BTLLasso (version 0.1-5)

boot.BTLLasso: Bootstrap function for BTLLasso

Description

Performs bootstrap for BTLLasso to get bootstrap confidence intervals. Main input argument is a cv.BTLLasso object. The bootstrap is performed on level of the cross-validation. Therefore, within every bootstrap iteration the complete cross-validation procedure from the cv.BTLLasso object is performed. The resulting boot.BTLLasso object is put into ci.BTLLasso to plot bootstrap confidence intervals.

Usage

boot.BTLLasso(model, quantiles = c(0.025, 0.975), B = 500, lambda = NULL,
  cores = 1, trace = TRUE, trace.cv = TRUE)

Arguments

model

A cv.BTLLasso object.

quantiles

Vector of two quantiles that are computed, will be used as borders of confidence intervals plotted by ci.BTLLasso.

B

Number of bootstrap iterations.

lambda

Vector of tuning parameters. If not specified (default), tuning parameters from cv.BTLLasso object are used. See also details.

cores

Number of cores for (parallelized) computation.

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.

Value

cv.model

cv.BTLLasso object

estimatesB

Matrix containing all B estimates for original parameters. For internal use.

estimatesBrepar

Matrix containing all B estimates for reparameterized (symmetric side constraints) parameters.

lambdaB

vector of used tuning parameters

conf.ints

Bootstrap confidence intervals for original parameters. For internal use.

conf.ints.repar

Bootstrap confidence intervals for reparameterized (symmetric side constraint) parameters.

lambda.max.alert

Was the largest value of lambda chosen in at least one bootstrap iteration?

lambda.min.alert

Was the smallest value of lambda chosen in at least one bootstrap iteration?

Details

The method can be highly time-consuming, for high numbers of tuning parameters, high numbers of folds in the crossvalidation and high number of bootstrap iterations B. The number of tuning parameters can be reduced by specifying lambda in the boot.BTLLasso function. You can control if the range of prespecified tuning parameters was to small by looking at the output values lambda.max.alert and lambda.min.alert. They are set TRUE if the smallest or largest of the specifed lambda values was chosen in at least one bootstrap iteration.

References

Schauberger, Gunther and Tutz, Gerhard (2015): Modelling Heterogeneity in Paired Comparison Data - an L1 Penalty Approach with an Application to Party Preference Data, Department of Statistics, LMU Munich, Technical Report 183

Schauberger, Gunther, Groll Andreas and Tutz, Gerhard (2016): Modelling Football Results in the German Bundesliga Using Match-specific Covariates, Department of Statistics, LMU Munich, Technical Report 197

See Also

BTLLasso, cv.BTLLasso, ci.BTLLasso

Examples

## Not run: ------------------------------------
# ##### Example with simulated data set containing X, Z1 and Z2
# data(SimData)
# 
# ## Specify tuning parameters
# lambda <- exp(seq(log(151), log(1.05), length = 30)) - 1
# 
# ## 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, lambda = lambda, control = ctrl)
# print(m.sim)
# 
# singlepaths(m.sim)
# 
# ## Cross-validate BTLLasso model for tuning parameters lambda
# set.seed(5)
# m.sim.cv <- cv.BTLLasso(Y = SimData$Y, X = SimData$X, Z1 = SimData$Z1, 
#                         Z2 = SimData$Z2, lambda = lambda, control = ctrl)
# print(m.sim.cv)
# 
# singlepaths(m.sim.cv, plot.order.effect = FALSE, 
#             plot.intercepts = FALSE, plot.Z2 = FALSE)
# paths(m.sim.cv, y.axis = 'L2')
# 
# ## Example for bootstrap confidence intervals for illustration only
# ## Don't calculate bootstrap confidence intervals with B = 10!!!!
# set.seed(5)
# m.sim.boot <- boot.BTLLasso(m.sim.cv, B = 10, cores = 10)
# print(m.sim.boot)
# ci.BTLLasso(m.sim.boot)
# 
# 
# ##### 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)')
# 
# ## vector of tuning parameters
# lambda <- exp(seq(log(61), log(1), length = 30)) - 1
# 
# 
# ## compute BTLLasso model 
# m.gles <- BTLLasso(Y = Y, X = X, Z1 = Z1, lambda = lambda)
# print(m.gles)
# 
# singlepaths(m.gles, subs.X = subs.X)
# paths(m.gles, y.axis = 'L2')
# 
# ## Cross-validate BTLLasso model 
# m.gles.cv <- cv.BTLLasso(Y = Y, X = X, Z1 = Z1, lambda = lambda)
# print(m.gles.cv)
# 
# singlepaths(m.gles.cv, subs.X = subs.X)
## ---------------------------------------------