boot.BTLLasso {BTLLasso}

Bootstrap function for BTLLasso

Description

Performs bootstrap for BTLLasso to get bootstrap intervals. Main input argument is a cv.BTLLasso object. The bootstrap is (recommended to be) performed on level of the cross-validation. Therefore, within every bootstrap iteration the complete cross-validation procedure from the cv.BTLLasso object is performed. A plot function can be applied to the resulting boot.BTLLasso object to plot bootstrap intervals.

Usage

boot.BTLLasso(
  model,
  B = 500,
  lambda = NULL,
  cores = 1,
  trace = TRUE,
  trace.cv = TRUE,
  with.cv = TRUE
)

Arguments

model

A cv.BTLLasso object.

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.

with.cv

Should cross-validation be performed separately on every bootstrap sample? If FALSE, the tuning parameter is fixed to the value chosen in the cv.BTLLasso object.

Details

The method can be highly time-consuming, for high numbers of tuning parameters, high numbers of folds in the cross-validation 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.

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

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?

number.na

Total number of failed bootstrap iterations.

Author(s)

Gunther Schauberger
[e-mail]

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, 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, plot.boot.BTLLasso

Examples

## 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)