r-score • TSDFGS

The r-score is the expected Pearson correlation between predicted and observed values of the test set, written in closed form for ridge regression. It was introduced with this package.

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

Definition

With training matrix $X$ ( $n \times p$ , PCs or markers), test matrix $X_0$ with $n_0$ rows, and penalty $\lambda = 1/p$ , the r-score is $q_{12}/\sqrt{q_1 q_2}$ : the covariance of predicted and true test values over the product of their variances. Ou and Liao (2019) derive the three terms. TSDFGS evaluates them with a $p \times p$ matrix when $p \le n$ and an $n \times n$ matrix otherwise.

Use in TSDFGS

library(TSDFGS)
data(geno)
r_score(geno[1:50, ], geno[51:100, ])

## [1] 0.7850248

fit <- optTrain(geno, cand = 1:404, n.train = 50, method = "rScore",
                 min.iter = 300, console = FALSE, seed = 1)
fit$OPTtrain

##  [1]   3 248 380 281 282 311 198  85 277 333 330 263  32 308 157 370 105  23 392
## [20] 389 390 368  73 245  65   1 323 394  42 301  20 134 166 185 278 237 158  15
## [39] 288 221 122 298 345 120 153 375 184  97 186 304

# targeted: the test set is known
fit2 <- optTrain(geno, cand = 1:300, n.train = 50, test = 301:404,
                  method = "rScore", min.iter = 300, console = FALSE, seed = 1)
fit2$OPTtrain

##  [1] 164  76 179 178 300  71 189 289 162 123  43  44  21 216 267 285 225 190 160
## [20] 287  67  69  64 151  47  89 196  85 172  31  65 246 221  39 130 214 157 129
## [39] 199 110  97 298  86 244  17 165  34  59 207 241

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

Ou, J.-H., & Liao, C.-T. (2019). Training set determination for genomic selection. Theoretical and Applied Genetics, 132, 2781-2792. https://doi.org/10.1007/s00122-019-03387-0

Repository or website of the original authors: github.com/oumarkme/TSDFGS, the package of the method’s authors.

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.

Method and software: Ou and Liao (2019); TSDFGS is GPL (>= 3), as v2.4.2 was.
Article license: Springer, not open access; cited, not reproduced.
Verdict: included.

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