Stability.cumu {ordPens}

Stability selection for ordinal-on-ordinal regression.

Description

This function performs stability selection for the cumulative logit model.

Usage

Stability.cumu(x, y, lambda, n_iter=100, type=c("selection", "fusion"), ...)

Arguments

x

a vector or matrix of integers 1,2,... giving the observed levels of the ordinal factor(s). If x is a matrix, it is assumed that each column corresponds to one ordinal factor.

y

the vector of response values.

lambda

vector of penalty parameters (in decreasing order).

n_iter

number of subsamples. Details below.

type

penalty to be applied. If "selection", group lasso penalty for smoothing and selection is used. If "fusion", a fused lasso penalty for fusiona dn selection is used.

...

additional arguments to ordFusion and ordSelect, respectively.

Details

The method assumes that ordinal factor levels (contained in vector/columns of matrix x) take values 1,2,...,max, where max denotes the highest level of the respective factor observed in the data. Every level between 1 and max has to be observed at least once.

Instead of selecting/fitting one model, the data are pertubed/subsampled iter times and we choose those variables that occur in a large fraction (pi) of runs. The stability path then shows the order of relevance of the predictors according to stability selection.

Value

Pi

the matrix of estimated selection probabilities. Columns correspond to different lambda values, rows correspond to covariates.

mSize

matrix of size n_iter x length(lambda) containing the corresponding model size.

Author(s)

Aisouda Hoshiyar

References

Hoshiyar, A., Gertheiss, L.H., and Gertheiss, J. (2023). Regularization and Model Selection for Item-on-Items Regression with Applications to Food Products' Survey Data. Preprint, available from https://arxiv.org/abs/2309.16373.

Meinshausen, N. and Buehlmann, P. (2010). Stability selection, Journal of the Royal Statistical Society B (Statistical Methodology), 72, 417-473.

See Also

ordSelect, ordFusion