The Role of Test Dimensionality Violation in Equating Errors of IRT and Classical Theory Models

Identification of the consequences of violations of the assumptions of measurement models is a major concern in the field of psychometrics. The purpose of the present study was to investigating the role of test dimensionality violation in equating errors of IRT and classical theory models. Research method was experimental and a 3 × 3 factorial design was used. The study population consisted of all the Mathematical and Technical Sciences Entrance Examiners in 2017 and 2018. The sample group consisted of 5000 examiners who were selected by random sampling. Mathematic test (55 items) was used for equating that three different types of data structure including one-dimensional, two- dimensional and three-dimensional data was generated from it. Data was equated with three equating methods including equipercentile method, true score and observed score equating method. Equating standard errors, bias and root mean square error were used to evaluate the effects of independent variables. To determine the error statistics, the equating results in all three datasets and the three equating methods were repeated 20 times in different samples. Data analysis showed that violation of dimensionality increases equating standard error, bias of equating results and the root mean square error. The bias of equating results in classical methods is more than the IRT methods. The effect of dimensionality violation on equating errors was not different between the classical theory and IRT models.