Divisive Latent Class Modeling as a Density Estimation Method for Categorical Data

Abstract

Traditionally latent class (LC) analysis is used by applied researchers as a tool for identifying substantively meaningful clusters. More recently, LC models have also been used as a density estimation tool for categorical variables. We introduce a divisive LC (DLC) model as a density estimation tool that may offer several advantages in comparison to a standard LC model. When using an LC model for density estimation, a considerable number of increasingly large LC models may have to be estimated before sufficient model-fit is achieved. A DLC model consists of a sequence of small LC models. Therefore, a DLC model can be estimated much faster and can easily utilize multiple processor cores, meaning that this model is more widely applicable and practical. In this study we describe the algorithm of fitting a DLC model, and discuss the various settings that indirectly influence the precision of a DLC model as a density estimation tool. These settings are illustrated using a synthetic data example, and the best performing algorithm is applied to a real-data example. The generated data example showed that, using specific decision rules, a DLC model is able to correctly model complex associations amongst categorical variables.

Estimating Classification Errors Under Edit Restrictions in Composite Survey-Register Data Using Multiple Imputation Latent Class Modelling (MILC)

“…These bootstrap samples are drawn because we want the imputations we create in a later step to take parameter uncertainty into account. Therefore, we do not use one LC model based on one data set, but we use m LC models based on m bootstrap samples of the original data set ( Van der Palm et al 2016 In the next step, we make use of LC analysis to estimate both visibly and invisibly present classification errors in categorical variables. We first link several data sets by unit identifiers, resulting in a composite data set matched on a common core set of identifiers (discarding all records where no match is obtained), and group variables measuring the same attribute present on more than one of the original source data sets.…”

Latent Class Trees with the Three-Step Approach

“…To circumvent the aforementioned issues, van Den Bergh, Schmittmann, and proposed the Latent Class Tree (LCT) modeling approach, which is based on an algorithm for latent-class based density estimation by Van der Palm, van der Ark, and Vermunt (2015). LCT modeling involves imposing a hierarchical tree structure on the latent classes.…”

Nonparametric statistical inference and imputation for incomplete categorical data

“…[8] extended this model to nested data structures in the presence of structural zeros. Other related works include the divisive latent class model [26], Bayesian multilevel latent class models [29] and so on. [28] presented a detailed overview of recent researches on multiple imputation using the latent class model.…”