British Journal of Mathematical & Statistical Psychology最新文献

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.

The analysis of multiple bivariate correlations is often carried out by conducting simple tests to check whether each of them is significantly different from zero. In addition, pairwise differences are often judged by eye or by comparing the p-values of the individual tests of significance despite the existence of statistical tests for differences between correlations. This paper uses simulation methods to assess the accuracy (empirical Type I error rate), power, and robustness of 10 tests designed to check the significance of the difference between two dependent correlations with overlapping variables (i.e., the correlation between X₁ and Y and the correlation between X₂ and Y). Five of the tests turned out to be inadvisable because their empirical Type I error rates under normality differ greatly from the nominal alpha level of .05 either across the board or within certain sub-ranges of the parameter space. The remaining five tests were acceptable and their merits were similar in terms of all comparison criteria, although none of them was robust across all forms of non-normality explored in the study. Practical recommendations are given for the choice of a statistical test to compare dependent correlations with overlapping variables.

Exploratory cognitive diagnosis models have been widely used in psychology, education and other fields. This paper focuses on determining the number of attributes in a widely used cognitive diagnosis model, the GDINA model. Under some conditions of cognitive diagnosis models, we prove that there exists a special structure for the covariance matrix of observed data. Due to the special structure of the covariance matrix, an estimator based on eigen-decomposition is proposed for the number of attributes for the GDINA model. The performance of the proposed estimator is verified by simulation studies. Finally, the proposed estimator is applied to two real data sets Examination for the Certificate of Proficiency in English (ECPE) and Big Five Personality (BFP).

Computerized adaptive testing for cognitive diagnosis (CD-CAT) achieves remarkable estimation efficiency and accuracy by adaptively selecting and then administering items tailored to each examinee. The process of item selection stands as a pivotal component of a CD-CAT algorithm, with various methods having been developed for binary responses. However, multiple-choice (MC) items, an important item type that allows for the extraction of richer diagnostic information from incorrect answers, have been underemphasized. Currently, the Jensen-Shannon divergence (JSD) index introduced by Yigit et al. (Applied Psychological Measurement, 2019, 43, 388) is the only item selection method exclusively designed for MC items. However, the JSD index requires a large sample to calibrate item parameters, which may be infeasible when there is only a small or no calibration sample. To bridge this gap, the study first proposes a nonparametric item selection method for MC items (MC-NPS) by implementing novel discrimination power that measures an item's ability to effectively distinguish among different attribute profiles. A Q-optimal procedure for MC items is also developed to improve the classification during the initial phase of a CD-CAT algorithm. The effectiveness and efficiency of the two proposed algorithms were confirmed by simulation studies.

Oral reading fluency (ORF) assessments are commonly used to screen at-risk readers and evaluate interventions' effectiveness as curriculum-based measurements. Similar to the standard practice in item response theory (IRT), calibrated passage parameter estimates are currently used as if they were population values in model-based ORF scoring. However, calibration errors that are unaccounted for may bias ORF score estimates and, in particular, lead to underestimated standard errors (SEs) of ORF scores. Therefore, we consider an approach that incorporates the calibration errors in latent variable scores. We further derive the SEs of ORF scores based on the delta method to incorporate the calibration uncertainty. We conduct a simulation study to evaluate the recovery of point estimates and SEs of latent variable scores and ORF scores in various simulated conditions. Results suggest that ignoring calibration errors leads to underestimated latent variable score SEs and ORF score SEs, especially when the calibration sample is small.

A sufficient number of participants should be included to adequately address the research interest in the surveys with sensitive questions. In this paper, sample size formulas/iterative algorithms are developed from the perspective of controlling the confidence interval width of the prevalence of a sensitive attribute under four non-randomized response models: the crosswise model, parallel model, Poisson item count technique model and negative binomial item count technique model. In contrast to the conventional approach for sample size determination, our sample size formulas/algorithms explicitly incorporate an assurance probability of controlling the width of a confidence interval within the pre-specified range. The performance of the proposed methods is evaluated with respect to the empirical coverage probability, empirical assurance probability and confidence width. Simulation results show that all formulas/algorithms are effective and hence are recommended for practical applications. A real example is used to illustrate the proposed methods.

Several new models based on item response theory have recently been suggested to analyse intensive longitudinal data. One of these new models is the time-varying dynamic partial credit model (TV-DPCM; Castro-Alvarez et al., Multivariate Behavioral Research, 2023, 1), which is a combination of the partial credit model and the time-varying autoregressive model. The model allows the study of the psychometric properties of the items and the modelling of nonlinear trends at the latent state level. However, there is a severe lack of tools to assess the fit of the TV-DPCM. In this paper, we propose and develop several test statistics and discrepancy measures based on the posterior predictive model checking (PPMC) method (PPMC; Rubin, The Annals of Statistics, 1984, 12, 1151) to assess the fit of the TV-DPCM. Simulated and empirical data are used to study the performance of and illustrate the effectiveness of the PPMC method.

Exploratory structural equation modelling (ESEM) is an alternative to the well-known method of confirmatory factor analysis (CFA). ESEM is mainly used to assess the quality of measurement models of common factors but can be efficiently extended to test structural models. However, ESEM may not be the best option in some model specifications, especially when structural models are involved, because the full flexibility of ESEM could result in technical difficulties in model estimation. Thus, set-ESEM was developed to accommodate the balance between full-ESEM and CFA. In the present paper, we show examples where set-ESEM should be used rather than full-ESEM. Rather than relying on a simulation study, we provide two applied examples using real data that are included in the OSF repository. Additionally, we provide the code needed to run set-ESEM in the free R package lavaan to make the paper practical. Set-ESEM structural models outperform their CFA-based counterparts in terms of goodness of fit and realistic factor correlation, and hence path coefficients in the two empirical examples. In several instances, effects that were non-significant (i.e., attenuated) in the CFA-based structural model become larger and significant in the set-ESEM structural model, suggesting that set-ESEM models may generate more accurate model parameters and, hence, lower Type II error rate.

Different data types often occur in psychological and educational measurement such as computer-based assessments that record performance and process data (e.g., response times and the number of actions). Modelling such data requires specific models for each data type and accommodating complex dependencies between multiple variables. Generalized linear latent variable models are suitable for modelling mixed data simultaneously, but estimation can be computationally demanding. A fast solution is to use Laplace approximations, but existing implementations of joint modelling of mixed data types are limited to ordinal and continuous data. To address this limitation, we derive an efficient estimation method that uses first- or second-order Laplace approximations to simultaneously model ordinal data, continuous data, and count data. We illustrate the approach with an example and conduct simulations to evaluate the performance of the method in terms of estimation efficiency, convergence, and parameter recovery. The results suggest that the second-order Laplace approximation achieves a higher convergence rate and produces accurate yet fast parameter estimates compared to the first-order Laplace approximation, while the time cost increases with higher model complexity. Additionally, models that consider the dependence of variables from the same stimulus fit the empirical data substantially better than models that disregarded the dependence.

Crossed random effects models (CREMs) are particularly useful in longitudinal data applications because they allow researchers to account for the impact of dynamic group membership on individual outcomes. However, no research has determined what data conditions need to be met to sufficiently identify these models, especially the group effects, in a longitudinal context. This is a significant gap in the current literature as future applications to real data may need to consider these conditions to yield accurate and precise model parameter estimates, specifically for the group effects on individual outcomes. Furthermore, there are no existing CREMs that can model intrinsically nonlinear growth. The goals of this study are to develop a Bayesian piecewise CREM to model intrinsically nonlinear growth and evaluate what data conditions are necessary to empirically identify both intrinsically linear and nonlinear longitudinal CREMs. This study includes an applied example that utilizes the piecewise CREM with real data and three simulation studies to assess the data conditions necessary to estimate linear, quadratic, and piecewise CREMs. Results show that the number of repeated measurements collected on groups impacts the ability to recover the group effects. Additionally, functional form complexity impacted data collection requirements for estimating longitudinal CREMs.