Bayesian approaches for estimating multilevel latent variable models can be beneficial in small samples. Prior distributions can be used to overcome small sample problems, for example, when priors that increase the accuracy of estimation are chosen. This article discusses two different but not mutually exclusive approaches for specifying priors. Both approaches aim at stabilizing estimators in such a way that the Mean Squared Error of the estimator of the between-group slope will be small. In the first approach, the MSE is (...) decreased by specifying a slightly informative prior for the group-level variance of the predictor variable, whereas in the second approach, the decrease is achieved directly by using a slightly informative prior for the slope. Mathematical and graphical inspections suggest that both approaches can be effective for reducing the MSE in small samples, thus rendering them attractive in these situations. The article also discusses how these approaches can be implemented in Mplus. (shrink)

In this article we evaluate claims that language structure adapts to sociolinguistic environment. We present the results of two typological case studies examining the effects of the number of native (=L1) speakers and the proportion of adult second language (=L2) learners on language structure. Data from more than 300 languages suggest that testing the effect of population size and proportion of adult L2 learners on features of verbal and nominal complexity produces conflicting results on different grammatical features. The results show (...) that verbal inflectional synthesis adapts to the sociolinguistic environment but the number of genders does not. The results also suggest that modeling population size together with proportion of L2 improves model fit compared to modeling them independently of one another. We thus argue that surveying population size alone may be insufficient to detect possible adaptation of linguistic structure to the sociolinguistic environment. Rather, other features, such as proportion of L2 speakers, prestige and social network density, should be studied, and if demographic numeric data are used, they should not be used in isolation but rather in competition with other sociolinguistic features. We also suggest that not all types of language structures within a given grammatical domain are equally sensitive to the effect of sociolinguistic variables, and that more exploratory studies are needed before we can arrive at a reliable set of grammatical features that may be potentially most (and least) adaptive to social structures. (shrink)

With small to modest sample sizes and complex models, maximum likelihood estimation of confirmatory factor analysis models can show serious estimation problems such as non-convergence or parameter estimates outside the admissible parameter space. In this article, we distinguish different Bayesian estimators that can be used to stabilize the parameter estimates of a CFA: the mode of the joint posterior distribution that is obtained from penalized maximum likelihood estimation, and the mean, median, or mode of the marginal posterior distribution that are (...) calculated by using Markov Chain Monte Carlo methods. In two simulation studies, we evaluated the performance of the Bayesian estimators from a frequentist point of view. The results show that the EAP produced more accurate estimates of the latent correlation in many conditions and outperformed the other Bayesian estimators in terms of root mean squared error. We also argue that it is often advantageous to choose a parameterization in which the main parameters of interest are bounded, and we suggest the four-parameter beta distribution as a prior distribution for loadings and correlations. Using simulated data, we show that selecting weakly informative four-parameter beta priors can further stabilize parameter estimates, even in cases when the priors were mildly misspecified. Finally, we derive recommendations and propose directions for further research. (shrink)

In the present paper we empirically investigate the psychometric properties of some of the most famous statistical and logical cognitive illusions from the “heuristics and biases” research program by Daniel Kahneman and Amos Tversky, who nearly 50 years ago introduced fascinating brain teasers such as the famous Linda problem, the Wason card selection task, and so-called Bayesian reasoning problems (e.g., the mammography task). In the meantime, a great number of articles has been published that empirically examine single cognitive illusions, theoretically (...) explaining people’s faulty thinking, or proposing and experimentally implementing measures to foster insight and to make these problems accessible to the human mind. Yet these problems have thus far usually been empirically analyzed on an individual-item level only (e.g., by experimentally comparing participants’ performance on various versions of one of these problems). In this paper, by contrast, we examine these illusions as a group and look at the ability to solve them as a psychological construct. Based on an sample ofN= 2,643 Luxembourgian school students of age 16–18 we investigate the internal psychometric structure of these illusions (i.e., Are they substantially correlated? Do they form a reflexive or a formative construct?), their connection to related constructs (e.g., Are they distinguishable from intelligence or mathematical competence in a confirmatory factor analysis?), and the question of which of a person’s abilities can predict the correct solution of these brain teasers (by means of a regression analysis). (shrink)