Estimating multilevel models for categorical data via generalized least squares

Abstract

Montero et al. (2002) proposed a strategy to formulate multilevel models related to a contingency table sample. This methodology is based on the application of the general linear model to hierarchical categorical data. In this paper we applied the method to a multilevel logistic regression model using simulated data. We find that the estimates of the random parameters are inadmissible in some circumstances; large bias and negative estimates of the variance are expected for unbalanced data sets. In order to correct the estimates we propose to use a numerical technique based on the Truncated Singular Value Decomposition (TSVD) in the solution of the problem of generalized least squares associated to the estimation of the random parameters. Finally a simulation study is presented to shows the effectiveness of this technique for reducing the bias of the estimates.

Keywords

• Multilevel models
• Generalized least squares
• Truncated Singular Value