British Journal of Mathematical & Statistical Psychology最新文献

An alternative closed-form expression for the marginal joint probability distribution of item scores under the random effects generalized partial credit model is presented. The closed-form expression involves a cumulant generating function and is therefore subjected to convexity constraints. As a consequence, complicated moment inequalities are taken into account in maximum likelihood estimation of the parameters of the model, so that the estimation solution is always proper. Another important favorable consequence is that the likelihood function has a single local extreme point, the global maximum. Furthermore, attention is paid to expected a posteriori person parameter estimation, generalizations of the model, and testing the goodness-of-fit of the model. Procedures proposed are demonstrated in an illustrative example.

Recently Variational Autoencoders (VAEs) have been proposed as a method to estimate high dimensional Item Response Theory (IRT) models on large datasets. Although these improve the efficiency of estimation drastically compared to traditional methods, they have no natural way to deal with missing values. In this paper, we adapt three existing methods from the VAE literature to the IRT setting and propose one new method. We compare the performance of the different VAE-based methods to each other and to marginal maximum likelihood estimation for increasing levels of missing data in a simulation study for both three- and ten-dimensional IRT models. Additionally, we demonstrate the use of the VAE-based models on an existing algebra test dataset. Results confirm that VAE-based methods are a time-efficient alternative to marginal maximum likelihood, but that a larger number of importance-weighted samples are needed when the proportion of missing values is large.

Networks (graphs) in psychology are often restricted to settings without interventions. Here we consider a framework borrowed from biology that involves multiple interventions from different contexts (observations and experiments) in a single analysis. The method is called perturbation graphs. In gene regulatory networks, the induced change in one gene is measured on all other genes in the analysis, thereby assessing possible causal relations. This is repeated for each gene in the analysis. A perturbation graph leads to the correct set of causes (not nec-essarily direct causes). Subsequent pruning of paths in the graph (called transitive reduction) should reveal direct causes. We show that transitive reduction will not in general lead to the correct underlying graph. We also show that invariant causal prediction is a generalisation of the perturbation graph method and does reveal direct causes, thereby replacing transitive re-duction. We conclude that perturbation graphs provide a promising new tool for experimental designs in psychology, and combined with invariant causal prediction make it possible to re-veal direct causes instead of causal paths. As an illustration we apply these ideas to a data set about attitudes on meat consumption and to a time series of a patient diagnosed with major depression disorder.

Reliability is an essential measure of how closely observed scores represent latent scores (reflecting constructs), assuming some latent variable measurement model. We present a general theoretical framework of reliability, placing emphasis on measuring the association between latent and observed scores. This framework was inspired by McDonald's (Psychometrika, 76, 511) regression framework, which highlighted the coefficient of determination as a measure of reliability. We extend McDonald's (Psychometrika, 76, 511) framework beyond coefficients of determination and introduce four desiderata for reliability measures (estimability, normalization, symmetry, and invariance). We also present theoretical examples to illustrate distinct measures of reliability and report on a numerical study that demonstrates the behaviour of different reliability measures. We conclude with a discussion on the use of reliability coefficients and outline future avenues of research.

This paper discusses estimation and limited-information goodness-of-fit test statistics in factor models for binary data using pairwise likelihood estimation and sampling weights. The paper extends the applicability of pairwise likelihood estimation for factor models with binary data to accommodate complex sampling designs. Additionally, it introduces two key limited-information test statistics: the Pearson chi-squared test and the Wald test. To enhance computational efficiency, the paper introduces modifications to both test statistics. The performance of the estimation and the proposed test statistics under simple random sampling and unequal probability sampling is evaluated using simulated data.

Bayesian analysis relies heavily on the Markov chain Monte Carlo (MCMC) algorithm to obtain random samples from posterior distributions. In this study, we compare the performance of MCMC stopping rules and provide a guideline for determining the termination point of the MCMC algorithm in latent variable models. In simulation studies, we examine the performance of four different MCMC stopping rules: potential scale reduction factor (PSRF), fixed-width stopping rule, Geweke's diagnostic, and effective sample size. Specifically, we evaluate these stopping rules in the context of the DINA model and the bifactor item response theory model, two commonly used latent variable models in educational and psychological measurement. Our simulation study findings suggest that single-chain approaches outperform multiple-chain approaches in terms of item parameter accuracy. However, when it comes to person parameter estimates, the effect of stopping rules diminishes. We caution against relying solely on the univariate PSRF, which is the most popular method, as it may terminate the algorithm prematurely and produce biased item parameter estimates if the cut-off value is not chosen carefully. Our research offers guidance to practitioners on choosing suitable stopping rules to improve the precision of the MCMC algorithm in models involving latent variables.

Normal ogive (NO) models have contributed substantially to the advancement of item response theory (IRT) and have become popular educational and psychological measurement models. However, estimating NO models remains computationally challenging. The purpose of this paper is to propose an efficient and reliable computational method for fitting NO models. Specifically, we introduce a novel and unified expectation-maximization (EM) algorithm for estimating NO models, including two-parameter, three-parameter, and four-parameter NO models. A key improvement in our EM algorithm lies in augmenting the NO model to be a complete data model within the exponential family, thereby substantially streamlining the implementation of the EM iteration and avoiding the numerical optimization computation in the M-step. Additionally, we propose a two-step expectation procedure for implementing the E-step, which reduces the dimensionality of the integration and effectively enables numerical integration. Moreover, we develop a computing procedure for estimating the standard errors (SEs) of the estimated parameters. Simulation results demonstrate the superior performance of our algorithm in terms of its recovery accuracy, robustness, and computational efficiency. To further validate our methods, we apply them to real data from the Programme for International Student Assessment (PISA). The results affirm the reliability of the parameter estimates obtained using our method.

Over several years, the evaluation of polytomous attributes in small-sample settings has posed a challenge to the application of cognitive diagnosis models. To enhance classification precision, the support vector machine (SVM) was introduced for estimating polytomous attribution, given its proven feasibility for dichotomous cases. Two simulation studies and an empirical study assessed the impact of various factors on SVM classification performance, including training sample size, attribute structures, guessing/slipping levels, number of attributes, number of attribute levels, and number of items. The results indicated that SVM outperformed the pG-DINA model in classification accuracy under dependent attribute structures and small sample sizes. SVM performance improved with an increased number of items but declined with higher guessing/slipping levels, more attributes, and more attribute levels. Empirical data further validated the application and advantages of SVMs.

When evaluating the effect of psychological treatments on a dichotomous outcome variable in a randomized controlled trial (RCT), covariate adjustment using logistic regression models is often applied. In the presence of covariates, average marginal effects (AMEs) are often preferred over odds ratios, as AMEs yield a clearer substantive and causal interpretation. However, standard error computation of AMEs neglects sampling-based uncertainty (i.e., covariate values are assumed to be fixed over repeated sampling), which leads to underestimation of AME standard errors in other generalized linear models (e.g., Poisson regression). In this paper, we present and compare approaches allowing for stochastic (i.e., randomly sampled) covariates in models for binary outcomes. In a simulation study, we investigated the quality of the AME and stochastic-covariate approaches focusing on statistical inference in finite samples. Our results indicate that the fixed-covariate approach provides reliable results only if there is no heterogeneity in interindividual treatment effects (i.e., presence of treatment–covariate interactions), while the stochastic-covariate approaches are preferable in all other simulated conditions. We provide an illustrative example from clinical psychology investigating the effect of a cognitive bias modification training on post-traumatic stress disorder while accounting for patients' anxiety using an RCT.