#> env (Intercept) 0.000 0.000
#> Residual 23.085 4.805
#> Number of obs: 60, groups:
#> env:check, 15; treatment:test, 12; env:block2, 9; env, 3
#>
#> Fixed effects:
#> Estimate Std. Error df t value Pr(>|t|)
#> (Intercept) 81.13454 1.77398 7.68157 45.736 1.22e-10 ***
#> check1 2.53213 2.80861 2.82615 0.902 0.437
#> check2 -1.80121 2.80861 2.82615 -0.641 0.570
#> check3 0.08768 2.80861 2.82615 0.031 0.977
#> check4 0.64324 2.80861 2.82615 0.229 0.834
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Correlation of Fixed Effects:
#> (Intr) check1 check2 check3
#> check1 0.067
#> check2 0.067 -0.303
#> check3 0.067 -0.303 -0.303
#> check4 0.067 -0.303 -0.303 -0.303
#> optimizer (bobyqa) convergence code: 0 (OK)
#> boundary (singular) fit: see help('isSingular')
#>
#>
#> Model Diagnostics
#> =========================
#> conv_opt conv_lme4
#> 1 0 boundary (singular) fit: see help('isSingular')
#> opt_message opt_warnings singular env.check treatment.test
#> 1 Normal exit from bobyqa TRUE 0 7.712414
#> env.block2 env Residual AIC BIC
#> 1 12.82638 0 23.08469 380.8263 401.7698
#>
#> ANOVA, Fixed Effects
#> =========================
#> Type III Analysis of Variance Table with Satterthwaite's method
#> Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
#> check 38.542 9.6356 4 2.9602 0.4174 0.7912
#>
#> LRT, Random Effects
#> =========================
#> ANOVA-like table for random-effects: Single term deletions
#>
#> Model:
#> y ~ check + (1 | env) + (1 | env:block2) + (1 | env:check) + (1 | treatment:test)
#> npar logLik AIC LRT Df Pr(>Chisq)
#> <none> 10 -180.41 380.83
#> (1 | env) 9 -180.41 378.83 0.0000 1 1.00000
#> (1 | env:block2) 9 -185.76 389.53 10.7030 1 0.00107 **
#> (1 | env:check) 9 -180.41 378.83 0.0000 1 1.00000
#> (1 | treatment:test) 9 -181.19 380.39 1.5587 1 0.21186
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Model Formula
#> =========================
#> treatment mean SE df type
#> 1 1 83.66667 3.420897 3.351039 BLUE
#> 2 2 79.33333 3.420897 3.351039 BLUE
#> 3 3 81.22222 3.420897 3.351039 BLUE
#> 4 4 81.77778 3.420897 3.351039 BLUE
#> 5 5 78.35828 2.044951 NA BLUP
#> 6 6 78.91023 2.042787 NA BLUP
#> 7 7 83.70619 2.039857 NA BLUP
#> 8 8 79.82877 2.040670 NA BLUP
#> 9 9 79.98128 2.045910 NA BLUP
#> 10 10 77.26612 2.040657 NA BLUP
#> 11 11 80.45126 2.039824 NA BLUP
#> 12 12 78.87954 2.043726 NA BLUP
# 07. Fixed Effects - check; Random Effects - env, test;
# Without dropping of non-significant env:test interaction
out7 <- augmentedRCBD.mix(env = data1$env1, block = data1$blk1,
treatment = data1$trt1,
y = data1$y1, checks = c("1", "2", "3", "4"),
env.random = TRUE,
check.random = FALSE, test.random = TRUE,
drop.nonsig.interaction = FALSE,
scenario = "I", console = TRUE)
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#>
#> Augmented Design Details
#> ========================
#> NULL
#>
#> Model Formula
#> =========================
#> y ~ check + (1 | env) + (1 | env:block2) + (1 | env:treatment) + (1 | treatment:test)
#> Model Details
#> =========================
#> Linear mixed model fit by REML. t-tests use Satterthwaite's method [
#> lmerModLmerTest]
#> Formula: frmla_int
#> Data: model.frame(mod_final)
#> Control: lmerControl(optimizer = "bobyqa")
#>
#> REML criterion at convergence: 360.8
#>
#> Scaled residuals:
#> Min 1Q Median 3Q Max
#> -1.50439 -0.63853 -0.03649 0.35541 2.43950
#>
#> Random effects:
#> Groups Name Variance Std.Dev.
#> env:treatment (Intercept) 0.000 0.000
#> treatment:test (Intercept) 7.712 2.777
#> env:block2 (Intercept) 12.826 3.581
#> env (Intercept) 0.000 0.000
#> Residual 23.085 4.805
#> Number of obs: 60, groups:
#> env:treatment, 36; treatment:test, 12; env:block2, 9; env, 3
#>
#> Fixed effects:
#> Estimate Std. Error df t value Pr(>|t|)
#> (Intercept) 81.13454 1.77398 7.68157 45.736 1.22e-10 ***
#> check1 2.53213 2.80861 2.82615 0.902 0.437
#> check2 -1.80121 2.80861 2.82615 -0.641 0.570
#> check3 0.08768 2.80861 2.82615 0.031 0.977
#> check4 0.64324 2.80861 2.82615 0.229 0.834
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Correlation of Fixed Effects:
#> (Intr) check1 check2 check3
#> check1 0.067
#> check2 0.067 -0.303
#> check3 0.067 -0.303 -0.303
#> check4 0.067 -0.303 -0.303 -0.303
#> optimizer (bobyqa) convergence code: 0 (OK)
#> boundary (singular) fit: see help('isSingular')
#>
#>
#> Model Diagnostics
#> =========================
#> conv_opt conv_lme4
#> 1 0 boundary (singular) fit: see help('isSingular')
#> opt_message opt_warnings singular env.treatment treatment.test
#> 1 Normal exit from bobyqa TRUE 0 7.712414
#> env.block2 env Residual AIC BIC
#> 1 12.82638 0 23.08469 380.8263 401.7698
#>
#> ANOVA, Fixed Effects
#> =========================
#> Type III Analysis of Variance Table with Satterthwaite's method
#> Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
#> check 38.542 9.6356 4 2.9602 0.4174 0.7912
#>
#> LRT, Random Effects
#> =========================
#> ANOVA-like table for random-effects: Single term deletions
#>
#> Model:
#> y ~ check + (1 | env) + (1 | env:block2) + (1 | env:treatment) + (1 | treatment:test)
#> npar logLik AIC LRT Df Pr(>Chisq)
#> <none> 10 -180.41 380.83
#> (1 | env) 9 -180.41 378.83 0.0000 1 1.00000
#> (1 | env:block2) 9 -185.76 389.53 10.7030 1 0.00107 **
#> (1 | env:treatment) 9 -180.41 378.83 0.0000 1 1.00000
#> (1 | treatment:test) 9 -181.19 380.39 1.5587 1 0.21186
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Model Formula
#> =========================
#> treatment mean SE df type
#> 1 1 83.66667 3.420897 3.40063 BLUE
#> 2 2 79.33333 3.420897 3.40063 BLUE
#> 3 3 81.22222 3.420897 3.40063 BLUE
#> 4 4 81.77778 3.420897 3.40063 BLUE
#> 5 5 78.35828 2.044951 NA BLUP
#> 6 6 78.91023 2.042787 NA BLUP
#> 7 7 83.70619 2.039857 NA BLUP
#> 8 8 79.82877 2.040670 NA BLUP
#> 9 9 79.98128 2.045910 NA BLUP
#> 10 10 77.26612 2.040657 NA BLUP
#> 11 11 80.45126 2.039824 NA BLUP
#> 12 12 78.87954 2.043726 NA BLUP
# 08. Fixed Effects - check, test; Random Effects - env;
# With dropping of non-significant env:test interaction
out8 <- augmentedRCBD.mix(env = data1$env1, block = data1$blk1,
treatment = data1$trt1,
y = data1$y1, checks = c("1", "2", "3", "4"),
env.random = TRUE,
check.random = FALSE, test.random = FALSE,
drop.nonsig.interaction = TRUE,
scenario = "I", console = TRUE)
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#>
#> Augmented Design Details
#> ========================
#> NULL
#>
#> Model Formula
#> =========================
#> y ~ treatment + (1 | env) + (1 | env:block2) + (1 | env:check)
#> Model Details
#> =========================
#> Linear mixed model fit by REML. t-tests use Satterthwaite's method [
#> lmerModLmerTest]
#> Formula: frmla_wo_int
#> Data: model.frame(mod_final)
#> Control: lmerControl(optimizer = "bobyqa")
#>
#> REML criterion at convergence: 321.1
#>
#> Scaled residuals:
#> Min 1Q Median 3Q Max
#> -1.48346 -0.70487 0.01713 0.38514 2.44862
#>
#> Random effects:
#> Groups Name Variance Std.Dev.
#> env:check (Intercept) 0.00 0.000
#> env:block2 (Intercept) 10.77 3.282
#> env (Intercept) 0.00 0.000
#> Residual 23.66 4.864
#> Number of obs: 60, groups: env:check, 15; env:block2, 9; env, 3
#>
#> Fixed effects:
#> Estimate Std. Error df t value Pr(>|t|)
#> (Intercept) 80.2956 1.3088 8.5982 61.351 1.16e-12 ***
#> treatment1 3.3710 1.6452 39.9670 2.049 0.04707 *
#> treatment2 -0.9623 1.6452 39.9670 -0.585 0.56189
#> treatment3 0.9266 1.6452 39.9670 0.563 0.57645
#> treatment4 1.4821 1.6452 39.9670 0.901 0.37305
#> treatment5 -3.3723 2.8017 42.9237 -1.204 0.23532
#> treatment6 -2.4937 2.7906 42.7117 -0.894 0.37654
#> treatment7 7.8618 2.7755 42.3215 2.833 0.00704 **
#> treatment8 -0.5720 2.7804 42.5238 -0.206 0.83798
#> treatment9 0.1712 2.8085 43.2029 0.061 0.95167
#> treatment10 -5.7575 2.7800 42.5096 -2.071 0.04446 *
#> treatment11 1.1022 2.7746 42.2854 0.397 0.69318
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Correlation of Fixed Effects:
#> (Intr) trtmn1 trtmn2 trtmn3 trtmn4 trtmn5 trtmn6 trtmn7 trtmn8
#> treatment1 -0.138
#> treatment2 -0.138 0.029
#> treatment3 -0.138 0.029 0.029
#> treatment4 -0.138 0.029 0.029 0.029
#> treatment5 0.030 -0.072 -0.072 -0.072 -0.072
#> treatment6 0.039 -0.079 -0.079 -0.079 -0.079 -0.096
#> treatment7 0.047 -0.085 -0.085 -0.085 -0.085 -0.149 -0.109
#> treatment8 0.047 -0.085 -0.085 -0.085 -0.085 -0.102 -0.103 -0.155
#> treatment9 0.030 -0.071 -0.071 -0.071 -0.071 -0.094 -0.147 -0.100 -0.153
#> treatment10 0.048 -0.086 -0.086 -0.086 -0.086 -0.146 -0.060 -0.111 -0.062
#> treatment11 0.047 -0.086 -0.086 -0.086 -0.086 -0.105 -0.148 -0.111 -0.064
#> trtmn9 trtm10
#> treatment1
#> treatment2
#> treatment3
#> treatment4
#> treatment5
#> treatment6
#> treatment7
#> treatment8
#> treatment9
#> treatment10 -0.153
#> treatment11 -0.147 -0.108
#> optimizer (bobyqa) convergence code: 0 (OK)
#> boundary (singular) fit: see help('isSingular')
#>
#>
#> Model Diagnostics
#> =========================
#> conv_opt conv_lme4
#> 1 0 boundary (singular) fit: see help('isSingular')
#> opt_message opt_warnings singular env.check env.block2 env
#> 1 Normal exit from bobyqa TRUE 0 10.77185 0
#> Residual AIC BIC
#> 1 23.65965 353.1243 386.6338
#>
#> ANOVA, Fixed Effects
#> =========================
#> Type III Analysis of Variance Table with Satterthwaite's method
#> Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
#> treatment 451.26 41.024 11 41.469 1.7339 0.09929 .
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> LRT, Random Effects
#> =========================
#> ANOVA-like table for random-effects: Single term deletions
#>
#> Model:
#> y ~ treatment + (1 | env) + (1 | env:block2) + (1 | env:check)
#> npar logLik AIC LRT Df Pr(>Chisq)
#> <none> 16 -160.56 353.12
#> (1 | env) 15 -160.56 351.12 0.000 1 1.000000
#> (1 | env:block2) 15 -164.17 358.34 7.213 1 0.007238 **
#> (1 | env:check) 15 -160.56 351.12 0.000 1 1.000000
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Model Formula
#> =========================
#> treatment mean SE df type
#> 1 1 83.66667 1.955945 9.380281 BLUE
#> 2 2 79.33333 1.955945 9.380281 BLUE
#> 3 3 81.22222 1.955945 9.380281 BLUE
#> 4 4 81.77778 1.955945 9.380281 BLUE
#> 5 5 76.92337 3.163385 33.641987 BLUE
#> 6 6 77.80193 3.163808 33.652457 BLUE
#> 7 7 88.15743 3.155753 33.499934 BLUE
#> 8 8 79.72363 3.163422 33.667519 BLUE
#> 9 9 80.46687 3.171783 33.825748 BLUE
#> 10 10 74.53810 3.163433 33.667827 BLUE
#> 11 11 81.39787 3.155737 33.499637 BLUE
#> 12 12 78.53853 3.171499 33.817383 BLUE
# 09.Fixed Effects - check, test; Random Effects - env;
# Without dropping of non-significant env:test interaction
out9 <- augmentedRCBD.mix(env = data1$env1, block = data1$blk1,
treatment = data1$trt1,
y = data1$y1, checks = c("1", "2", "3", "4"),
env.random = TRUE,
check.random = FALSE, test.random = FALSE,
drop.nonsig.interaction = FALSE,
scenario = "I", console = TRUE)
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#>
#> Augmented Design Details
#> ========================
#> NULL
#>
#> Model Formula
#> =========================
#> y ~ treatment + (1 | env) + (1 | env:block2) + (1 | env:treatment)
#> Model Details
#> =========================
#> Linear mixed model fit by REML. t-tests use Satterthwaite's method [
#> lmerModLmerTest]
#> Formula: frmla_int
#> Data: model.frame(mod_final)
#> Control: lmerControl(optimizer = "bobyqa")
#>
#> REML criterion at convergence: 321.1
#>
#> Scaled residuals:
#> Min 1Q Median 3Q Max
#> -1.48346 -0.70487 0.01713 0.38514 2.44862
#>
#> Random effects:
#> Groups Name Variance Std.Dev.
#> env:treatment (Intercept) 0.00 0.000
#> env:block2 (Intercept) 10.77 3.282
#> env (Intercept) 0.00 0.000
#> Residual 23.66 4.864
#> Number of obs: 60, groups: env:treatment, 36; env:block2, 9; env, 3
#>
#> Fixed effects:
#> Estimate Std. Error df t value Pr(>|t|)
#> (Intercept) 80.2956 1.3088 8.5982 61.351 1.16e-12 ***
#> treatment1 3.3710 1.6452 39.9670 2.049 0.04707 *
#> treatment2 -0.9623 1.6452 39.9670 -0.585 0.56189
#> treatment3 0.9266 1.6452 39.9670 0.563 0.57645
#> treatment4 1.4821 1.6452 39.9670 0.901 0.37305
#> treatment5 -3.3723 2.8017 42.9237 -1.204 0.23532
#> treatment6 -2.4937 2.7906 42.7117 -0.894 0.37654
#> treatment7 7.8618 2.7755 42.3215 2.833 0.00704 **
#> treatment8 -0.5720 2.7804 42.5238 -0.206 0.83798
#> treatment9 0.1712 2.8085 43.2029 0.061 0.95167
#> treatment10 -5.7575 2.7800 42.5096 -2.071 0.04446 *
#> treatment11 1.1022 2.7746 42.2854 0.397 0.69318
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Correlation of Fixed Effects:
#> (Intr) trtmn1 trtmn2 trtmn3 trtmn4 trtmn5 trtmn6 trtmn7 trtmn8
#> treatment1 -0.138
#> treatment2 -0.138 0.029
#> treatment3 -0.138 0.029 0.029
#> treatment4 -0.138 0.029 0.029 0.029
#> treatment5 0.030 -0.072 -0.072 -0.072 -0.072
#> treatment6 0.039 -0.079 -0.079 -0.079 -0.079 -0.096
#> treatment7 0.047 -0.085 -0.085 -0.085 -0.085 -0.149 -0.109
#> treatment8 0.047 -0.085 -0.085 -0.085 -0.085 -0.102 -0.103 -0.155
#> treatment9 0.030 -0.071 -0.071 -0.071 -0.071 -0.094 -0.147 -0.100 -0.153
#> treatment10 0.048 -0.086 -0.086 -0.086 -0.086 -0.146 -0.060 -0.111 -0.062
#> treatment11 0.047 -0.086 -0.086 -0.086 -0.086 -0.105 -0.148 -0.111 -0.064
#> trtmn9 trtm10
#> treatment1
#> treatment2
#> treatment3
#> treatment4
#> treatment5
#> treatment6
#> treatment7
#> treatment8
#> treatment9
#> treatment10 -0.153
#> treatment11 -0.147 -0.108
#> optimizer (bobyqa) convergence code: 0 (OK)
#> boundary (singular) fit: see help('isSingular')
#>
#>
#> Model Diagnostics
#> =========================
#> conv_opt conv_lme4
#> 1 0 boundary (singular) fit: see help('isSingular')
#> opt_message opt_warnings singular env.treatment env.block2 env
#> 1 Normal exit from bobyqa TRUE 0 10.77185 0
#> Residual AIC BIC
#> 1 23.65965 353.1243 386.6338
#>
#> ANOVA, Fixed Effects
#> =========================
#> Type III Analysis of Variance Table with Satterthwaite's method
#> Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
#> treatment 451.26 41.024 11 41.469 1.7339 0.09929 .
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> LRT, Random Effects
#> =========================
#> ANOVA-like table for random-effects: Single term deletions
#>
#> Model:
#> y ~ treatment + (1 | env) + (1 | env:block2) + (1 | env:treatment)
#> npar logLik AIC LRT Df Pr(>Chisq)
#> <none> 16 -160.56 353.12
#> (1 | env) 15 -160.56 351.12 0.000 1 1.000000
#> (1 | env:block2) 15 -164.17 358.34 7.213 1 0.007238 **
#> (1 | env:treatment) 15 -160.56 351.12 0.000 1 1.000000
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Model Formula
#> =========================
#> treatment mean SE df type
#> 1 1 83.66667 1.955945 7.376537 BLUE
#> 2 2 79.33333 1.955945 7.376537 BLUE
#> 3 3 81.22222 1.955945 7.376537 BLUE
#> 4 4 81.77778 1.955945 7.376537 BLUE
#> 5 5 76.92337 3.164642 33.592744 BLUE
#> 6 6 77.80193 3.165037 33.603731 BLUE
#> 7 7 88.15743 3.157459 33.445174 BLUE
#> 8 8 79.72363 3.165176 33.619369 BLUE
#> 9 9 80.46687 3.173055 33.783634 BLUE
#> 10 10 74.53810 3.165186 33.619694 BLUE
#> 11 11 81.39787 3.157447 33.444860 BLUE
#> 12 12 78.53853 3.172753 33.774900 BLUE
# 10. Fixed Effects - env; Random Effects - check, test;
# With dropping of non-significant env:test interaction
out10 <- augmentedRCBD.mix(env = data1$env1, block = data1$blk1,
treatment = data1$trt1,
y = data1$y1, checks = c("1", "2", "3", "4"),
env.random = FALSE,
check.random = TRUE, test.random = TRUE,
drop.nonsig.interaction = TRUE,
scenario = "I", console = TRUE)
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#>
#> Augmented Design Details
#> ========================
#> NULL
#>
#> Model Formula
#> =========================
#> y ~ env + (1 | treatment) + (1 | env:block2) + (1 | env:treatment:check)
#> Model Details
#> =========================
#> Linear mixed model fit by REML. t-tests use Satterthwaite's method [
#> lmerModLmerTest]
#> Formula: frmla_wo_int
#> Data: model.frame(mod_final)
#> Control: lmerControl(optimizer = "bobyqa")
#>
#> REML criterion at convergence: 369.4
#>
#> Scaled residuals:
#> Min 1Q Median 3Q Max
#> -1.5341 -0.5766 -0.1672 0.4757 2.2693
#>
#> Random effects:
#> Groups Name Variance Std.Dev.
#> env:treatment:check (Intercept) 0.000 0.000
#> treatment (Intercept) 3.077 1.754
#> env:block2 (Intercept) 18.531 4.305
#> Residual 23.760 4.874
#> Number of obs: 60, groups:
#> env:treatment:check, 36; treatment, 12; env:block2, 9
#>
#> Fixed effects:
#> Estimate Std. Error df t value Pr(>|t|)
#> (Intercept) 80.5653 1.6621 7.3369 48.472 1.81e-10 ***
#> env1 0.7355 2.2166 5.9363 0.332 0.751
#> env2 -0.8470 2.2166 5.9365 -0.382 0.716
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Correlation of Fixed Effects:
#> (Intr) env1
#> env1 0.000
#> env2 0.000 -0.500
#> optimizer (bobyqa) convergence code: 0 (OK)
#> boundary (singular) fit: see help('isSingular')
#>
#>
#> Model Diagnostics
#> =========================
#> conv_opt conv_lme4
#> 1 0 boundary (singular) fit: see help('isSingular')
#> opt_message opt_warnings singular env.treatment.check treatment
#> 1 Normal exit from bobyqa TRUE 0 3.076909
#> env.block2 Residual AIC BIC
#> 1 18.5308 23.75951 383.4009 398.0613
#>
#> ANOVA, Fixed Effects
#> =========================
#> Type III Analysis of Variance Table with Satterthwaite's method
#> Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
#> env 4.0964 2.0482 2 5.9364 0.0862 0.9185
#>
#> LRT, Random Effects
#> =========================
#> ANOVA-like table for random-effects: Single term deletions
#>
#> Model:
#> y ~ env + (1 | treatment) + (1 | env:block2) + (1 | env:treatment:check)
#> npar logLik AIC LRT Df Pr(>Chisq)
#> <none> 7 -184.70 383.40
#> (1 | treatment) 6 -185.13 382.26 0.8618 1 0.3532338
#> (1 | env:block2) 6 -191.66 395.33 13.9265 1 0.0001901 ***
#> (1 | env:treatment:check) 6 -184.70 381.40 0.0000 1 1.0000000
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Model Formula
#> =========================
#> treatment mean SE df type
#> 1 1 82.23451 1.254103 NA BLUP
#> 2 2 79.90224 1.254103 NA BLUP
#> 3 3 80.91887 1.254103 NA BLUP
#> 4 4 81.21788 1.254103 NA BLUP
#> 5 5 79.57354 1.521652 NA BLUP
#> 6 6 79.96497 1.520450 NA BLUP
#> 7 7 82.51007 1.519063 NA BLUP
#> 8 8 80.44859 1.519266 NA BLUP
#> 9 9 80.44819 1.521893 NA BLUP
#> 10 10 79.05562 1.519263 NA BLUP
#> 11 11 80.71496 1.519056 NA BLUP
#> 12 12 79.79421 1.520690 NA BLUP
# 11. Fixed Effects - env; Random Effects - check, test;
# Without dropping of non-significant env:test interaction
out11 <- augmentedRCBD.mix(env = data1$env1, block = data1$blk1,
treatment = data1$trt1,
y = data1$y1, checks = c("1", "2", "3", "4"),
env.random = FALSE,
check.random = TRUE, test.random = TRUE,
drop.nonsig.interaction = FALSE,
scenario = "I", console = TRUE)
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#>
#> Augmented Design Details
#> ========================
#> NULL
#>
#> Model Formula
#> =========================
#> y ~ env + (1 | treatment) + (1 | env:block2) + (1 | env:treatment)
#> Model Details
#> =========================
#> Linear mixed model fit by REML. t-tests use Satterthwaite's method [
#> lmerModLmerTest]
#> Formula: frmla_int
#> Data: model.frame(mod_final)
#> Control: lmerControl(optimizer = "bobyqa")
#>
#> REML criterion at convergence: 369.4
#>
#> Scaled residuals:
#> Min 1Q Median 3Q Max
#> -1.5341 -0.5766 -0.1672 0.4757 2.2693
#>
#> Random effects:
#> Groups Name Variance Std.Dev.
#> env:treatment (Intercept) 0.000 0.000
#> treatment (Intercept) 3.077 1.754
#> env:block2 (Intercept) 18.531 4.305
#> Residual 23.760 4.874
#> Number of obs: 60, groups: env:treatment, 36; treatment, 12; env:block2, 9
#>
#> Fixed effects:
#> Estimate Std. Error df t value Pr(>|t|)
#> (Intercept) 80.5653 1.6621 7.3369 48.472 1.81e-10 ***
#> env1 0.7355 2.2166 5.9363 0.332 0.751
#> env2 -0.8470 2.2166 5.9365 -0.382 0.716
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Correlation of Fixed Effects:
#> (Intr) env1
#> env1 0.000
#> env2 0.000 -0.500
#> optimizer (bobyqa) convergence code: 0 (OK)
#> boundary (singular) fit: see help('isSingular')
#>
#>
#> Model Diagnostics
#> =========================
#> conv_opt conv_lme4
#> 1 0 boundary (singular) fit: see help('isSingular')
#> opt_message opt_warnings singular env.treatment treatment
#> 1 Normal exit from bobyqa TRUE 0 3.076909
#> env.block2 Residual AIC BIC
#> 1 18.5308 23.75951 383.4009 398.0613
#>
#> ANOVA, Fixed Effects
#> =========================
#> Type III Analysis of Variance Table with Satterthwaite's method
#> Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
#> env 4.0964 2.0482 2 5.9364 0.0862 0.9185
#>
#> LRT, Random Effects
#> =========================
#> ANOVA-like table for random-effects: Single term deletions
#>
#> Model:
#> y ~ env + (1 | treatment) + (1 | env:block2) + (1 | env:treatment)
#> npar logLik AIC LRT Df Pr(>Chisq)
#> <none> 7 -184.70 383.40
#> (1 | treatment) 6 -185.13 382.26 0.8618 1 0.3532338
#> (1 | env:block2) 6 -191.66 395.33 13.9265 1 0.0001901 ***
#> (1 | env:treatment) 6 -184.70 381.40 0.0000 1 1.0000000
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Model Formula
#> =========================
#> treatment mean SE df type
#> 1 1 82.23451 1.254103 NA BLUP
#> 2 2 79.90224 1.254103 NA BLUP
#> 3 3 80.91887 1.254103 NA BLUP
#> 4 4 81.21788 1.254103 NA BLUP
#> 5 5 79.57354 1.521652 NA BLUP
#> 6 6 79.96497 1.520450 NA BLUP
#> 7 7 82.51007 1.519063 NA BLUP
#> 8 8 80.44859 1.519266 NA BLUP
#> 9 9 80.44819 1.521893 NA BLUP
#> 10 10 79.05562 1.519263 NA BLUP
#> 11 11 80.71496 1.519056 NA BLUP
#> 12 12 79.79421 1.520690 NA BLUP
# 12. Fixed Effects - env, check; Random Effects - test;
# With dropping of non-significant env:test interaction
out12 <- augmentedRCBD.mix(env = data1$env1, block = data1$blk1,
treatment = data1$trt1,
y = data1$y1, checks = c("1", "2", "3", "4"),
env.random = FALSE,
check.random = FALSE, test.random = TRUE,
drop.nonsig.interaction = TRUE,
scenario = "I", console = TRUE)
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> NOTE: Results may be misleading due to involvement in interactions
#> NOTE: Results may be misleading due to involvement in interactions
#>
#> Augmented Design Details
#> ========================
#> NULL
#>
#> Model Formula
#> =========================
#> y ~ env + check + env:check + (1 | env:block2) + (1 | treatment:test)
#> Model Details
#> =========================
#> Linear mixed model fit by REML. t-tests use Satterthwaite's method [
#> lmerModLmerTest]
#> Formula: frmla_wo_int
#> Data: model.frame(mod_final)
#> Control: lmerControl(optimizer = "bobyqa")
#>
#> REML criterion at convergence: 329.4
#>
#> Scaled residuals:
#> Min 1Q Median 3Q Max
#> -1.2844 -0.5023 -0.1338 0.3901 2.0383
#>
#> Random effects:
#> Groups Name Variance Std.Dev.
#> treatment:test (Intercept) 6.024 2.454
#> env:block2 (Intercept) 17.691 4.206
#> Residual 26.998 5.196
#> Number of obs: 60, groups: treatment:test, 12; env:block2, 9
#>
#> Fixed effects:
#> Estimate Std. Error df t value Pr(>|t|)
#> (Intercept) 81.13327 1.86685 6.90079 43.460 1.13e-09 ***
#> env1 0.74197 2.23210 6.19031 0.332 0.751
#> env2 -1.25472 2.23210 6.19036 -0.562 0.594
#> check1 2.53339 2.63322 2.24482 0.962 0.428
#> check2 -1.79994 2.63322 2.24482 -0.684 0.558
#> check3 0.08895 2.63322 2.24482 0.034 0.976
#> check4 0.64450 2.63322 2.24482 0.245 0.827
#> env1:check1 0.25803 2.15655 33.66923 0.120 0.905
#> env2:check1 0.25472 2.15656 33.67000 0.118 0.907
#> env1:check2 -1.07530 2.15655 33.66923 -0.499 0.621
#> env2:check2 -0.07861 2.15656 33.67000 -0.036 0.971
#> env1:check3 0.03581 2.15655 33.66923 0.017 0.987
#> env2:check3 -1.30083 2.15656 33.67000 -0.603 0.550
#> env1:check4 0.81359 2.15655 33.66923 0.377 0.708
#> env2:check4 -0.52306 2.15656 33.67000 -0.243 0.810
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Correlation matrix not shown by default, as p = 15 > 12.
#> Use print(summary(x$Model), correlation=TRUE) or
#> vcov(summary(x$Model)) if you need it
#>
#> Model Diagnostics
#> =========================
#> conv_opt conv_lme4 opt_message opt_warnings singular
#> 1 0 Normal exit from bobyqa FALSE
#> treatment.test env.block2 Residual AIC BIC
#> 1 6.024114 17.69102 26.9985 365.4463 403.1445
#>
#> ANOVA, Fixed Effects
#> =========================
#> Type III Analysis of Variance Table with Satterthwaite's method
#> Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
#> env 8.626 4.3130 2 6.190 0.1598 0.8558
#> check 50.443 12.6108 4 2.289 0.4671 0.7649
#> env:check 57.291 7.1614 8 33.696 0.2653 0.9729
#>
#> LRT, Random Effects
#> =========================
#> ANOVA-like table for random-effects: Single term deletions
#>
#> Model:
#> y ~ env + check + env:check + (1 | env:block2) + (1 | treatment:test)
#> npar logLik AIC LRT Df Pr(>Chisq)
#> <none> 18 -164.72 365.45
#> (1 | env:block2) 17 -169.84 373.68 10.2346 1 0.001378 **
#> (1 | treatment:test) 17 -165.11 364.22 0.7767 1 0.378149
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Model Formula
#> =========================
#> treatment mean SE df type
#> 1 1 83.66667 3.315059 3.125624 BLUE
#> 2 2 79.33333 3.315059 3.125624 BLUE
#> 3 3 81.22222 3.315059 3.125624 BLUE
#> 4 4 81.77778 3.315059 3.125624 BLUE
#> 5 5 78.63559 1.962439 NA BLUP
#> 6 6 79.13449 1.960477 NA BLUP
#> 7 7 82.85302 1.958030 NA BLUP
#> 8 8 79.82048 1.958552 NA BLUP
#> 9 9 79.87122 1.963058 NA BLUP
#> 10 10 77.79771 1.958543 NA BLUP
#> 11 11 80.26108 1.958009 NA BLUP
#> 12 12 78.95737 1.961087 NA BLUP
# 13. Fixed Effects - env, check; Random Effects - test;
# Without dropping of non-significant env:test interaction
out13 <- augmentedRCBD.mix(env = data1$env1, block = data1$blk1,
treatment = data1$trt1,
y = data1$y1, checks = c("1", "2", "3", "4"),
env.random = FALSE,
check.random = FALSE, test.random = TRUE,
drop.nonsig.interaction = FALSE,
scenario = "I", console = TRUE)
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> NOTE: Results may be misleading due to involvement in interactions
#> NOTE: Results may be misleading due to involvement in interactions
#>
#> Augmented Design Details
#> ========================
#> NULL
#>
#> Model Formula
#> =========================
#> y ~ env + check + env:check + (1 | env:block2) + (1 | treatment:test) + (1 | env:treatment:test)
#> Model Details
#> =========================
#> Linear mixed model fit by REML. t-tests use Satterthwaite's method [
#> lmerModLmerTest]
#> Formula: frmla_int
#> Data: model.frame(mod_final)
#> Control: lmerControl(optimizer = "bobyqa")
#>
#> REML criterion at convergence: 329.4
#>
#> Scaled residuals:
#> Min 1Q Median 3Q Max
#> -1.2844 -0.5023 -0.1338 0.3901 2.0383
#>
#> Random effects:
#> Groups Name Variance Std.Dev.
#> env:treatment:test (Intercept) 4.186e-15 6.470e-08
#> treatment:test (Intercept) 6.024e+00 2.454e+00
#> env:block2 (Intercept) 1.769e+01 4.206e+00
#> Residual 2.700e+01 5.196e+00
#> Number of obs: 60, groups:
#> env:treatment:test, 36; treatment:test, 12; env:block2, 9
#>
#> Fixed effects:
#> Estimate Std. Error df t value Pr(>|t|)
#> (Intercept) 81.13327 1.86685 6.90079 43.460 1.13e-09 ***
#> env1 0.74197 2.23210 6.19031 0.332 0.751
#> env2 -1.25472 2.23210 6.19036 -0.562 0.594
#> check1 2.53339 2.63322 2.24482 0.962 0.428
#> check2 -1.79994 2.63322 2.24482 -0.684 0.558
#> check3 0.08895 2.63322 2.24482 0.034 0.976
#> check4 0.64450 2.63322 2.24482 0.245 0.827
#> env1:check1 0.25803 2.15655 33.66923 0.120 0.905
#> env2:check1 0.25472 2.15656 33.67000 0.118 0.907
#> env1:check2 -1.07530 2.15655 33.66923 -0.499 0.621
#> env2:check2 -0.07861 2.15656 33.67000 -0.036 0.971
#> env1:check3 0.03581 2.15655 33.66923 0.017 0.987
#> env2:check3 -1.30083 2.15656 33.67000 -0.603 0.550
#> env1:check4 0.81359 2.15655 33.66923 0.377 0.708
#> env2:check4 -0.52306 2.15656 33.67000 -0.243 0.810
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Correlation matrix not shown by default, as p = 15 > 12.
#> Use print(summary(x$Model), correlation=TRUE) or
#> vcov(summary(x$Model)) if you need it
#> optimizer (bobyqa) convergence code: 0 (OK)
#> boundary (singular) fit: see help('isSingular')
#>
#>
#> Model Diagnostics
#> =========================
#> conv_opt conv_lme4
#> 1 0 boundary (singular) fit: see help('isSingular')
#> opt_message opt_warnings singular env.treatment.test
#> 1 Normal exit from bobyqa TRUE 4.185786e-15
#> treatment.test env.block2 Residual AIC BIC
#> 1 6.024113 17.69103 26.9985 367.4463 407.2389
#>
#> ANOVA, Fixed Effects
#> =========================
#> Type III Analysis of Variance Table with Satterthwaite's method
#> Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
#> env 8.626 4.3130 2 6.190 0.1598 0.8558
#> check 50.443 12.6108 4 2.289 0.4671 0.7649
#> env:check 57.291 7.1614 8 33.696 0.2653 0.9729
#>
#> LRT, Random Effects
#> =========================
#> ANOVA-like table for random-effects: Single term deletions
#>
#> Model:
#> y ~ env + check + env:check + (1 | env:block2) + (1 | treatment:test) + (1 | env:treatment:test)
#> npar logLik AIC LRT Df Pr(>Chisq)
#> <none> 19 -164.72 367.45
#> (1 | env:block2) 18 -168.90 373.79 8.3428 1 0.003872 **
#> (1 | treatment:test) 18 -165.09 366.18 0.7356 1 0.391085
#> (1 | env:treatment:test) 18 -164.72 365.45 0.0000 1 1.000000
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Model Formula
#> =========================
#> treatment mean SE df type
#> 1 1 83.66667 3.315059 3.059302 BLUE
#> 2 2 79.33333 3.315059 3.059302 BLUE
#> 3 3 81.22222 3.315059 3.059302 BLUE
#> 4 4 81.77778 3.315059 3.059302 BLUE
#> 5 5 78.63559 1.962439 NA BLUP
#> 6 6 79.13449 1.960477 NA BLUP
#> 7 7 82.85302 1.958030 NA BLUP
#> 8 8 79.82048 1.958552 NA BLUP
#> 9 9 79.87122 1.963058 NA BLUP
#> 10 10 77.79771 1.958543 NA BLUP
#> 11 11 80.26108 1.958009 NA BLUP
#> 12 12 78.95737 1.961087 NA BLUP
# 14. Fixed Effects - env, check, test;
# With dropping of non-significant env:test interaction
out14 <- augmentedRCBD.mix(env = data1$env1, block = data1$blk1,
treatment = data1$trt1,
y = data1$y1, checks = c("1", "2", "3", "4"),
env.random = FALSE,
check.random = FALSE, test.random = FALSE,
drop.nonsig.interaction = TRUE,
scenario = "I", console = TRUE)
#> fixed-effect model matrix is rank deficient so dropping 4 columns / coefficients
#> NOTE: Results may be misleading due to involvement in interactions
#>
#> Augmented Design Details
#> ========================
#> NULL
#>
#> Model Formula
#> =========================
#> y ~ env + treatment + env:treatment + (1 | env:block2)
#> Model Details
#> =========================
#> Linear mixed model fit by REML. t-tests use Satterthwaite's method [
#> lmerModLmerTest]
#> Formula: frmla_int
#> Data: model.frame(mod_final)
#>
#> REML criterion at convergence: 204.9
#>
#> Scaled residuals:
#> Min 1Q Median 3Q Max
#> -1.081 -0.330 0.000 0.000 1.469
#>
#> Random effects:
#> Groups Name Variance Std.Dev.
#> env:block2 (Intercept) 0.5278 0.7265
#> Residual 30.3611 5.5101
#> Number of obs: 60, groups: env:block2, 9
#>
#> Fixed effects:
#> Estimate Std. Error df t value Pr(>|t|)
#> (Intercept) 80.33243 0.84579 3.62711 94.980 2.72e-07 ***
#> env1 0.67163 1.19612 3.62711 0.562 0.60731
#> env2 -0.30375 1.19612 3.62711 -0.254 0.81327
#> treatment1 3.33424 1.86224 18.11368 1.790 0.09011 .
#> treatment2 -0.99910 1.86224 18.11368 -0.537 0.59814
#> treatment3 0.88979 1.86224 18.11368 0.478 0.63850
#> treatment4 1.44535 1.86224 18.11368 0.776 0.44769
#> treatment5 -2.39203 3.03466 23.49801 -0.788 0.43844
#> treatment6 -4.82031 3.03315 23.25712 -1.589 0.12552
#> treatment7 8.64590 3.03165 22.97380 2.852 0.00903 **
#> treatment8 -0.98826 3.03165 22.97380 -0.326 0.74739
#> treatment9 0.93589 3.03466 23.49801 0.308 0.76050
#> treatment10 -8.50323 3.03165 22.97380 -2.805 0.01006 *
#> treatment11 2.55380 3.03165 22.97380 0.842 0.40826
#> env1:treatment1 0.32837 2.63360 18.11368 0.125 0.90215
#> env2:treatment1 -0.69625 2.63360 18.11368 -0.264 0.79448
#> env1:treatment2 -1.00497 2.63360 18.11368 -0.382 0.70720
#> env2:treatment2 -1.02958 2.63360 18.11368 -0.391 0.70040
#> env1:treatment3 0.10614 2.63360 18.11368 0.040 0.96829
#> env2:treatment3 -2.25181 2.63360 18.11368 -0.855 0.40370
#> env1:treatment4 0.88392 2.63360 18.11368 0.336 0.74100
#> env2:treatment4 -1.47403 2.63360 18.11368 -0.560 0.58254
#> env1:treatment5 0.33920 4.29272 23.60172 0.079 0.93768
#> env2:treatment5 3.14122 4.28953 23.25712 0.732 0.47130
#> env1:treatment6 -0.97246 4.28846 23.12059 -0.227 0.82260
#> env2:treatment6 0.02459 4.28846 23.12059 0.006 0.99547
#> env1:treatment7 6.18751 4.28739 22.97380 1.443 0.16247
#> env2:treatment7 -11.44162 4.28739 22.97380 -2.669 0.01373 *
#> env1:treatment8 -9.80451 4.28739 22.97380 -2.287 0.03175 *
#> env2:treatment8 15.73745 4.28739 22.97380 3.671 0.00127 **
#> env1:treatment9 -3.98871 4.29272 23.60172 -0.929 0.36220
#> env2:treatment9 -1.97541 4.29272 23.60172 -0.460 0.64960
#> env1:treatment10 1.71046 4.28739 22.97380 0.399 0.69361
#> env2:treatment10 0.70751 4.28739 22.97380 0.165 0.87037
#> env1:treatment11 5.27961 4.28739 22.97380 1.231 0.23062
#> env2:treatment11 3.19539 4.28739 22.97380 0.745 0.46365
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Correlation matrix not shown by default, as p = 36 > 12.
#> Use print(summary(x$Model), correlation=TRUE) or
#> vcov(summary(x$Model)) if you need it
#>
#> Model Diagnostics
#> =========================
#> conv_opt conv_lme4
#> 1 0
#> opt_message
#> 1 NLOPT_XTOL_REACHED: Optimization stopped because xtol_rel or xtol_abs (above) was reached.
#> opt_warnings singular env.block2 Residual AIC BIC
#> 1 FALSE 0.5277775 30.36111 280.8878 360.4729
#>
#> ANOVA, Fixed Effects
#> =========================
#> Type III Analysis of Variance Table with Satterthwaite's method
#> Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
#> env 9.60 4.801 2 3.6271 0.1581 0.85933
#> treatment 666.86 60.624 11 19.6446 1.9968 0.08737 .
#> env:treatment 826.77 37.580 22 18.9500 1.2378 0.32180
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> LRT, Random Effects
#> =========================
#> ANOVA-like table for random-effects: Single term deletions
#>
#> Model:
#> y ~ env + treatment + env:treatment + (1 | env:block2)
#> npar logLik AIC LRT Df Pr(>Chisq)
#> <none> 38 -102.44 280.89
#> (1 | env:block2) 37 -102.45 278.90 0.010281 1 0.9192
#>
#> Model Formula
#> =========================
#> treatment mean SE df type
#> 1 1 83.66667 1.852592 23.97900 BLUE
#> 2 2 79.33333 1.852592 23.97900 BLUE
#> 3 3 81.22222 1.852592 23.97900 BLUE
#> 4 4 81.77778 1.852592 23.97900 BLUE
#> 5 5 77.94040 3.419139 23.98953 BLUE
#> 6 6 75.51212 3.419139 23.98953 BLUE
#> 7 7 88.97833 3.419139 23.98953 BLUE
#> 8 8 79.34417 3.419139 23.98953 BLUE
#> 9 9 81.26832 3.419139 23.98953 BLUE
#> 10 10 71.82920 3.419139 23.98953 BLUE
#> 11 11 82.88623 3.419139 23.98953 BLUE
#> 12 12 80.23040 3.419139 23.98953 BLUE
# 15. Fixed Effects - env, check, test;
# Without dropping of non-significant env:test interaction
out15 <- augmentedRCBD.mix(env = data1$env1, block = data1$blk1,
treatment = data1$trt1,
y = data1$y1, checks = c("1", "2", "3", "4"),
env.random = FALSE,
check.random = FALSE, test.random = FALSE,
drop.nonsig.interaction = FALSE,
scenario = "I", console = TRUE)
#> NOTE: Results may be misleading due to involvement in interactions
#>
#> Augmented Design Details
#> ========================
#> NULL
#>
#> Model Formula
#> =========================
#> y ~ env + treatment + env:treatment + (1 | env:block2)
#> Model Details
#> =========================
#> Linear mixed model fit by REML. t-tests use Satterthwaite's method [
#> lmerModLmerTest]
#> Formula: frmla_int
#> Data: model.frame(mod_final)
#>
#> REML criterion at convergence: 204.9
#>
#> Scaled residuals:
#> Min 1Q Median 3Q Max
#> -1.081 -0.330 0.000 0.000 1.469
#>
#> Random effects:
#> Groups Name Variance Std.Dev.
#> env:block2 (Intercept) 0.5278 0.7265
#> Residual 30.3611 5.5101
#> Number of obs: 60, groups: env:block2, 9
#>
#> Fixed effects:
#> Estimate Std. Error df t value Pr(>|t|)
#> (Intercept) 80.33243 0.84579 3.62711 94.980 2.72e-07 ***
#> env1 0.67163 1.19612 3.62711 0.562 0.60731
#> env2 -0.30375 1.19612 3.62711 -0.254 0.81327
#> treatment1 3.33424 1.86224 18.11368 1.790 0.09011 .
#> treatment2 -0.99910 1.86224 18.11368 -0.537 0.59814
#> treatment3 0.88979 1.86224 18.11368 0.478 0.63850
#> treatment4 1.44535 1.86224 18.11368 0.776 0.44769
#> treatment5 -2.39203 3.03466 23.49801 -0.788 0.43844
#> treatment6 -4.82031 3.03315 23.25712 -1.589 0.12552
#> treatment7 8.64590 3.03165 22.97380 2.852 0.00903 **
#> treatment8 -0.98826 3.03165 22.97380 -0.326 0.74739
#> treatment9 0.93589 3.03466 23.49801 0.308 0.76050
#> treatment10 -8.50323 3.03165 22.97380 -2.805 0.01006 *
#> treatment11 2.55380 3.03165 22.97380 0.842 0.40826
#> env1:treatment1 0.32837 2.63360 18.11368 0.125 0.90215
#> env2:treatment1 -0.69625 2.63360 18.11368 -0.264 0.79448
#> env1:treatment2 -1.00497 2.63360 18.11368 -0.382 0.70720
#> env2:treatment2 -1.02958 2.63360 18.11368 -0.391 0.70040
#> env1:treatment3 0.10614 2.63360 18.11368 0.040 0.96829
#> env2:treatment3 -2.25181 2.63360 18.11368 -0.855 0.40370
#> env1:treatment4 0.88392 2.63360 18.11368 0.336 0.74100
#> env2:treatment4 -1.47403 2.63360 18.11368 -0.560 0.58254
#> env1:treatment5 0.33920 4.29272 23.60172 0.079 0.93768
#> env2:treatment5 3.14122 4.28953 23.25712 0.732 0.47130
#> env1:treatment6 -0.97246 4.28846 23.12059 -0.227 0.82260
#> env2:treatment6 0.02459 4.28846 23.12059 0.006 0.99547
#> env1:treatment7 6.18751 4.28739 22.97380 1.443 0.16247
#> env2:treatment7 -11.44162 4.28739 22.97380 -2.669 0.01373 *
#> env1:treatment8 -9.80451 4.28739 22.97380 -2.287 0.03175 *
#> env2:treatment8 15.73745 4.28739 22.97380 3.671 0.00127 **
#> env1:treatment9 -3.98871 4.29272 23.60172 -0.929 0.36220
#> env2:treatment9 -1.97541 4.29272 23.60172 -0.460 0.64960
#> env1:treatment10 1.71046 4.28739 22.97380 0.399 0.69361
#> env2:treatment10 0.70751 4.28739 22.97380 0.165 0.87037
#> env1:treatment11 5.27961 4.28739 22.97380 1.231 0.23062
#> env2:treatment11 3.19539 4.28739 22.97380 0.745 0.46365
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Correlation matrix not shown by default, as p = 36 > 12.
#> Use print(summary(x$Model), correlation=TRUE) or
#> vcov(summary(x$Model)) if you need it
#>
#> Model Diagnostics
#> =========================
#> conv_opt conv_lme4
#> 1 0
#> opt_message
#> 1 NLOPT_XTOL_REACHED: Optimization stopped because xtol_rel or xtol_abs (above) was reached.
#> opt_warnings singular env.block2 Residual AIC BIC
#> 1 FALSE 0.5277775 30.36111 280.8878 360.4729
#>
#> ANOVA, Fixed Effects
#> =========================
#> Type III Analysis of Variance Table with Satterthwaite's method
#> Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
#> env 9.60 4.801 2 3.6271 0.1581 0.85933
#> treatment 666.86 60.624 11 19.6446 1.9968 0.08737 .
#> env:treatment 826.77 37.580 22 18.9500 1.2378 0.32180
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> LRT, Random Effects
#> =========================
#> ANOVA-like table for random-effects: Single term deletions
#>
#> Model:
#> y ~ env + treatment + env:treatment + (1 | env:block2)
#> npar logLik AIC LRT Df Pr(>Chisq)
#> <none> 38 -102.44 280.89
#> (1 | env:block2) 37 -102.45 278.90 0.010281 1 0.9192
#>
#> Model Formula
#> =========================
#> treatment mean SE df type
#> 1 1 83.66667 1.852592 23.97900 BLUE
#> 2 2 79.33333 1.852592 23.97900 BLUE
#> 3 3 81.22222 1.852592 23.97900 BLUE
#> 4 4 81.77778 1.852592 23.97900 BLUE
#> 5 5 77.94040 3.419139 23.98953 BLUE
#> 6 6 75.51212 3.419139 23.98953 BLUE
#> 7 7 88.97833 3.419139 23.98953 BLUE
#> 8 8 79.34417 3.419139 23.98953 BLUE
#> 9 9 81.26832 3.419139 23.98953 BLUE
#> 10 10 71.82920 3.419139 23.98953 BLUE
#> 11 11 82.88623 3.419139 23.98953 BLUE
#> 12 12 80.23040 3.419139 23.98953 BLUE
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Multiple Environments - Scenario 2:
# Test treatments are replicated across all environments
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Example data
blk2 <- c(1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3,
4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6,
7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9)
trt2 <- c(1, 2, 3, 4, 7, 10, 11, 1, 2, 3, 4, 5, 9, 1, 2, 3, 4, 8, 6, 12,
1, 2, 3, 4, 16, 19, 13, 1, 2, 3, 4, 20, 17, 1, 2, 3, 4, 15, 14, 18,
1, 2, 3, 4, 22, 25, 27, 1, 2, 3, 4, 21, 23, 1, 2, 3, 4, 24, 26, 28)
y2 <- c(92, 79, 87, 81, 96, 89, 82, 79, 81, 81, 91, 79, 78, 83, 77,
78, 78, 70, 75, 74, 90, 80, 85, 78, 95, 86, 81, 78, 78, 76, 88,
76, 79, 80, 76, 75, 74, 77, 75, 72, 91, 81, 86, 80, 94, 87, 83,
78, 79, 77, 90, 74, 76, 82, 83, 86, 76, 73, 74, 69)
env2 <- c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3)
data2 <- data.frame(env2, blk2, trt2, y2)
chks2 <- c(1, 2, 3, 4)
# Convert block, treatment and environment to factors
data2$blk2 <- as.factor(data2$blk2)
data2$trt2 <- as.factor(data2$trt2)
data2$env2 <- as.factor(data2$env2)
# Contingency tables of factors
table(data2$env2, data2$trt2)
#>
#> 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
#> 1 3 3 3 3 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
#> 2 3 3 3 3 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0
#> 3 3 3 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1
table(data2$env2, data2$blk2)
#>
#> 1 2 3 4 5 6 7 8 9
#> 1 7 6 7 0 0 0 0 0 0
#> 2 0 0 0 7 6 7 0 0 0
#> 3 0 0 0 0 0 0 7 6 7
table(data2$blk2, data2$trt2)
#>
#> 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
#> 1 1 1 1 1 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
#> 2 1 1 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
#> 3 1 1 1 1 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
#> 4 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0
#> 5 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0
#> 6 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0
#> 7 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0
#> 8 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0
#> 9 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1
# 16. Random Effects - env, check, test
out16 <- augmentedRCBD.mix(env = data2$env2, block = data2$blk2,
treatment = data2$trt2,
y = data2$y2, checks = c("1", "2", "3", "4"),
env.random = TRUE,
check.random = TRUE, test.random = TRUE,
scenario = "II", console = TRUE)
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#>
#> Augmented Design Details
#> ========================
#> NULL
#>
#> Model Formula
#> =========================
#> y ~ (1 | env) + (1 | treatment) + (1 | env:block2) + (1 | env:treatment:check)
#> Model Details
#> =========================
#> Linear mixed model fit by REML. t-tests use Satterthwaite's method [
#> lmerModLmerTest]
#> Formula: frmla_int
#> Data: model.frame(mod_final)
#> Control: lmerControl(optimizer = "bobyqa")
#>
#> REML criterion at convergence: 376.6
#>
#> Scaled residuals:
#> Min 1Q Median 3Q Max
#> -1.7191 -0.6154 -0.2276 0.4480 2.0900
#>
#> Random effects:
#> Groups Name Variance Std.Dev.
#> env:treatment:check (Intercept) 0.000 0.000
#> treatment (Intercept) 1.695 1.302
#> env:block2 (Intercept) 13.614 3.690
#> env (Intercept) 0.000 0.000
#> Residual 24.958 4.996
#> Number of obs: 60, groups:
#> env:treatment:check, 36; treatment, 28; env:block2, 9; env, 3
#>
#> Fixed effects:
#> Estimate Std. Error df t value Pr(>|t|)
#> (Intercept) 80.581 1.440 9.074 55.98 7.76e-13 ***
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> optimizer (bobyqa) convergence code: 0 (OK)
#> boundary (singular) fit: see help('isSingular')
#>
#>
#> Model Diagnostics
#> =========================
#> conv_opt conv_lme4
#> 1 0 boundary (singular) fit: see help('isSingular')
#> opt_message opt_warnings singular env.treatment.check treatment
#> 1 Normal exit from bobyqa TRUE 0 1.695004
#> env.block2 env Residual AIC BIC
#> 1 13.61394 0 24.9579 388.6321 401.1981
#>
#> ANOVA, Fixed Effects
#> =========================
#> NULL
#>
#> LRT, Random Effects
#> =========================
#> ANOVA-like table for random-effects: Single term deletions
#>
#> Model:
#> y ~ 1 + (1 | env) + (1 | treatment) + (1 | env:block2) + (1 | env:treatment:check)
#> npar logLik AIC LRT Df Pr(>Chisq)
#> <none> 6 -188.32 388.63
#> (1 | env) 5 -188.32 386.63 0.0000 1 1.0000000
#> (1 | treatment) 5 -188.43 386.85 0.2229 1 0.6368575
#> (1 | env:block2) 5 -193.84 397.68 11.0471 1 0.0008883 ***
#> (1 | env:treatment:check) 5 -188.32 386.63 0.0000 1 1.0000000
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Model Formula
#> =========================
#> treatment mean SE df type
#> 1 1 81.75159 1.053935 NA BLUP
#> 2 2 80.10771 1.053935 NA BLUP
#> 3 3 80.82427 1.053935 NA BLUP
#> 4 4 81.03503 1.053935 NA BLUP
#> 5 5 80.44431 1.265171 NA BLUP
#> 6 6 80.43961 1.264582 NA BLUP
#> 7 7 81.27513 1.264582 NA BLUP
#> 8 8 80.12164 1.264582 NA BLUP
#> 9 9 80.38071 1.265171 NA BLUP
#> 10 10 80.82996 1.264582 NA BLUP
#> 11 11 80.38479 1.264582 NA BLUP
#> 12 12 80.37602 1.264582 NA BLUP
#> 13 13 80.39980 1.264582 NA BLUP
#> 14 14 80.48610 1.264582 NA BLUP
#> 15 15 80.61330 1.264582 NA BLUP
#> 16 16 81.29014 1.264582 NA BLUP
#> 17 17 80.55879 1.265171 NA BLUP
#> 18 18 80.29532 1.264582 NA BLUP
#> 19 19 80.71778 1.264582 NA BLUP
#> 20 20 80.36801 1.265171 NA BLUP
#> 21 21 80.24645 1.265171 NA BLUP
#> 22 22 81.17597 1.264582 NA BLUP
#> 23 23 80.37364 1.265171 NA BLUP
#> 24 24 80.25215 1.264582 NA BLUP
#> 25 25 80.73080 1.264582 NA BLUP
#> 26 26 80.31575 1.264582 NA BLUP
#> 27 27 80.47642 1.264582 NA BLUP
#> 28 28 79.99777 1.264582 NA BLUP
# 17. Fixed Effects - check; Random Effects - env, test
out17 <- augmentedRCBD.mix(env = data2$env2, block = data2$blk2,
treatment = data2$trt2,
y = data2$y2, checks = c("1", "2", "3", "4"),
env.random = TRUE,
check.random = FALSE, test.random = TRUE,
scenario = "II", console = TRUE)
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#>
#> Augmented Design Details
#> ========================
#> NULL
#>
#> Model Formula
#> =========================
#> y ~ check + (1 | env) + (1 | env:block2) + (1 | env:check) + (1 | treatment:test)
#> Model Details
#> =========================
#> Linear mixed model fit by REML. t-tests use Satterthwaite's method [
#> lmerModLmerTest]
#> Formula: frmla_int
#> Data: model.frame(mod_final)
#> Control: lmerControl(optimizer = "bobyqa")
#>
#> REML criterion at convergence: 361.5
#>
#> Scaled residuals:
#> Min 1Q Median 3Q Max
#> -1.4007 -0.5591 -0.1435 0.4250 2.0065
#>
#> Random effects:
#> Groups Name Variance Std.Dev.
#> treatment:test (Intercept) 12.69 3.563
#> env:check (Intercept) 0.00 0.000
#> env:block2 (Intercept) 10.81 3.288
#> env (Intercept) 0.00 0.000
#> Residual 21.53 4.640
#> Number of obs: 60, groups:
#> treatment:test, 28; env:check, 15; env:block2, 9; env, 3
#>
#> Fixed effects:
#> Estimate Std. Error df t value Pr(>|t|)
#> (Intercept) 81.13607 1.91634 5.99805 42.339 1.17e-08 ***
#> check1 2.53060 3.39433 2.24198 0.746 0.526
#> check2 -1.80274 3.39433 2.24198 -0.531 0.643
#> check3 0.08615 3.39433 2.24198 0.025 0.982
#> check4 0.64171 3.39433 2.24198 0.189 0.866
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Correlation of Fixed Effects:
#> (Intr) check1 check2 check3
#> check1 0.084
#> check2 0.084 -0.309
#> check3 0.084 -0.309 -0.309
#> check4 0.084 -0.309 -0.309 -0.309
#> optimizer (bobyqa) convergence code: 0 (OK)
#> boundary (singular) fit: see help('isSingular')
#>
#>
#> Model Diagnostics
#> =========================
#> conv_opt conv_lme4
#> 1 0 boundary (singular) fit: see help('isSingular')
#> opt_message opt_warnings singular treatment.test env.check
#> 1 Normal exit from bobyqa TRUE 12.69184 0
#> env.block2 env Residual AIC BIC
#> 1 10.81295 0 21.5321 381.5266 402.47
#>
#> ANOVA, Fixed Effects
#> =========================
#> Type III Analysis of Variance Table with Satterthwaite's method
#> Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
#> check 27.314 6.8286 4 2.3058 0.3171 0.8501
#>
#> LRT, Random Effects
#> =========================
#> ANOVA-like table for random-effects: Single term deletions
#>
#> Model:
#> y ~ check + (1 | env) + (1 | env:block2) + (1 | env:check) + (1 | treatment:test)
#> npar logLik AIC LRT Df Pr(>Chisq)
#> <none> 10 -180.76 381.53
#> (1 | env) 9 -180.76 379.53 0.0000 1 1.000000
#> (1 | env:block2) 9 -184.52 387.05 7.5193 1 0.006104 **
#> (1 | env:check) 9 -180.76 379.53 0.0000 1 1.000000
#> (1 | treatment:test) 9 -181.19 380.39 0.8584 1 0.354174
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Model Formula
#> =========================
#> treatment mean SE df type
#> 1 1 83.66667 4.035559 3.389111 BLUE
#> 2 2 79.33333 4.035559 3.389111 BLUE
#> 3 3 81.22222 4.035559 3.389111 BLUE
#> 4 4 81.77778 4.035559 3.389111 BLUE
#> 5 5 79.19710 2.903648 NA BLUP
#> 6 6 79.00884 2.897031 NA BLUP
#> 7 7 84.29258 2.897031 NA BLUP
#> 8 8 77.15460 2.897031 NA BLUP
#> 9 9 78.82625 2.903648 NA BLUP
#> 10 10 81.69665 2.897031 NA BLUP
#> 11 11 79.10072 2.897031 NA BLUP
#> 12 12 78.63799 2.897031 NA BLUP
#> 13 13 79.16036 2.897031 NA BLUP
#> 14 14 79.37853 2.897031 NA BLUP
#> 15 15 80.12022 2.897031 NA BLUP
#> 16 16 84.35221 2.897031 NA BLUP
#> 17 17 79.87531 2.903648 NA BLUP
#> 18 18 78.26599 2.897031 NA BLUP
#> 19 19 81.01459 2.897031 NA BLUP
#> 20 20 78.76277 2.903648 NA BLUP
#> 21 21 77.97738 2.903648 NA BLUP
#> 22 22 83.68680 2.897031 NA BLUP
#> 23 23 78.71907 2.903648 NA BLUP
#> 24 24 77.83822 2.897031 NA BLUP
#> 25 25 81.09087 2.897031 NA BLUP
#> 26 26 78.20907 2.897031 NA BLUP
#> 27 27 79.60748 2.897031 NA BLUP
#> 28 28 76.35484 2.897031 NA BLUP
# 18. Fixed Effects - check, test; Random Effects - env
out18 <- augmentedRCBD.mix(env = data2$env2, block = data2$blk2,
treatment = data2$trt2,
y = data2$y2, checks = c("1", "2", "3", "4"),
env.random = TRUE,
check.random = FALSE, test.random = FALSE,
scenario = "II", console = TRUE)
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#>
#> Augmented Design Details
#> ========================
#> NULL
#>
#> Model Formula
#> =========================
#> y ~ treatment + (1 | env) + (1 | env:block2) + (1 | env:check)
#> Model Details
#> =========================
#> Linear mixed model fit by REML. t-tests use Satterthwaite's method [
#> lmerModLmerTest]
#> Formula: frmla_int
#> Data: model.frame(mod_final)
#> Control: lmerControl(optimizer = "bobyqa")
#>
#> REML criterion at convergence: 209.4
#>
#> Scaled residuals:
#> Min 1Q Median 3Q Max
#> -1.3525 -0.3572 0.0000 0.0000 1.8303
#>
#> Random effects:
#> Groups Name Variance Std.Dev.
#> env:check (Intercept) 0.00 0.000
#> env:block2 (Intercept) 1.78 1.334
#> env (Intercept) 0.00 0.000
#> Residual 23.50 4.848
#> Number of obs: 60, groups: env:check, 15; env:block2, 9; env, 3
#>
#> Fixed effects:
#> Estimate Std. Error df t value Pr(>|t|)
#> (Intercept) 79.9958 0.9665 9.3687 82.768 9.68e-15 ***
#> treatment1 3.6708 1.7780 24.1747 2.065 0.04985 *
#> treatment2 -0.6625 1.7780 24.1747 -0.373 0.71269
#> treatment3 1.2264 1.7780 24.1747 0.690 0.49693
#> treatment4 1.7819 1.7780 24.1747 1.002 0.32618
#> treatment5 -1.3446 4.8828 31.1306 -0.275 0.78485
#> treatment6 -4.4146 4.8728 30.8073 -0.906 0.37198
#> treatment7 15.2485 4.8728 30.8073 3.129 0.00382 **
#> treatment8 -9.4146 4.8728 30.8073 -1.932 0.06259 .
#> treatment9 -2.3446 4.8828 31.1306 -0.480 0.63446
#> treatment10 8.2485 4.8728 30.8073 1.693 0.10059
#> treatment11 1.2485 4.8728 30.8073 0.256 0.79948
#> treatment12 -5.4146 4.8728 30.8073 -1.111 0.27508
#> treatment13 0.5973 4.8728 30.8073 0.123 0.90324
#> treatment14 -3.7752 4.8728 30.8073 -0.775 0.44439
#> treatment15 -1.7752 4.8728 30.8073 -0.364 0.71811
#> treatment16 14.5973 4.8728 30.8073 2.996 0.00537 **
#> treatment17 -0.6471 4.8828 31.1306 -0.133 0.89542
#> treatment18 -6.7752 4.8728 30.8073 -1.390 0.17436
#> treatment19 5.5973 4.8728 30.8073 1.149 0.25953
#> treatment20 -3.6471 4.8828 31.1306 -0.747 0.46071
#> treatment21 -5.8796 4.8828 31.1306 -1.204 0.23761
#> treatment22 13.3066 4.8728 30.8073 2.731 0.01036 *
#> treatment23 -3.8796 4.8828 31.1306 -0.795 0.43289
#> treatment24 -7.0540 4.8728 30.8073 -1.448 0.15782
#> treatment25 6.3066 4.8728 30.8073 1.294 0.20519
#> treatment26 -6.0540 4.8728 30.8073 -1.242 0.22346
#> treatment27 2.3066 4.8728 30.8073 0.473 0.63928
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Correlation matrix not shown by default, as p = 28 > 12.
#> Use print(summary(x$Model), correlation=TRUE) or
#> vcov(summary(x$Model)) if you need it
#> optimizer (bobyqa) convergence code: 0 (OK)
#> boundary (singular) fit: see help('isSingular')
#>
#>
#> Model Diagnostics
#> =========================
#> conv_opt conv_lme4
#> 1 0 boundary (singular) fit: see help('isSingular')
#> opt_message opt_warnings singular env.check env.block2 env
#> 1 Normal exit from bobyqa TRUE 0 1.780093 0
#> Residual AIC BIC
#> 1 23.50463 273.4126 340.4317
#>
#> ANOVA, Fixed Effects
#> =========================
#> Type III Analysis of Variance Table with Satterthwaite's method
#> Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
#> treatment 1242.4 46.014 27 25.469 1.9577 0.04661 *
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> LRT, Random Effects
#> =========================
#> ANOVA-like table for random-effects: Single term deletions
#>
#> Model:
#> y ~ treatment + (1 | env) + (1 | env:block2) + (1 | env:check)
#> npar logLik AIC LRT Df Pr(>Chisq)
#> <none> 32 -104.71 273.41
#> (1 | env) 31 -104.71 271.41 0.00000 1 1.0000
#> (1 | env:block2) 31 -104.82 271.63 0.21914 1 0.6397
#> (1 | env:check) 31 -104.71 271.41 0.00000 1 1.0000
#>
#> Model Formula
#> =========================
#> treatment mean SE df type
#> 1 1 83.66667 1.676131 7.882789 BLUE
#> 2 2 79.33333 1.676131 7.882789 BLUE
#> 3 3 81.22222 1.676131 7.882789 BLUE
#> 4 4 81.77778 1.676131 7.882789 BLUE
#> 5 5 78.65125 5.501086 30.336883 BLUE
#> 6 6 75.58125 5.501086 30.336883 BLUE
#> 7 7 95.24437 5.501086 30.336883 BLUE
#> 8 8 70.58125 5.501086 30.336883 BLUE
#> 9 9 77.65125 5.501086 30.336883 BLUE
#> 10 10 88.24437 5.501086 30.336883 BLUE
#> 11 11 81.24437 5.501086 30.336883 BLUE
#> 12 12 74.58125 5.501086 30.336883 BLUE
#> 13 13 80.59312 5.501086 30.336883 BLUE
#> 14 14 76.22063 5.501086 30.336883 BLUE
#> 15 15 78.22063 5.501086 30.336883 BLUE
#> 16 16 94.59312 5.501086 30.336883 BLUE
#> 17 17 79.34875 5.501086 30.336883 BLUE
#> 18 18 73.22063 5.501086 30.336883 BLUE
#> 19 19 85.59312 5.501086 30.336883 BLUE
#> 20 20 76.34875 5.501086 30.336883 BLUE
#> 21 21 74.11625 5.501086 30.336883 BLUE
#> 22 22 93.30249 5.501086 30.336883 BLUE
#> 23 23 76.11625 5.501086 30.336883 BLUE
#> 24 24 72.94187 5.501086 30.336883 BLUE
#> 25 25 86.30249 5.501086 30.336883 BLUE
#> 26 26 73.94187 5.501086 30.336883 BLUE
#> 27 27 82.30249 5.501086 30.336883 BLUE
#> 28 28 68.94187 5.501086 30.336883 BLUE
# 19. Fixed Effects - env; Random Effects - check, test
out19 <- augmentedRCBD.mix(env = data2$env2, block = data2$blk2,
treatment = data2$trt2,
y = data2$y2, checks = c("1", "2", "3", "4"),
env.random = FALSE,
check.random = TRUE, test.random = TRUE,
scenario = "II", console = TRUE)
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#>
#> Augmented Design Details
#> ========================
#> NULL
#>
#> Model Formula
#> =========================
#> y ~ env + (1 | treatment) + (1 | env:block2) + (1 | env:treatment:check)
#> Model Details
#> =========================
#> Linear mixed model fit by REML. t-tests use Satterthwaite's method [
#> lmerModLmerTest]
#> Formula: frmla_int
#> Data: model.frame(mod_final)
#> Control: lmerControl(optimizer = "bobyqa")
#>
#> REML criterion at convergence: 370.1
#>
#> Scaled residuals:
#> Min 1Q Median 3Q Max
#> -1.7073 -0.6393 -0.1755 0.4327 2.0857
#>
#> Random effects:
#> Groups Name Variance Std.Dev.
#> env:treatment:check (Intercept) 0.000 0.000
#> treatment (Intercept) 1.429 1.195
#> env:block2 (Intercept) 18.778 4.333
#> Residual 25.171 5.017
#> Number of obs: 60, groups:
#> env:treatment:check, 36; treatment, 28; env:block2, 9
#>
#> Fixed effects:
#> Estimate Std. Error df t value Pr(>|t|)
#> (Intercept) 80.6029 1.6217 6.6253 49.702 8.97e-10 ***
#> env1 0.7362 2.2436 5.9724 0.328 0.754
#> env2 -0.8719 2.2436 5.9724 -0.389 0.711
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Correlation of Fixed Effects:
#> (Intr) env1
#> env1 0.000
#> env2 0.000 -0.500
#> optimizer (bobyqa) convergence code: 0 (OK)
#> boundary (singular) fit: see help('isSingular')
#>
#>
#> Model Diagnostics
#> =========================
#> conv_opt conv_lme4
#> 1 0 boundary (singular) fit: see help('isSingular')
#> opt_message opt_warnings singular env.treatment.check treatment
#> 1 Normal exit from bobyqa TRUE 0 1.428706
#> env.block2 Residual AIC BIC
#> 1 18.77751 25.17089 384.0833 398.7437
#>
#> ANOVA, Fixed Effects
#> =========================
#> Type III Analysis of Variance Table with Satterthwaite's method
#> Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
#> env 4.4023 2.2011 2 5.9724 0.0874 0.9174
#>
#> LRT, Random Effects
#> =========================
#> ANOVA-like table for random-effects: Single term deletions
#>
#> Model:
#> y ~ env + (1 | treatment) + (1 | env:block2) + (1 | env:treatment:check)
#> npar logLik AIC LRT Df Pr(>Chisq)
#> <none> 7 -185.04 384.08
#> (1 | treatment) 6 -185.13 382.26 0.1794 1 0.6718853
#> (1 | env:block2) 6 -191.48 394.96 12.8756 1 0.0003329 ***
#> (1 | env:treatment:check) 6 -185.04 382.08 0.0000 1 1.0000000
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Model Formula
#> =========================
#> treatment mean SE df type
#> 1 1 81.63881 0.9974662 NA BLUP
#> 2 2 80.17364 0.9974662 NA BLUP
#> 3 3 80.81230 0.9974662 NA BLUP
#> 4 4 81.00015 0.9974662 NA BLUP
#> 5 5 80.47684 1.1671588 NA BLUP
#> 6 6 80.48728 1.1666376 NA BLUP
#> 7 7 81.16592 1.1666376 NA BLUP
#> 8 8 80.21873 1.1666376 NA BLUP
#> 9 9 80.42313 1.1671588 NA BLUP
#> 10 10 80.78994 1.1666376 NA BLUP
#> 11 11 80.41396 1.1666376 NA BLUP
#> 12 12 80.43357 1.1666376 NA BLUP
#> 13 13 80.44487 1.1666376 NA BLUP
#> 14 14 80.54260 1.1666376 NA BLUP
#> 15 15 80.65003 1.1666376 NA BLUP
#> 16 16 81.19683 1.1666376 NA BLUP
#> 17 17 80.59601 1.1671588 NA BLUP
#> 18 18 80.38147 1.1666376 NA BLUP
#> 19 19 80.71343 1.1666376 NA BLUP
#> 20 20 80.43488 1.1671588 NA BLUP
#> 21 21 80.32286 1.1671588 NA BLUP
#> 22 22 81.08899 1.1666376 NA BLUP
#> 23 23 80.43028 1.1671588 NA BLUP
#> 24 24 80.33155 1.1666376 NA BLUP
#> 25 25 80.71301 1.1666376 NA BLUP
#> 26 26 80.38527 1.1666376 NA BLUP
#> 27 27 80.49816 1.1666376 NA BLUP
#> 28 28 80.11671 1.1666376 NA BLUP
# 20. Fixed Effects - env, check; Random Effects - test
out20 <- augmentedRCBD.mix(env = data2$env2, block = data2$blk2,
treatment = data2$trt2,
y = data2$y2, checks = c("1", "2", "3", "4"),
env.random = FALSE,
check.random = FALSE, test.random = TRUE,
scenario = "II", console = TRUE)
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> NOTE: Results may be misleading due to involvement in interactions
#> NOTE: Results may be misleading due to involvement in interactions
#>
#> Augmented Design Details
#> ========================
#> NULL
#>
#> Model Formula
#> =========================
#> y ~ env + check + env:check + (1 | env:block2) + (1 | treatment:test)
#> Model Details
#> =========================
#> Linear mixed model fit by REML. t-tests use Satterthwaite's method [
#> lmerModLmerTest]
#> Formula: frmla_int
#> Data: model.frame(mod_final)
#> Control: lmerControl(optimizer = "bobyqa")
#>
#> REML criterion at convergence: 330.2
#>
#> Scaled residuals:
#> Min 1Q Median 3Q Max
#> -1.1920 -0.5147 -0.1671 0.3962 1.9464
#>
#> Random effects:
#> Groups Name Variance Std.Dev.
#> treatment:test (Intercept) 3.522 1.877
#> env:block2 (Intercept) 17.760 4.214
#> Residual 28.225 5.313
#> Number of obs: 60, groups: treatment:test, 28; env:block2, 9
#>
#> Fixed effects:
#> Estimate Std. Error df t value Pr(>|t|)
#> (Intercept) 81.13170 1.75844 3.21727 46.139 1.19e-05 ***
#> env1 0.74220 2.24880 4.81716 0.330 0.755
#> env2 -1.25321 2.24880 4.81716 -0.557 0.602
#> check1 2.53497 2.26136 0.32012 1.121 0.652
#> check2 -1.79836 2.26136 0.32012 -0.795 0.715
#> check3 0.09053 2.26136 0.32012 0.040 0.981
#> check4 0.64608 2.26136 0.32012 0.286 0.873
#> env1:check1 0.25780 2.20767 20.10997 0.117 0.908
#> env2:check1 0.25321 2.20767 20.10997 0.115 0.910
#> env1:check2 -1.07554 2.20767 20.10997 -0.487 0.631
#> env2:check2 -0.08012 2.20767 20.10997 -0.036 0.971
#> env1:check3 0.03557 2.20767 20.10997 0.016 0.987
#> env2:check3 -1.30235 2.20767 20.10997 -0.590 0.562
#> env1:check4 0.81335 2.20767 20.10997 0.368 0.716
#> env2:check4 -0.52457 2.20767 20.10997 -0.238 0.815
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Correlation matrix not shown by default, as p = 15 > 12.
#> Use print(summary(x$Model), correlation=TRUE) or
#> vcov(summary(x$Model)) if you need it
#>
#> Model Diagnostics
#> =========================
#> conv_opt conv_lme4 opt_message opt_warnings singular
#> 1 0 Normal exit from bobyqa FALSE
#> treatment.test env.block2 Residual AIC BIC
#> 1 3.522165 17.76004 28.22528 366.1819 403.8801
#>
#> ANOVA, Fixed Effects
#> =========================
#> Type III Analysis of Variance Table with Satterthwaite's method
#> Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
#> env 8.865 4.4325 2 4.8172 0.1570 0.8589
#> check 72.357 18.0893 4 2.0000 0.6409 0.6844
#> env:check 54.846 6.8558 8 21.2312 0.2429 0.9774
#>
#> LRT, Random Effects
#> =========================
#> ANOVA-like table for random-effects: Single term deletions
#>
#> Model:
#> y ~ env + check + env:check + (1 | env:block2) + (1 | treatment:test)
#> npar logLik AIC LRT Df Pr(>Chisq)
#> <none> 18 -165.09 366.18
#> (1 | env:block2) 17 -169.01 372.02 7.8424 1 0.005104 **
#> (1 | treatment:test) 17 -165.11 364.22 0.0411 1 0.839259
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Model Formula
#> =========================
#> treatment mean SE df type
#> 1 1 83.66667 2.937966 0.7943792 BLUE
#> 2 2 79.33333 2.937966 0.7943792 BLUE
#> 3 3 81.22222 2.937966 0.7943792 BLUE
#> 4 4 81.77778 2.937966 0.7943792 BLUE
#> 5 5 79.51143 1.783427 NA BLUP
#> 6 6 79.50158 1.781885 NA BLUP
#> 7 7 80.94890 1.781885 NA BLUP
#> 8 8 78.94686 1.781885 NA BLUP
#> 9 9 79.40049 1.783427 NA BLUP
#> 10 10 80.17230 1.781885 NA BLUP
#> 11 11 79.39570 1.781885 NA BLUP
#> 12 12 79.39063 1.781885 NA BLUP
#> 13 13 79.31853 1.781885 NA BLUP
#> 14 14 79.48307 1.781885 NA BLUP
#> 15 15 79.70496 1.781885 NA BLUP
#> 16 16 80.87173 1.781885 NA BLUP
#> 17 17 79.59947 1.783427 NA BLUP
#> 18 18 79.15024 1.781885 NA BLUP
#> 19 19 79.87324 1.781885 NA BLUP
#> 20 20 79.26664 1.783427 NA BLUP
#> 21 21 79.33435 1.783427 NA BLUP
#> 22 22 80.92214 1.781885 NA BLUP
#> 23 23 79.55623 1.783427 NA BLUP
#> 24 24 79.31357 1.781885 NA BLUP
#> 25 25 80.14553 1.781885 NA BLUP
#> 26 26 79.42451 1.781885 NA BLUP
#> 27 27 79.70176 1.781885 NA BLUP
#> 28 28 78.86979 1.781885 NA BLUP
# 21. Fixed Effects - env, check, test
out21 <- augmentedRCBD.mix(env = data2$env2, block = data2$blk2,
treatment = data2$trt2,
y = data2$y2, checks = c("1", "2", "3", "4"),
env.random = FALSE,
check.random = FALSE, test.random = FALSE,
scenario = "II", console = TRUE)
#> fixed-effect model matrix is rank deficient so dropping 6 columns / coefficients
#> fixed-effect model matrix is rank deficient so dropping 6 columns / coefficients
#>
#> Augmented Design Details
#> ========================
#> NULL
#>
#> Model Formula
#> =========================
#> y ~ env + treatment + env:check + (1 | env:block2)
#> Model Details
#> =========================
#> Linear mixed model fit by REML. t-tests use Satterthwaite's method [
#> lmerModLmerTest]
#> Formula: frmla_int
#> Data: model.frame(mod_final)
#>
#> REML criterion at convergence: 172.5
#>
#> Scaled residuals:
#> Min 1Q Median 3Q Max
#> -1.081 -0.330 0.000 0.000 1.469
#>
#> Random effects:
#> Groups Name Variance Std.Dev.
#> env:block2 (Intercept) 0.5278 0.7265
#> Residual 30.3611 5.5101
#> Number of obs: 60, groups: env:block2, 9
#>
#> Fixed effects:
#> Estimate Std. Error df t value Pr(>|t|)
#> (Intercept) 77.7171 7.4589 18.5947 10.419 3.38e-09 ***
#> env1 1.5556 2.6200 23.9790 0.594 0.558
#> env2 -1.7778 2.6200 23.9790 -0.679 0.504
#> treatment1 5.7274 10.7954 18.0056 0.531 0.602
#> treatment2 3.0607 10.7954 18.0056 0.284 0.780
#> treatment3 5.0607 10.7954 18.0056 0.469 0.645
#> treatment4 4.0607 7.6622 18.0111 0.530 0.603
#> treatment5 -6.3214 13.3543 19.0234 -0.473 0.641
#> treatment6 -10.0614 13.3530 18.9222 -0.753 0.460
#> treatment7 10.5648 13.3530 18.9222 0.791 0.439
#> treatment8 -15.0614 13.3530 18.9222 -1.128 0.273
#> treatment9 -7.3214 13.3543 19.0234 -0.548 0.590
#> treatment10 3.5648 13.3530 18.9222 0.267 0.792
#> treatment11 -3.4352 13.3530 18.9222 -0.257 0.800
#> treatment12 -11.0614 13.3530 18.9222 -0.828 0.418
#> treatment13 2.5052 13.3530 18.9222 0.188 0.853
#> treatment14 -3.0397 13.3530 18.9222 -0.228 0.822
#> treatment15 -1.0397 13.3530 18.9222 -0.078 0.939
#> treatment16 16.5052 13.3530 18.9222 1.236 0.232
#> treatment17 0.7165 13.3543 19.0234 0.054 0.958
#> treatment18 -6.0397 13.3530 18.9222 -0.452 0.656
#> treatment19 7.5052 13.3530 18.9222 0.562 0.581
#> treatment20 -2.2835 13.3543 19.0234 -0.171 0.866
#> treatment21 -3.8472 11.1410 19.4648 -0.345 0.734
#> treatment22 15.9252 11.1394 19.3211 1.430 0.169
#> treatment23 -1.8472 11.1410 19.4648 -0.166 0.870
#> treatment24 -4.8960 11.1394 19.3211 -0.440 0.665
#> treatment25 8.9252 11.1394 19.3211 0.801 0.433
#> treatment26 -3.8960 11.1394 19.3211 -0.350 0.730
#> treatment27 4.9252 11.1394 19.3211 0.442 0.663
#> env1:check1 -0.3333 6.3625 18.0000 -0.052 0.959
#> env2:check1 1.0000 6.3625 18.0000 0.157 0.877
#> env1:check2 -3.3333 6.3625 18.0000 -0.524 0.607
#> env2:check2 -1.0000 6.3625 18.0000 -0.157 0.877
#> env1:check3 -2.3333 6.3625 18.0000 -0.367 0.718
#> env2:check3 -2.3333 6.3625 18.0000 -0.367 0.718
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Correlation matrix not shown by default, as p = 36 > 12.
#> Use print(summary(x$Model), correlation=TRUE) or
#> vcov(summary(x$Model)) if you need it
#> fit warnings:
#> fixed-effect model matrix is rank deficient so dropping 6 columns / coefficients
#>
#> Model Diagnostics
#> =========================
#> conv_opt conv_lme4
#> 1 0
#> opt_message
#> 1 NLOPT_XTOL_REACHED: Optimization stopped because xtol_rel or xtol_abs (above) was reached.
#> opt_warnings singular env.block2 Residual AIC BIC
#> 1 FALSE 0.5277775 30.36111 248.4733 328.0584
#>
#> ANOVA, Fixed Effects
#> =========================
#> Type III Analysis of Variance Table with Satterthwaite's method
#> Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
#> env 5.90 2.949 2 23.979 0.0971 0.9078
#> treatment 1422.58 52.688 27 17.098 1.7354 0.1186
#> env:check 17.61 2.935 6 18.000 0.0967 0.9958
#>
#> LRT, Random Effects
#> =========================
#> ANOVA-like table for random-effects: Single term deletions
#>
#> Model:
#> y ~ env + treatment + env:check + (1 | env:block2)
#> npar logLik AIC LRT Df Pr(>Chisq)
#> <none> 38 -86.237 248.47
#> (1 | env:block2) 37 -86.242 246.48 0.010281 1 0.9192
#>
#> Model Formula
#> =========================
#> treatment mean SE df type
#> 1 1 84.66667 3.208784 23.97900 BLUE
#> 29 1 82.66667 3.208784 23.97900 BLUE
#> 57 1 83.66667 3.208784 23.97900 BLUE
#> 86 2 79.00000 3.208784 23.97900 BLUE
#> 114 2 78.00000 3.208784 23.97900 BLUE
#> 142 2 81.00000 3.208784 23.97900 BLUE
#> 171 3 82.00000 3.208784 23.97900 BLUE
#> 199 3 78.66667 3.208784 23.97900 BLUE
#> 227 3 83.00000 3.208784 23.97900 BLUE
#> 256 4 83.33333 3.208784 23.97900 BLUE
#> 284 4 80.00000 3.208784 23.97900 BLUE
#> 312 4 82.00000 3.208784 23.97900 BLUE
#> 341 5 78.95124 5.922122 23.98953 BLUE
#> 342 6 75.21129 5.922122 23.98953 BLUE
#> 343 7 95.83747 5.922122 23.98953 BLUE
#> 344 8 70.21129 5.922122 23.98953 BLUE
#> 345 9 77.95124 5.922122 23.98953 BLUE
#> 346 10 88.83747 5.922122 23.98953 BLUE
#> 347 11 81.83747 5.922122 23.98953 BLUE
#> 348 12 74.21129 5.922122 23.98953 BLUE
#> 377 13 80.77787 5.922122 23.98953 BLUE
#> 378 14 75.23296 5.922122 23.98953 BLUE
#> 379 15 77.23296 5.922122 23.98953 BLUE
#> 380 16 94.77787 5.922122 23.98953 BLUE
#> 381 17 78.98916 5.922122 23.98953 BLUE
#> 382 18 72.23296 5.922122 23.98953 BLUE
#> 383 19 85.77787 5.922122 23.98953 BLUE
#> 384 20 75.98916 5.922122 23.98953 BLUE
#> 413 21 74.09210 5.922122 23.98953 BLUE
#> 414 22 93.86456 5.922122 23.98953 BLUE
#> 415 23 76.09210 5.922122 23.98953 BLUE
#> 416 24 73.04334 5.922122 23.98953 BLUE
#> 417 25 86.86456 5.922122 23.98953 BLUE
#> 418 26 74.04334 5.922122 23.98953 BLUE
#> 419 27 82.86456 5.922122 23.98953 BLUE
#> 420 28 69.04334 5.922122 23.98953 BLUE