# Plot parameter paths for BTLLasso Plots single paths for every parameter of a `BTLLasso` object or a `cv.BTLLasso` object. In contrast, to `paths`, one plot per covariate is created, every single parameter is illustrated by one path. For `cv.BTLLasso` objects, the optimal model according to the cross-validation is marked by a vertical dashed line. ```r ## S3 method for class 'BTLLasso' plot( x, plots_per_page = 1, ask_new = TRUE, rescale = FALSE, which = "all", equal.ranges = FALSE, x.axis = c("loglambda", "lambda"), rows = NULL, subs.X = NULL, subs.Z1 = NULL, main.Z2 = "Obj-spec. Covariates", ... ) ``` ## Arguments - `x`: BTLLasso or cv.BTLLasso object - `plots_per_page`: Number of plots per page, internally specified by `par(mfrow=...)`. - `ask_new`: If TRUE, the user is asked before each plot. - `rescale`: Should the parameter estimates be rescaled for plotting? Only applies if `scale = TRUE` was specified in `BTLLasso` or `cv.BTLLasso`. - `which`: Integer vector to specify which parameters/variables to plot. - `equal.ranges`: Should all single plots (for different covariates) have equal ranges on the y-axes. FALSE by default. - `x.axis`: Should the paths be plotted against log(lambda+1) or against lambda? - `rows`: Optional argument for the number of rows in the plot. Only applies if `plots_per_page>1`. - `subs.X`: Optional vector of subtitles for variables in `X`. Can be used to note the encoding of the single covariates, especially for dummy variables. - `subs.Z1`: Optional vector of subtitles for variables in `Z1`. Can be used to note the encoding of the single covariates, especially for dummy variables. - `main.Z2`: Optional character containg main for plot containing intervals for Z2 parameters. - `...`: Further plot arguments. ## 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`, `cv.BTLLasso`, `paths` ## Author(s) Gunther Schauberger gunther.schauberger@tum.de

plot.BTLLasso function