BTLLasso (version 0.1-1)

cv.BTLLasso: Cross-validation function for BTLLasso

Description

Performs crossvalidation of BTLLasso, including the BTLLasso algorithm for the whole data set.

Usage

cv.BTLLasso(Y, X, folds = 10, lambda, control = BTLLasso.ctrl(), 
            cores = folds, trace = TRUE, trace.cv = TRUE)

Arguments

Y

Matrix containing paired comparisons, ordered or binary. For K categories, the colmuns have to be ordered as follows: 1 vs. 2, 1 vs.3, ..., 1 vs. K, 2 vs. 3, 2 vs. 4, ..., 2 vs. K, ..., K-1 vs. K. One row represents one subject.

X

Matrix containing all subject-specific covariates. One row represents one subject, one column represents one covariate. Has to be standardized.

folds

Number of folds for the crossvalidation. Default is 10.

lambda

Vector of tuning parameters.

control

Function for control arguments, mostly for internal use. See also BTLLasso.ctrl.

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.

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 per tuning parameter.
• design
  Design matrix, NULL if return.design=FALSE in BTLLasso.ctrl
• Y
  Y matrix
• q
  q=K-1, K is the number of different categories in Y
• acoefs
  Matrix containing penalties, for internal use.
• response
  Vector containing 0-1 coded response.
• n
  Number of persons/subjects
• I
  Number of paired comparisons
• m
  Number of objects
• p
  Number of covariates
• X
  X matrix
• n.theta
  Number of estimated threshold parameters
• lambda
  Vector of tuning parameters
• deviances
  Vector of cross-validation deviances, one value per tuning parameter.
• folds
  Number of folds in cross validation.
• labels
  Labels of objects, only correct if Y specified correctly by "1 vs. 2","1 vs. 3",...
• epsilon
  Threshold value for convergence of the algorithm, specified in BTLLasso.ctrl

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 confidence intervalls using boot.BTLLasso and ci.BTLLasso.

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

See Also

BTLLasso, boot.BTLLasso, singlepaths, paths

Examples

# load data set
data(GLESsmall)

# define response and covariate matrix
X <- scale(GLESsmall[, 11:14])
Y <- as.matrix(GLESsmall[, 1:10])

# vector of subtitles, containing the coding of the single covariates
subs <- c("(in years)","female (1); male (0)",
"East Germany (1); West Germany (0)","(very) good (1); else (0)")

# vector of tuning parameters
lambda <- exp(seq(log(31),log(1),length=50))-1

# compute BTLLasso model
m <- BTLLasso(Y = Y, X = X, lambda = lambda)

op <- par(no.readonly = TRUE) 
par(mar=c(5,4,4,8))

# plot covariate paths
paths(m)

# plot parameter paths
singlepaths(m, subs = subs)

# compute 10-fold cross-validation
set.seed(5)
m.cv <- cv.BTLLasso(Y = Y, X = X, folds = 10, lambda = lambda, cores = 10)

# plot covariate paths, together with cv-optimal model
paths(m.cv)

# plot parameter paths, together with cv-optimal model
singlepaths(m.cv, subs = subs)

# compute bootstrap confidence intervals
m.boot <- boot.BTLLasso(m.cv, B = 100, cores = 25)

# plot bootstrap confidence intervals
par(mar=c(5,5,4,3))
ci.BTLLasso(m.boot, subs = subs)

par(op)