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CD (ridge, PCs)

Source: vignettes/articles/criterion-cd.Rmd
criterion-cd.Rmd

CD is the squared correlation between true and predicted genetic value (reliability). The score is the mean CD of the test individuals, computed on PCs.

Type Model-based
Direction Larger is better
Uses a test set yes
Score a given set cd_score()
Search with it optTrain(method = "CD")

Definition

With B=(X′X+I)−1B = (X'X + I)^{-1} and xix_i a test row:

CD=1n0∑ixi′BX′XBxixi′xi.\mathrm{CD} = \frac{1}{n_0}\sum_i \frac{x_i' B X'X B x_i}{x_i' x_i}.

This equals the CDMEAN2 of STPGA in our tests. For the GBLUP form with contrasts, see CDmean.

Use in TSDFGS 

library(TSDFGS)
data(geno)
cd_score(geno[1:50, ], geno[51:100, ])
## [1] 1.05567e-05
fit <- optTrain(geno, cand = 1:404, n.train = 50, method = "CD",
                 min.iter = 300, console = FALSE, seed = 1)
fit$OPTtrain
##  [1] 230 193 129 183 325  73 307  85 245 345 101 263 349 298 261  37 301  21 199
## [20] 215 304 287 393  96 289 371 214 375  42 306 178 143 342 302 155 357 260  48
## [39] 390  13  92 133  81  77 156 130 352 137 281 246
# targeted: the test set is known
fit2 <- optTrain(geno, cand = 1:300, n.train = 50, test = 301:404,
                  method = "CD", min.iter = 300, console = FALSE, seed = 1)
fit2$OPTtrain
##  [1] 254  32 163 131  85 252 263 138 273 261 128 217  67 262 151 276 282  10 207
## [20]  97  39 259 133 241 272   1 147  14  28 127 204 271  55 193 194 179 206 250
## [39] 268 289 123  34 157 234 239 144  61 221 156 117

The search is a random-start exchange (hill-climbing) search; see How the scores are computed. Use min.iter larger than 300 on real data and check fit$converged.

Original work

Laloë, D., Phocas, F., & Ménissier, F. (1996). Considerations on measures of precision and connectedness in mixed linear models of genetic evaluation. Genetics Selection Evolution, 28, 359. https://doi.org/10.1186/1297-9686-28-4-359

Rincent, R., Laloë, D., Nicolas, S., Altmann, T., Brunel, D., Revilla, P., et al. (2012). Maximizing the reliability of genomic selection by optimizing the calibration set of reference individuals: comparison of methods in two diverse groups of maize inbreds (Zea mays L.). Genetics, 192, 715-728. https://doi.org/10.1534/genetics.112.141473

Repository or website of the original authors: R package STPGA by Akdemir and colleagues: CRAN.R-project.org/package=STPGA (GPL-3).

License review

Formulas and algorithms are ideas and methods, which copyright does not protect. Where an original package is under a GPL license, we read it to check our results and credit it; TSDFGS is GPL-3, which is compatible with GPL-3 and GPL (>= 3) code. This is our reading of the public record, not legal advice; see the license review.

  • Original software: STPGA, GPL-3; compared, not copied.
  • Article license: Laloë et al. (1996) Genetics Selection Evolution; Rincent et al. (2012) CHORUS.
  • Verdict: included.

Reviewed 2026-11-04. All criteria and the ones left out.