# Cross-validation function for BTLLasso Performs cross-validation of BTLLasso, including the BTLLasso algorithm for the whole data set. ```r cv.BTLLasso( Y, X = NULL, Z1 = NULL, Z2 = NULL, folds = 10, lambda = NULL, control = ctrl.BTLLasso(), cores = folds, trace = TRUE, trace.cv = TRUE, cv.crit = c("RPS", "Deviance") ) ``` ## Arguments - `Y`: A `response.BTLLasso` object created by `response.BTLLasso`. - `X`: Matrix containing all subject-specific covariates that are to be included with object-specific effects . One row represents one subject, one column represents one covariate. X has to be standardized. - `Z1`: Matrix containing all object-subject-specific covariates that are to be included with object-specific effects . One row represents one subject, one column represents one combination between covariate and object. Column names have to follow the scheme 'firstvar.object1',...,'firstvar.objectm',...,'lastvar.objectm'. The object names 'object1',...,'objectm' have to be identical to the object names used in the `response.BTLLasso` object `Y`. The variable names and the object names have to be separated by '.'. The rownames of the matrix', Z.name, 'have to be equal to the subjects specified in the response object. Z1 has to be standardized. - `Z2`: Matrix containing all object-subject-specific covariates or object-specific covariates that are to be included with global effects . One row represents one subject, one column represents one combination between covariate and object. Column names have to follow the scheme 'firstvar.object1',...,'firstvar.objectm',...,'lastvar.objectm'. The object names 'object1',...,'objectm' have to be identical to the object names used in the `response.BTLLasso` object `Y`. The variable names and the object names have to be separated by '.'. The rownames of the matrix', Z.name, 'have to be equal to the subjects specified in the response object. Z2 has to be standardized. - `folds`: Number of folds for the crossvalidation. Default is 10. - `lambda`: Vector of tuning parameters. If `NULL`, automatically a grid of tuning parameters is created. - `control`: Function for control arguments, mostly for internal use. See also `ctrl.BTLLasso`. - `cores`: Number of cores used for (parallelized) cross-validation. By default, equal to the number of folds. - `trace`: Should the trace of the BTLLasso algorithm be printed? - `trace.cv`: Should the trace fo the cross-validation be printed? If parallelized, the trace is not working on Windows machines. - `cv.crit`: Which criterion should be used to evaluate cross-validation. Choice is between Ranked probability score and deviance. Only `RPS` considers the ordinal structure of the response. ## Returns - **coefs**: Matrix containing all (original) coefficients, one row per tuning parameter, one column per coefficient. - **coefs.repar**: Matrix containing all reparameterized (for symmetric side constraint) coefficients, one row per tuning parameter, one column per coefficient. - **logLik**: Vector of log-likelihoods, one value per tuning parameter. - **design**: List containing design matrix and several additional information like, e.g., number and names of covariates. - **Y**: Response object. - **penalty**: List containing all penalty matrices and some further information on penalties - **response**: Vector containing 0-1 coded response. - **X**: X matrix containing subject-specific covariates. - **Z1**: Z1 matrix containing subject-object-specific covariates. - **Z2**: Z2 matrix containing (subject)-object-specific covariates. - **lambda**: Vector of tuning parameters. - **control**: Control argument, specified by `ctrl.BTLLasso`. - **criterion**: Vector containing values of the chosen cross-validation criterion, one value per tuning parameter. - **folds**: Number of folds in cross validation. - **cv.crit**: Cross-validation criterion, either `RPS` or `Deviance`. - **df**: Vector containing degrees of freedom for all models along the grid of tuning parameters. ## Details Cross-validation can be performed parallel, default is 10-fold cross-validation on 10 cores. Output is a cv.BTLLasso object which can then be used for bootstrap intervalls using `boot.BTLLasso`. ## Examples ```r ## Not run: op <- par(no.readonly = TRUE) ############################## ##### Example with simulated data set containing X, Z1 and Z2 ############################## data(SimData) ## Specify control argument ## -> allow for object-specific order effects and penalize intercepts ctrl <- ctrl.BTLLasso(penalize.intercepts = TRUE, object.order.effect = TRUE, penalize.order.effect.diffs = TRUE) ## Simple BTLLasso model for tuning parameters lambda m.sim <- BTLLasso(Y = SimData$Y, X = SimData$X, Z1 = SimData$Z1, Z2 = SimData$Z2, control = ctrl) m.sim par(xpd = TRUE) plot(m.sim) ## Cross-validate BTLLasso model for tuning parameters lambda set.seed(1860) m.sim.cv <- cv.BTLLasso(Y = SimData$Y, X = SimData$X, Z1 = SimData$Z1, Z2 = SimData$Z2, control = ctrl) m.sim.cv coef(m.sim.cv) logLik(m.sim.cv) head(predict(m.sim.cv, type="response")) head(predict(m.sim.cv, type="trait")) plot(m.sim.cv, plots_per_page = 4) ## Example for bootstrap intervals for illustration only ## Don't calculate bootstrap intervals with B = 20!!!! set.seed(1860) m.sim.boot <- boot.BTLLasso(m.sim.cv, B = 20, cores = 20) m.sim.boot plot(m.sim.boot, plots_per_page = 4) ############################## ##### Example with small version from GLES data set ############################## data(GLESsmall) ## extract data and center covariates for better interpretability Y <- GLESsmall$Y X <- scale(GLESsmall$X, scale = FALSE) Z1 <- scale(GLESsmall$Z1, scale = FALSE) ## vector of subtitles, containing the coding of the X covariates subs.X <- c('', 'female (1); male (0)') ## Cross-validate BTLLasso model m.gles.cv <- cv.BTLLasso(Y = Y, X = X, Z1 = Z1) m.gles.cv coef(m.gles.cv) logLik(m.gles.cv) head(predict(m.gles.cv, type="response")) head(predict(m.gles.cv, type="trait")) par(xpd = TRUE, mar = c(5,4,4,6)) plot(m.gles.cv, subs.X = subs.X, plots_per_page = 4, which = 2:5) paths(m.gles.cv, y.axis = 'L2') ############################## ##### Example with Bundesliga data set ############################## data(Buli1516) Y <- Buli1516$Y5 Z1 <- scale(Buli1516$Z1, scale = FALSE) ctrl.buli <- ctrl.BTLLasso(object.order.effect = TRUE, name.order = "Home", penalize.order.effect.diffs = TRUE, penalize.order.effect.absolute = FALSE, order.center = TRUE, lambda2 = 1e-2) set.seed(1860) m.buli <- cv.BTLLasso(Y = Y, Z1 = Z1, control = ctrl.buli) m.buli par(xpd = TRUE, mar = c(5,4,4,6)) plot(m.buli) ############################## ##### Example with Topmodel data set ############################## data("Topmodel2007", package = "psychotree") Y.models <- response.BTLLasso(Topmodel2007$preference) X.models <- scale(model.matrix(preference~., data = Topmodel2007)[,-1]) rownames(X.models) <- paste0("Subject",1:nrow(X.models)) colnames(X.models) <- c("Gender","Age","KnowShow","WatchShow","WatchFinal") set.seed(5) m.models <- cv.BTLLasso(Y = Y.models, X = X.models) plot(m.models, plots_per_page = 6) par(op) ## End(Not run) ``` ## References Schauberger, Gunther and Tutz, Gerhard (2019): BTLLasso - A Common Framework and Software Package for the Inclusion and Selection of Covariates in Bradley-Terry Models, **Journal of Statistical Software**, 88(9), 1-29, tools:::Rd_expr_doi("10.18637/jss.v088.i09") Schauberger, Gunther and Tutz, Gerhard (2017): Subject-specific modelling of paired comparison data: A lasso-type penalty approach, **Statistical Modelling**, 17(3), 223 - 243 Schauberger, Gunther, Groll Andreas and Tutz, Gerhard (2018): Analysis of the importance of on-field covariates in the German Bundesliga, **Journal of Applied Statistics**, 45(9), 1561 - 1578 ## See Also `BTLLasso`, `boot.BTLLasso`, `ctrl.BTLLasso`, `plot.BTLLasso`, `paths`, `print.cv.BTLLasso`, `predict.BTLLasso`, `coef` ## Author(s) Gunther Schauberger gunther.schauberger@tum.de

cv.BTLLasso function