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Compute the Length of Encoded Attribute Values

Source: R/LEAV.R
LEAV.Rd

For accessions in a collection compute the Length of Encoded Attribute Values (LEAV) information measure from qualitative and quantitative trait data (Wallace and Boulton 1968; Balakrishnan and Suresh 2001; Balakrishnan and Suresh 2001; Balakrishnan and Nair 2003) .

Usage

LEAV(
  data,
  names,
  quantitative = NULL,
  qualitative = NULL,
  freq,
  adj = TRUE,
  mean,
  sd,
  e
)

Arguments

data

The data as a data frame object. The data frame should possess one row per individual and columns with the individual names and multiple trait/character data.

names

Name of column with the individual names as a character string.

quantitative

Name of columns with the quantitative traits as a character vector.

qualitative

Name of columns with the qualitative traits as a character vector.

freq

A named list with the target absolute frequencies of the descriptor states for each qualitative trait specified in qualitative. The list names should be same as qualitative.

adj

logical. If TRUE, the proportion estimates are slightly biased to include zero frequency descriptor states in the computation (See Details). Default is TRUE.

mean

A named numeric vector of target means for each quantitative trait specified in quantitative. The list names should be same as quantitative.

sd

A named numeric vector of target standard deviation for each quantitative trait specified in quantitative. The list names should be same as quantitative.

e

A named numeric vector of least count of measurement for each quantitative trait specified in quantitative. The list names should be same as quantitative.

Value

A data frame with one row per accession in data and the following columns:

names

Accession identifiers, as specified by the names argument.

lt

The log-ratio message length term, \(\log(N / n)\), where \(N\) is the total number of accessions in data and \(n\) is the sum of frequencies in freq.

<qualitative traits>

One column per trait specified in qualitative, giving the information length \(-\log(p_k)\) for the level \(k\) of that trait observed for each accession.

<quantitative traits>

One column per trait specified in quantitative, giving the Gaussian information length \(\log(\sigma / c \varepsilon) + (x - \mu)^2 / 2\sigma^2\) for each accession, where \(c = 1/\sqrt{2\pi}\).

LEAV

The total information length for each accession, equal to the row sum of lt and all trait information length columns.

Details

For each accession \(s\) in the collection, the message length \(F_{s}\) to optimally encode all the \(d\) traits/descriptors is computed as follows using the joint density distribution of the whole collection.

\[F_{s} = l_{t} + \sum_{i=1}^{p} c_{m_{s},d_{i},t} + \sum_{j=1}^{q} c_{x_{s},d_{j},t}\]

Here, the first expression \(l_{t}\) is the message length for the subset \(t\) to which an accession belongs when there are \(N\) accessions in the whole collection and \(n_{t}\) accessions in the subset \(t\).

\[l_{t} = l_{t} = - \ln{\left ( \frac{N}{n_{t}} \right )}\]

Similarly \(\sum_{i=1}^{p} c_{m_{s},d_{i},t}\) is sum of the optimum message length for \(p\) qualitative traits, \(\sum_{j=1}^{q} c_{x_{s},d_{j},t}\) is sum of the optimum optimum message length for \(q\) quantitative traits. See inflen.qual and inflen.quant for more details.

References

Balakrishnan R, Nair NV (2003). “Strategies for developing core collections of sugarcane (Saccharum officinarum L.) germplasm-comparison of sampling from diversity groups constituted by three different methods.” Plant Genetic Resources Newsletter, 134, 33–41.

Balakrishnan R, Suresh KK (2001). “Strategies for developing core collections of safflower (Carthamus tinctorius L.) germplasm-part II. Using an information measure for obtaining a core sample with pre-determined diversity levels for several descriptors simultaneously.” Indian Journal of Plant Genetic Resources, 14(1), 32–42.

Balakrishnan R, Suresh KK (2001). “Strategies for developing core collections of safflower (Carthamus tinctorius L.) germplasm-part III. Obtaining diversity groups based on an information measure.” Indian Journal of Plant Genetic Resources, 14(3), 342–349.

Wallace CS, Boulton DM (1968). “An information measure for classification.” The Computer Journal, 11(2), 185–194.

See also

inflen.qual, inflen.quant

Examples

suppressPackageStartupMessages(library(EvaluateCore))

# Get data from EvaluateCore
data("cassava_EC", package = "EvaluateCore")

cassava_EC <- cassava_EC[sample(1:nrow(cassava_EC), 500), ]

cassava_EC <- cbind(genotypes = rownames(cassava_EC), cassava_EC)


quant <- c("NMSR", "TTRN", "TFWSR", "TTRW", "TFWSS", "TTSW", "TTPW", "AVPW",
                  "ARSR", "SRDM")
qual <- c("CUAL", "LNGS", "PTLC", "DSTA", "LFRT", "LBTEF", "CBTR", "NMLB",
                 "ANGB", "CUAL9M", "LVC9M", "TNPR9M", "PL9M", "STRP", "STRC",
                 "PSTR")

cassava_EC[, qual] <- lapply(cassava_EC[, qual], as.factor)

size <- 0.2

freq_list <- lapply(qual, function(x) {
  prop <-  prop.adj(cassava_EC[, x], method = "sqrt")
  size.count <- ceiling(size * length(x))
  round_preserve_sum(prop * size.count)
})
names(freq_list) <- qual

mean_vec <- sapply(cassava_EC[, quant],
                   function(x) {
                     floor(mean(x))
                   })
names(mean_vec) <- quant

sd_vec <- sapply(cassava_EC[quant],
             function(x) {
               round(sd(x), 1)
             })
names(sd_vec) <- quant

e_vec <- rep(1, length(quant))
names(e_vec) <- quant


# Compute LEAV
LEAV_cassava <- LEAV(data = cassava_EC, names = "genotypes",
                     quantitative = quant, qualitative = qual,
                     freq = freq_list, adj = TRUE,
                     mean = mean_vec, sd = sd_vec, e = e_vec)

head(LEAV_cassava)
#>   genotypes       lt      CUAL      LNGS     PTLC     DSTA      LFRT   LBTEF
#> 1  TMe-1005 6.214608 0.9162907 0.6931472 1.098612 1.098612 0.9162907 1.94591
#> 2  TMe-1006 6.214608 0.9162907 0.6931472 1.791759 1.791759 1.6094379 1.94591
#> 3  TMe-1007 6.214608 0.9162907 0.6931472 1.098612 1.098612 1.6094379 1.94591
#> 4  TMe-1010 6.214608 0.9162907 0.6931472 1.791759 1.791759 0.9162907 1.94591
#> 5  TMe-1016 6.214608 0.9162907 0.6931472 1.791759 1.791759 0.9162907 1.94591
#> 6  TMe-1025 6.214608 0.9162907 0.6931472 1.098612 1.098612 1.6094379 1.94591
#>        CBTR     NMLB      ANGB   CUAL9M    LVC9M   TNPR9M      PL9M      STRP
#> 1 1.3862944 2.079442 1.6094379 1.098612 1.791759 1.791759 1.3862944 1.6094379
#> 2 1.3862944 2.079442 1.6094379 1.791759 1.098612 1.791759 0.6931472 0.9162907
#> 3 0.6931472 2.079442 0.9162907 1.098612 1.791759 1.791759 0.6931472 1.6094379
#> 4 1.3862944 2.079442 0.9162907 1.098612 1.098612 1.791759 0.6931472 1.6094379
#> 5 0.6931472 2.079442 1.6094379 1.098612 1.098612 1.791759 1.3862944 1.6094379
#> 6 0.6931472 2.079442 0.9162907 1.098612 1.791759 1.791759 1.3862944 1.6094379
#>        STRC      PSTR     NMSR     TTRN    TFWSR     TTRW    TFWSS     TTSW
#> 1 1.0986123 1.0986123 3.375758 1.699297 2.657660 1.449567 2.708255 1.775477
#> 2 0.4054651 1.0986123 3.375758 1.945526 2.718152 1.487245 2.923710 1.919880
#> 3 0.4054651 1.0986123 3.104555 2.114809 3.035732 2.391512 4.495672 3.069218
#> 4 1.0986123 1.0986123 3.268920 2.545711 2.468624 1.468790 2.823164 1.846366
#> 5 1.0986123 0.4054651 3.047027 1.699297 2.559362 2.619117 2.751346 2.129919
#> 6 0.4054651 1.0986123 3.178519 1.699297 3.186016 1.920588 3.707393 1.993814
#>       TTPW     AVPW     ARSR     SRDM     LEAV
#> 1 3.293098 2.262596 1.846366 3.168110 52.06992
#> 2 3.490833 2.525408 1.846366 4.245367 54.31198
#> 3 4.550316 3.142828 1.751848 2.592589 56.00337
#> 4 3.231879 2.257787 1.751848 3.807867 52.61154
#> 5 3.301464 2.702693 1.846366 2.491027 52.28820
#> 6 4.211371 2.429234 1.846366 2.682867 53.30290