Cognitive diagnosis models (CDMs) allow classifying respondents into a set of discrete attribute profiles. The internal structure of the test is determined in a Q-matrix, whose correct specification is necessary to achieve an accurate attribute profile classification. Several empirical Q-matrix estimation and validation methods have been proposed with the aim of providing well-specified Q-matrices. However, these methods require the number of attributes to be set in advance. No systematic studies about CDMs dimensionality assessment have been conducted, which contrasts with the vast existing literature for the factor analysis framework. To address this gap, the present study evaluates the performance of several dimensionality assessment methods from the factor analysis literature in determining the number of attributes in the context of CDMs. The explored methods were parallel analysis, minimum average partial, very simple structure, DETECT, empirical Kaiser criterion, exploratory graph analysis, and a machine learning factor forest model. Additionally, a model comparison approach was considered, which consists in comparing the model-fit of empirically estimated Q-matrices. The performance of these methods was assessed by means of a comprehensive simulation study that included different generating number of attributes, item qualities, sample sizes, ratios of the number of items to attribute, correlations among the attributes, attributes thresholds, and generating CDM. Results showed that parallel analysis (with Pearson correlations and mean eigenvalue criterion), factor forest model, and model comparison (with AIC) are suitable alternatives to determine the number of attributes in CDM applications, with an overall percentage of correct estimates above 76% of the conditions. The accuracy increased to 97% when these three methods agreed on the number of attributes. In short, the present study supports the use of three methods in assessing the dimensionality of CDMs. This will allow to test the assumption of correct dimensionality present in the Q-matrix estimation and validation methods, as well as to gather evidence of validity to support the use of the scores obtained with these models. The findings of this study are illustrated using real data from an intelligence test to provide guidelines for assessing the dimensionality of CDM data in applied settings.
Determining the Number of Attributes in Cognitive Diagnosis Modeling