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CDmax (ridge, PCs)

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

CDmax is the largest coefficient of determination among the target individuals. It is the maximum where CD takes the mean.

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

Definition

With B=(X′X+I)−1B = (X'X + I)^{-1} and test rows xix_i: CDmax=max⁡ixi′BX′XBxi/(xi′xi)\mathrm{CDmax} = \max_i \, x_i' B X'X B x_i / (x_i' x_i). The formula is the CDMAX2 of STPGA. Because it is a maximum over targets, it depends on the single best-determined individual.

Use in TSDFGS 

library(TSDFGS)
data(geno)
cdmax_score(geno[1:50, ], geno[51:100, ])
## [1] 4.920842e-05
fit <- optTrain(geno, cand = 1:404, n.train = 50, method = "CDmax",
                 min.iter = 300, console = FALSE, seed = 1)
fit$OPTtrain
##  [1] 228 305 316 339 278 163 286 273 403 251  14 263 318 329 242 279  59 217 212
## [20] 233 200 395  57 241 351   1 326 394  42 224 171 133 267 308 396 334 404  25
## [39] 284 261  95  58 280 352 328 400  45 247 300 112
# targeted: the test set is known
fit2 <- optTrain(geno, cand = 1:300, n.train = 50, test = 301:404,
                  method = "CDmax", min.iter = 300, console = FALSE, seed = 1)
fit2$OPTtrain
##  [1] 223  92 167 187 219 259 263 285 265  41 286 217  75 267 220  56   1 249 281
## [20] 229 242 208   9 241 236  95 231  14  29 181 134 206  58 233  30 273 266 160
## [39]  96 256 176 115 204 123 159 212 150 252 271 148

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

Akdemir, D., Sanchez, J. I., & Jannink, J.-L. (2015). Optimization of genomic selection training populations with a genetic algorithm. Genetics Selection Evolution, 47, 38. https://doi.org/10.1186/s12711-015-0116-6

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 (CDMAX2); compared with the definition, not copied.
  • Article license: see the CD page.
  • Verdict: included.

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