Building Latent Class Trees, With an Application to a Study of Social Capital

Abstract

Abstract. Researchers use latent class (LC) analysis to derive meaningful clusters from sets of categorical variables. However, especially when the number of classes required to obtain a good fit is large, interpretation of the latent classes may not be straightforward. To overcome this problem, we propose an alternative way of performing LC analysis, Latent Class Tree (LCT) modeling. For this purpose, a recursive partitioning procedure similar to divisive hierarchical cluster analysis is used: classes are split until a certain criterion indicates that the fit does not improve. The advantage of the LCT approach compared to the standard LC approach is that it gives a clear insight into how the latent classes are formed and how solutions with different numbers of classes relate. We also propose measures to evaluate the relative importance of the splits. The practical use of the approach is illustrated by the analysis of a data set on social capital.

Classification of Hearing Aids Into Feature Profiles Using Hierarchical Latent Class Analysis Applied to a Large Dataset of Hearing Aids

“…Such a result can become exceedingly complicated and difficult to interpret, reducing the practical use of the model. To overcome this problem, Van Den Bergh et al (2017) suggested an extension to LCA, which they called Latent Class Trees (LCT) analysis.…”

“…LCT analysis was developed to provide a solution to some common difficulties when interpreting LCA results, such as the absence of a distinct optimum number of classes that fits a model or the fact that it is often unclear how different model results are interconnected. LCT addresses these problems by imposing a hierarchical structure on the latent classes ( Van Den Bergh et al 2017 ). In short, LCT is defined by a structure of mutually linked classes that are formed by sequentially splitting classes into two subclasses (using LCA with weighted membership probabilities).…”

Latent Class Trees with the Three-Step Approach

“…The bias-adjusted three-step method has become quite popular among applied researchers, but the basis of this method, the LC and LCG models, are not easy at all for applied researchers (Van De Schoot, Sijbrandij, Winter, Depaoli,& Vermunt, 2016). The tree approach facilitates the use of these models, which can lead to more interpretable and more meaningful classes.…”

Deciding on the Starting Number of Classes of a Latent Class Tree

“…To overcome the above-mentioned problems associated with LC analysis applications with large data sets, van den Bergh, Schmittmann, and Vermunt (2017) proposed an alternative way of performing an LC analysis, which they called latent class tree (LCT) analysis. Their approach involves performing a divisive hierarchical cluster analysis using an algorithm developed by Van der Palm, Van der Ark, and Vermunt (2016) for density estimation with a large number of categorical variables.…”