Tests of Measurement Invariance Without Subgroups: A Generalization of Classical Methods

The issue of measurement invariance commonly arises in factor-analytic contexts, with methods for assessment including likelihood ratio tests, Lagrange multiplier tests, and Wald tests. These tests all require advance definition of the number of groups, group membership, and offending model parameters. In this paper, we study tests of measurement invariance based on stochastic processes of casewise derivatives of the likelihood function. These tests can be viewed as generalizations of the Lagrange multiplier test, and they are especially useful for: (i) identifying subgroups of individuals that violate measurement invariance along a continuous auxiliary variable without prespecified thresholds, and (ii) identifying specific parameters impacted by measurement invariance violations. The tests are presented and illustrated in detail, including an application to a study of stereotype threat and simulations examining the tests’ abilities in controlled conditions.     

Toddlers with Elevated Autism Symptoms Show Slowed Habituation to Faces

We explored social information processing and its relation to social and communicative symptoms in toddlers with Autism Spectrum Disorder (ASD) and their siblings. Toddlers with more severe symptoms of autism showed slower habituation to faces than comparison groups; slower face learning correlated with poorer social skills and lower verbal ability. Unaffected toddlers who were siblings of children with ASD also showed slower habituation to faces compared with toddlers without siblings with ASD. We conclude that slower rates of face learning may be an endophenotype of ASD and is associated with more severe symptoms among affected individuals.     

True overconfidence: The inability of rational information processing to account for apparent overconfidence

The better-than-average effect describes the tendency of people to perceive their skills and virtues as being above average. We derive a new experimental paradigm to distinguish between two possible explanations for the effect, namely rational information processing and overconfidence. Experiment participants evaluate their relative position within the population by stating their complete belief distribution. This approach sidesteps recent methodology concerns associated with previous research. We find that people hold beliefs about their abilities in different domains and tasks which are inconsistent with rational information processing. Both on an aggregated and an individual level, they show considerable overplacement. We conclude that overconfidence is not only apparent overconfidence but rather the consequence of a psychological bias.     

The disutility of the hard-easy effect in choice confidence

A common finding in confidence research is the hard-easy effect, in which judges exhibit greater overconfidence for more difficult sets of questions. Many explanations have been advanced for the hard-easy effect, including systematic cognitive mechanisms, experimenter bias, random error, and statistical artifact. In this article, I mathematically derive necessary and sufficient conditions for observing a hard-easy effect, and I relate these conditions to previous explanations for the effect. I conclude that all types of judges exhibit the hard-easy effect in almost all realistic situations. Thus, the effect’s presence cannot be used to distinguish between judges or to draw support for specific models of confidence elicitation.     

Computation and application of generalized linear mixed model derivatives using lme4

Psychometrika - Maximum likelihood estimation of generalized linear mixed models (GLMMs) is difficult due to marginalization of the random effects. Derivative computations of a fitted GLMM’s...     

Model Selection of Nested and Non-Nested Item Response Models Using Vuong Tests

Abstract

In this paper, we apply Vuong’s general approach of model selection to the comparison of nested and non-nested unidimensional and multidimensional item response theory (IRT) models. Vuong’s approach of model selection is useful because it allows for formal statistical tests of both nested and non-nested models. However, only the test of non-nested models has been applied in the context of IRT models to date. After summarizing the statistical theory underlying the tests, we investigate the performance of all three distinct Vuong tests in the context of IRT models using simulation studies and real data. In the non-nested case we observed that the tests can reliably distinguish between the graded response model and the generalized partial credit model. In the nested case, we observed that the tests typically perform as well as or sometimes better than the traditional likelihood ratio test. Based on these results, we argue that Vuong’s approach provides a useful set of tools for researchers and practitioners to effectively compare competing nested and non-nested IRT models.