Logistic Multidimensional Data Analysis for Ordinal Response Variables Using a Cumulative Link Function

Psychometrika, vol. 90, pp. 833–869

Abstract

We present a multidimensional data analysis framework for the analysis of ordinal response variables. Underlying the ordinal variables, we assume a continuous latent variable, leading to cumulative logit models. The framework includes unsupervised methods, when no predictor variables are available, and supervised methods, when predictor variables are available. We distinguish between dominance variables and proximity variables, where dominance variables are analyzed using inner product models, whereas the proximity variables are analyzed using distance models. An expectation-majorization-minimization algorithm is derived for estimation of the parameters of the models. We illustrate our methodology with three empirical data sets highlighting the advantages of the proposed framework. A simulation study is conducted to evaluate the performance of the algorithm.

Authors 4

1. Mark de Rooij Aachen Methodology and Statistics Department

   Leiden University

   Affiliation as printed

   Leiden University

   Methodology and Statistics Department, Leiden University, Leiden, The Netherlands

2. Ligaya Breemer Aachen Methodology and Statistics Department

   Leiden University

   Affiliation as printed

   Leiden University

   Methodology and Statistics Department, Leiden University, Leiden, The Netherlands

3. Dion H. A. Woestenburg Aachen Methodology and Statistics Department

   Leiden University

   Affiliation as printed

   Leiden University

   Methodology and Statistics Department, Leiden University, Leiden, The Netherlands

4. Frank M. T. A. Busing Aachen Methodology and Statistics Department

   Leiden University

   Affiliation as printed

   Leiden University

   Methodology and Statistics Department, Leiden University, Leiden, The Netherlands