BTLLasso {BTLLasso}

Function to perform BTLLasso

Description

Performs BTLLasso, a method to model heterogeneity in paired comparison data. Different types of covariates are allowed to have an influence on the attractivity/strength of the objects. Covariates can be subject-specific, object-specific or subject-object-specific. L1 penalties are used to reduce the complexiy of the model by enforcing clusters of equal effects or by elimination of irrelevant covariates.

Usage

BTLLasso(
  Y,
  X = NULL,
  Z1 = NULL,
  Z2 = NULL,
  lambda = NULL,
  control = ctrl.BTLLasso(),
  trace = TRUE
)

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.

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.

trace

Should the trace of the BTLLasso algorithm be printed?

Value

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.

df

Vector containing degrees of freedom for all models along the grid of tuning parameters.

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, to appear

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

cv.BTLLasso, boot.BTLLasso, ctrl.BTLLasso, plot.BTLLasso, paths, print.BTLLasso, predict.BTLLasso, coef

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)