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A sample suffers range restriction (RR) when its variance is reduced comparing with its population variance and, in turn, it fails representing such population. If the RR occurs over the latent factor, not directly over the observed variable, the researcher deals with an indirect RR, common when using convenience samples. This work explores how this problem affects different outputs of the factor analysis: multivariate normality (MVN), estimation process, goodness-of-fit, recovery of factor loadings, and reliability. In doing so, a Monte Carlo study was conducted. Data were generated following the linear selective sampling model, simulating tests varying their sample size (N = 200 and 500 cases), test size (J = 6, 12, 18, and 24 items), loading size (L =.50,.70, and.90), and restriction size (from R = 1,.90,.80, and so on till.10 selection ratio). Our results systematically suggest that an interaction between decreasing the loading size and increasing the restriction size affects the MVN assessment, obstructs the estimation process, and leads to an underestimation of the factor loadings and reliability. However, most of the MVN tests and most of the fit indices employed were nonsensitive to the RR problem. We provide some recommendations to applied researchers. [ABSTRACT FROM AUTHOR]

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The Q‐matrix identifies the subset of attributes measured by each item in the cognitive diagnosis modelling framework. Usually constructed by domain experts, the Q‐matrix might contain some misspecifications, disrupting classification accuracy. Empirical Q‐matrix validation methods such as the general discrimination index (GDI) and Wald have shown promising results in addressing this problem. However, a cut‐off point is used in both methods, which might be suboptimal. To address this limitation, the Hull method is proposed and evaluated in the present study. This method aims to find the optimal balance between fit and parsimony, and it is flexible enough to be used either with a measure of item discrimination (the proportion of variance accounted for, PVAF) or a coefficient of determination (pseudo‐R2). Results from a simulation study showed that the Hull method consistently showed the best performance and shortest computation time, especially when used with the PVAF. The Wald method also performed very well overall, while the GDI method obtained poor results when the number of attributes was high. The absence of a cut‐off point provides greater flexibility to the Hull method, and it places it as a comprehensive solution to the Q‐matrix specification problem in applied settings. This proposal is illustrated using real data. [ABSTRACT FROM AUTHOR]

In the context of cognitive diagnosis models (CDMs), a Q-matrix reflects the correspondence between attributes and items. The Q-matrix construction process is typically subjective in nature, which may lead to misspecifications. All this can negatively affect the attribute classification accuracy. In response, several methods of empirical Q-matrix validation have been developed. The general discrimination index (GDI) method has some relevant advantages such as the possibility of being applied to several CDMs. However, the estimation of the GDI relies on the estimation of the latent group sizes and success probabilities, which is made with the original (possibly misspecified) Q-matrix. This can be a problem, especially in those situations in which there is a great uncertainty about the Q-matrix specification. To address this, the present study investigates the iterative application of the GDI method, where only one item is modified at each step of the iterative procedure, and the required cutoff is updated considering the new parameter estimates. A simulation study was conducted to test the performance of the new procedure. Results showed that the performance of the GDI method improved when the application was iterative at the item level and an appropriate cutoff point was used. This was most notable when the original Q-matrix misspecification rate was high, where the proposed procedure performed better 96.5% of the times. The results are illustrated using Tatsuoka's fraction-subtraction data set. [ABSTRACT FROM AUTHOR]

Cognitive diagnosis models (CDMs) are latent class multidimensional statistical models that help classify people accurately by using a set of discrete latent variables, commonly referred to as attributes. These models require a Q-matrix that indicates the attributes involved in each item. A potential problem is that the Q-matrix construction process, typically performed by domain experts, is subjective in nature. This might lead to the existence of Q-matrix misspecifications that can lead to inaccurate classifications. For this reason, several empirical Q-matrix validation methods have been developed in the recent years. de la Torre and Chiu proposed one of the most popular methods, based on a discrimination index. However, some questions related to the usefulness of the method with empirical data remained open due the restricted number of conditions examined, and the use of a unique cutoff point (EPS) regardless of the data conditions. This article includes two simulation studies to test this validation method under a wider range of conditions, with the purpose of providing it with a higher generalization, and to empirically determine the most suitable EPS considering the data conditions. Results show a good overall performance of the method, the relevance of the different studied factors, and that using a single indiscriminate EPS is not acceptable. Specific guidelines for selecting an appropriate EPS are provided in the discussion. [ABSTRACT FROM AUTHOR]