Classical and modern test theories provide a framework to evaluate the psychometric properties of an instrument, such as item analysis, test development, test-score equating, and differential function analysis. These theories rely on formulating a statistical model to specify the relationship among a set of test concepts while making certain assumptions about these concepts and their relationships. Consequently, it is essential to understand the conditions and assumptions that are necessary for an accurate estimation of the model and hence an adequate fit to the data before the application of a test theory and related models.

Today, as the focus in data analysis is moving from univariate to multivariate procedures, the statistical modeling of test data is becoming more complex involving item response theory, generalizability theory, or structural equation modeling. Fitting a complex psychometric model relies on the ability to accurately estimate the model parameters, which can be realized with the availability of enhanced computational technology and the emergence of advanced statistical estimation methods, such as the iteratively re-weighted least squares, the maximum likelihood estimation, the EM algorithm, and the Markov chain Monte Carlo simulation techniques.

This Research Topic seeks to create a forum for psychometricians and researchers to (1) discuss issues associated with fitting or estimation of an existing psychometric model so that a set of guidelines can be provided when it comes to the application of the test theory and models, and (2) propose new test models or estimation methods that offer advantages not realized with existing ones.

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