BTLLasso (version 0.1-1)

BTLLasso: Function to perform BTLLasso

Description

Performs BTLLasso, a method to model heterogeneity in paired comparison data. Subject-specific covariates are allowd to have an influence on the attractivity/strength of the objects. An L1 penalty on the pairwise differences between the object-specific parameters allows for both clustering of object with regard to covariates and elimination of irrelevant covariates.

Usage

BTLLasso(Y, X, lambda, control = BTLLasso.ctrl(), trace = 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.

lambda

Vector of tuning parameters.

control

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

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 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
• 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

Y matrix needs a special format. Column names need to be in the style "1 vs 2","1 vs 3",... If so, object labels "1", "2", ... are extracted from the column names.

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

cv.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)

par(op)