Maximum augmented empirical likelihood estimation of categorical marginal models for large sparse contingency tables

Categorical marginal models (CMMs) are flexible tools for modelling dependent or clustered categorical data, when the dependencies themselves are not of interest. A major limitation of maximum likelihood (ML) estimation of CMMs is that the size of the contingency table increases exponentially with the number of variables, so even for a moderate number of variables, say between 10 and 20, ML estimation can become computationally infeasible. An alternative method, which retains the optimal asymptotic efficiency of ML, is maximum empirical likelihood (MEL) estimation. However, we show that MEL tends to break down for large, sparse contingency tables. As a solution, we propose a new method, which we call maximum augmented empirical likelihood (MAEL) estimation and which involves augmentation of the empirical likelihood support with a number of well-chosen cells. Simulation results show good finite sample performance for very large contingency tables

The development of interaction skills in preservice teacher education:A mixed-methods study of Dutch pre-service teachers

Significant attention has been paid in the international literature to the effect of in-service training on the interaction skills of teachers in early childhood education and care. The growth of pre-service teachers during teacher education has received relatively little attention to date, however. In a mixed-methods longitudinal study, we monitored the development of interaction skills among a group of Dutch pre-service teachers with repeated measures for 3 years and structured interviews. The results of a linear mixed-effects model revealed an impressive growth of interaction skills during the pre-service training. The qualitative interview data revealed progress of pre-service teachers’ professional reflection on their interaction with young children. These outcomes show the effectiveness of pre-service training for the development of interaction skills and professional reflection in early childhood education and care. However, progress is relatively modest for instructional skills and this domain needs further investment in pre-service training

Evaluating Model Fit in Two-Level Mokken Scale Analysis

Currently, two-level Mokken scale analysis for clustered test data is being developed. This paper contributes to this development by providing model-fit procedures for two-level Mokken scale analysis. New theoretical insights suggested that the existing model-fit procedure from traditional (one-level) Mokken scale analyses can be used for investigating model fit at both level 1 (respondent level) and level 2 (cluster level) of two-level Mokken scale analysis. However, the traditional model-fit procedure requires some modifications before it can be used at level 2. In this paper, we made these modifications and investigated the resulting model-fit procedure. For two model assumptions, monotonicity and invariant item ordering, we investigated the false-positive count and the sensitivity count of the level 2 model-fit procedure, with respect to the number of model violations detected, and the number of detected model violations deemed statistically significant. For monotonicity, the detection of model violations was satisfactory, but the significance test lacked power. For invariant item ordering, both aspects were satisfactory