Jay Magidson

Latent class cluster analysis

Users may download and print one copy of any publication from the public portal for the purpose of private study or research You may not further distribute the material or use it for any profit-making activity or commercial gain You may freely distribute the URL identifying the publication in the public portal Take down policy If you believe that this document breaches copyright, please contact us providing details, and we will remove access to the work immediately and investigate your claim.

Latent Class Factor and Cluster Models, Bi‐Plots, and Related Graphical Displays

We propose an alternative method of conducting exploratory latent class analysis that utilizes latent class factor models, and compare it to the more traditional approach based on latent class cluster models. We show that when formulated in terms of R mutually independent, dichotomous latent factors, the LC factor model has the same number of distinct parameters as an LC cluster model with R+1 clusters. Analyses over several data sets suggest that LC factor models typically fit data better and provide results that are easier to interpret than the corresponding LC cluster models. We also introduce a new graphical bi-plot display for LC factor models and compare it to similar plots used in correspondence analysis and to a barycentric coordinate display for LC cluster models. New results on identification of LC models are also presented. We conclude by describing various model extensions and an approach for eliminating boundary solutions in identified and unidentified LC models, which we have implemented in a new computer program.

Latent class models for classification

An overview is provided of recent developments in the use of latent class (LC) and other types of finite mixture models for classification purposes. Several extensions of existing models are presented. Two basic types of LC models for classification are defined: supervised and unsupervised structures. Their most important special cases are presented and illustrated with an empirical example.

An Extension of the CHAID Tree-based Segmentation Algorithm to Multiple Dependent Variables ?

The CHAID algorithm has proven to be an effective approach for obtaining a quick but meaningful segmentation where segments are defined in terms of demographic or other variables that are predictive of a single categorical criterion (dependent) variable. However, response data may contain ratings or purchase history on several products, or, in discrete choice experiments, preferences among alternatives in each of several choice sets. We propose an efficient hybrid methodology combining features of CHAID and latent class modeling (LCM) to build a classification tree that is predictive of multiple criteria. The resulting method provides an alternative to the standard method of profiling latent classes in LCM through the inclusion of (active) covariates.

Latent Class Analysis With Sampling Weights: A Maximum-Likelihood Approach

The authors illustrate how to perform maximum-likelihood estimation in latent class (LC) analysis when there are sampling weights. The methods are natural extensions of the approaches proposed by Clogg and Eliason (1987) and Magidson (1987) for dealing with sampling weights in the log-linear analysis of frequency tables. For the log-linear form of the LC model, the approach corresponds to a special case of Habermans (1979) log-linear LC model with cell weights. This approach can also be applied to the probability formulation of the LC model with cell weights, which can accommodate many indicators. The authors propose an efficient estimation-maximization algorithm for estimating the parameters for this formulation. A small simulation study shows that the probability estimates obtained by this approach compare favorably to other weighting approaches. Several empirical examples are provided to illustrate various possible weighting methods in LC analysis.

Hierarchical mixture models for nested data structures

A hierarchical extension of the finite mixture model is presented that can be used for the analysis of nested data structures. The model permits a simultaneous model-based clustering of lower- and higher-level units. Lower-level observations within higher-level units are assumed to be mutually independent given cluster membership of the higher-level units. The proposed model can be seen as a finite mixture model in which the prior class membership probabilities are assumed to be random, which makes it very similar to the grade-of-membership (GoM) model. The new model is illustrated with an example from organizational psychology.

Use of latent class regression models with a random intercept to remove the effects of the overall response rating level

Latent class regression models may be used to identify segments that differ with respect to the contribution of product attributes on their ratings of the associated products. However, such solutions tend be dominated by the overall liking (or the respondents’ response tendency) rather than differences in the liking of the presented products. In this paper, we show how to overcome this problem by including a continuous factor (CFactor) in the model to function as a random intercept. As such, it provides an elegant model-based alternative and general extension of the common practice of within-case ‘centering’ of the data. An application involving cracker products is used to illustrate the approach which results in segments that show clear differences in their sensory preferences.