Accounting for model misspecification in Bayesian structural equation models is an active area of research. We present a uniquely Bayesian approach to misspecification that models the degree of misspecification as a parameter-a parameter akin to the correlation root mean squared residual. The misspecification parameter can be interpreted on its own terms as a measure of absolute model fit and allows for comparing different models fit to the same data. By estimating the degree of misspecification simultaneously with structural parameters, the uncertainty about structural parameters reflects the degree of model misspecification. This results in a model that produces more reliable inference than extant Bayesian structural equation modeling. In addition, the approach estimates the residual covariance matrix that can be the basis for diagnosing misspecifications and updating a hypothesized model. These features are confirmed using simulation studies. Demonstrations with a variety of real-world examples show additional properties of the approach.
Disengaged responding poses a severe threat to the validity of educational large-scale assessments, because item responses from unmotivated test-takers do not reflect their actual ability. Existing identification approaches rely primarily on item response times, which bears the risk of misclassifying fast engaged or slow disengaged responses. Process data with its rich pool of additional information on the test-taking process could thus be used to improve existing identification approaches. In this study, three process data variables-text reread, item revisit, and answer change-were introduced as potential indicators of response engagement for multiple-choice items in a reading comprehension test. An extended latent class item response model for disengaged responding was developed by including the three new indicators as additional predictors of response engagement. In a sample of 1,932 German university students, the extended model indicated a better model fit than the baseline model, which included item response time as only indicator of response engagement. In the extended model, both item response time and text reread were significant predictors of response engagement. However, graphical analyses revealed no systematic differences in the item and person parameter estimation or item response classification between the models. These results suggest only a marginal improvement of the identification of disengaged responding by the new indicators. Implications of these results for future research on disengaged responding with process data are discussed.
The questionnaire method has always been an important research method in psychology. The increasing prevalence of multidimensional trait measures in psychological research has led researchers to use longer questionnaires. However, questionnaires that are too long will inevitably reduce the quality of the completed questionnaires and the efficiency of collection. Computer adaptive testing (CAT) can be used to reduce the test length while preserving the measurement accuracy. However, it is more often used in aptitude testing and involves a large number of parametric assumptions. Applying CAT to psychological questionnaires often requires question-specific model design and preexperimentation. The present article proposes a nonparametric and item response theory (IRT)-independent CAT algorithm. The new algorithm is simple and highly generalizable. It can be quickly used in a variety of questionnaires and tests without being limited by theoretical assumptions in different research areas. Simulation and empirical studies were conducted to demonstrate the validity of the new algorithm in aptitude tests and personality measures.
Rapid guessing (RG) is a form of non-effortful responding that is characterized by short response latencies. This construct-irrelevant behavior has been shown in previous research to bias inferences concerning measurement properties and scores. To mitigate these deleterious effects, a number of response time threshold scoring procedures have been proposed, which recode RG responses (e.g., treat them as incorrect or missing, or impute probable values) and then estimate parameters for the recoded dataset using a unidimensional or multidimensional IRT model. To date, there have been limited attempts to compare these methods under the possibility that RG may be misclassified in practice. To address this shortcoming, the present simulation study compared item and ability parameter recovery for four scoring procedures by manipulating sample size, the linear relationship between RG propensity and ability, the percentage of RG responses, and the type and rate of RG misclassifications. Results demonstrated two general trends. First, across all conditions, treating RG responses as incorrect produced the largest degree of combined systematic and random error (larger than ignoring RG). Second, the remaining scoring approaches generally provided equal accuracy in parameter recovery when RG was perfectly identified; however, the multidimensional IRT approach was susceptible to increased error as misclassification rates grew. Overall, the findings suggest that recoding RG as missing and employing a unidimensional IRT model is a promising approach.
This note demonstrates that the widely used Bayesian Information Criterion (BIC) need not be generally viewed as a routinely dependable index for model selection when the bifactor and second-order factor models are examined as rival means for data description and explanation. To this end, we use an empirically relevant setting with multidimensional measuring instrument components, where the bifactor model is found consistently inferior to the second-order model in terms of the BIC even though the data on a large number of replications at different sample sizes were generated following the bifactor model. We therefore caution researchers that routine reliance on the BIC for the purpose of discriminating between these two widely used models may not always lead to correct decisions with respect to model choice.