Suchergebnisse

Researchers using latent class (LC) analysis often proceed using the following three steps: (1) an LC model is built for a set of response variables, (2) subjects are assigned to LCs based on their posterior class membership probabilities, and (3) the association between the assigned class membership and external variables is investigated using simple cross-tabulations or multinomial logistic regression analysis. Bolck, Croon, and Hagenaars (2004) demonstrated that such a three-step approach underestimates the associations between covariates and class membership. They proposed resolving this problem by means of a specific correction method that involves modifying the third step. In this article, I extend the correction method of Bolck, Croon, and Hagenaars by showing that it involves maximizing a weighted log-likelihood function for clustered data. This conceptualization makes it possible to apply the method not only with categorical but also with continuous explanatory variables, to obtain correct tests using complex sampling variance estimation methods, and to implement it in standard software for logistic regression analysis. In addition, a new maximum likelihood (ML)—based correction method is proposed, which is more direct in the sense that it does not require analyzing weighted data. This new three-step ML method can be easily implemented in software for LC analysis. The reported simulation study shows that both correction methods perform very well in the sense that their parameter estimates and their SEs can be trusted, except for situations with very poorly separated classes. The main advantage of the ML method compared with the Bolck, Croon, and Hagenaars approach is that it is much more efficient and almost as efficient as one-step ML estimation.

It is shown how to implement an EM algorithm for maximum likelihood estimation of hierarchical nonlinear models for data sets consisting of more than two levels of nesting. This upward–downward algorithm makes use of the conditional independence assumptions implied by the hierarchical model. It cannot only be used for the estimation of models with a parametric specification of the random effects, but also to extend the two‐level nonparametric approach – sometimes referred to as latent class regression – to three or more levels. The proposed approach is illustrated with an empirical application.

'In diesem Artikel wird ein allgemeiner Ansatz zur Analyse von kategorialem Panel-Daten vorgestellt, der ein log-lineares Pfadmodell für den strukturellen Teil mit einem Meßmodell für kategorialen Daten verbindet. Während das Strukturmodell aus einem System von Logit-Gleichungen besteht, die die kausalen Zusammenhänge zwischen den latenten Variablen spezifizieren, wird als Meßmodell für die kategorialen Indikatoren ein latent class Modell verwendet, das es erlaubt, wirklichen Wechsel von zufälligem, meßfehlerbedingten Wechsel zu unterscheiden. Mit Hilfe von Restriktionen, die den Kategorien der Indikatoren oder der latenten Klassen auferlegt werden, können in diesem Rahmen diskretisierte Varianten der meisten latent trait Modelle (so des Rasch-Modell, des Lord-Birnbaum-Modell oder des partial credit Modells) als restringierte latent class Modelle formuliert werden. Log-lineare Pfadmodelle mit latenten Variablen können mit Hilfe des Programms EM geschätzt werden. Am Beispiel der Skala 'Jugendzentrismus', die über zwei Zeitpunkte gemessen wurde, werden mit Hilfe dieses Programms mehrere Meßmodelle getestet und in einem zweiten Schritt der Einfluß unterschiedlicher Kovarianten auf die Ausgangsposition und die latenten Übergänge der latenten Variablen 'Jugendzentrismus' untersucht.' (Autorenreferat)

An important aspect of applied research is the assessment of the goodness‐of‐fit of an estimated statistical model. In the analysis of contingency tables, this usually involves determining the discrepancy between observed and estimated frequencies using the likelihood‐ratio statistic. In models with inequality constraints, however, the asymptotic distribution of this statistic depends on the unknown model parameters and, as a result, there no longer exists an unique p‐value. Bootstrap p‐values obtained by replacing the unknown parameters by their maximum likelihood estimates may also be inaccurate, especially if many of the imposed inequality constraints are violated in the available sample. We describe the various problems associated with the use of asymptotic and bootstrap p‐values and propose the use of Bayesian posterior predictive checks as a better alternative for assessing the fit of log‐linear models with inequality constraints.

In the social and behavioral sciences, variables are often categorical and people are often nested in groups. Models for such data, such as multilevel logistic regression or the multilevel latent class model, should account for not only the categorical nature of the variables, but also the nested structure of the persons. To assess whether the model accomplishes this goal adequately, local fit measures for multilevel categorical data were recently introduced by Nagelkerke, Oberski, and Vermunt (2015). The BVR-group evaluates the variable–group fit, and the BVR-pair evaluates the person–person fit within groups. In this article, we evaluate the performance of these 2 measures for the multilevel latent class model (Vermunt, 2003). An extensive simulation study indicates that whenever multilevel latent class modeling itself is viable, Type I error is controlled and power is adequate for both fit statistics. Thus, the BVR-group and BVR-pair are useful measures to locate important sources of misfit in multilevel latent class analysis.