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Mokken scale analysis is a popular method for scaling dichotomous and polytomous items. Whether or not items form a scale is determined by three types of scalability coefficients: (1) for pairs of items, (2) for items, and (3) for the entire scale. It has become standard practice to interpret the sample values of these scalability coefficients using Mokken’s guidelines, which have been available since the 1970s. For valid assessment of the scalability coefficients, the standard errors of the scalability coefficients must be taken into account. So far, standard errors were not available for scales consisting of Likert items, the most popular item type in sociology, and standard errors could only be computed for dichotomous items if the number of items was small. This study solves these two problems. First, we derived standard errors for Mokken’s scalability coefficients using a marginal modeling framework. These standard errors can be computed for all types of items used in Mokken scale analysis. Second, we proved that the method can be applied to scales consisting of large numbers of items. Third, we applied Mokken scale analysis to a set of polytomous items measuring tolerance. The analysis showed that ignoring standard errors of scalability coefficients might result in incorrect inferences.Keywords: Mokken scale analysis, standard errors, scalability coefficients, marginal models.

We propose using latent class analysis as an alternative to log-linear analysis for the multiple imputation of incomplete categorical data. Similar to log-linear models, latent class models can be used to describe complex association structures between the variables used in the imputation model. However, unlike log-linear models, latent class models can be used to build large imputation models containing more than a few categorical variables. To obtain imputations reflecting uncertainty about the unknown model parameters, we use a nonparametric bootstrap procedure as an alternative to the more common full Bayesian approach. The proposed multiple imputation method, which is implemented in Latent GOLD software for latent class analysis, is illustrated with two examples. In a simulated data example, we compare the new method to well-established methods such as maximum likelihood estimation with incomplete data and multiple imputation using a saturated log-linear model. This example shows that the proposed method yields unbiased parameter estimates and standard errors. The second example concerns an application using a typical social sciences data set. It contains 79 variables that are all included in the imputation model. The proposed method is especially useful for such large data sets because standard methods for dealing with missing data in categorical variables break down when the number of variables is so large.

Researchers dealing with frequency data today can choose from a vast range of methods, descriptive and inferential. Two such well-known and useful methods are correspondence analysis and latent class analysis. Although these two methods were initially used for different research objectives, they are mathematically related to each other. Relations between these methods, however, have only been reported in the literature regarding the bivariate case. In this paper, we extend the study of such relations to the multivariate case. In particular the multivariate X latent class model is shown to imply the (relatively new) joint multivariate correspondence model with X − 1 positive eigenvalues. Such relations allow the underlying methods to be treated as variants of the same conceptual idea, providing some new meaningful aspects, which may help researchers better interpret the findings of their investigation.