A1195
Title: Goodness of fit assessment of item response theory models for binary data
Authors: Federico Bacchi - University of Bologna (Italy) [presenting]
Maria Rosaria Ferrante - University of Bologna (Italy)
Pinuccia Pasqualina Calia - University of Bologna (Italy)
Abstract: The goodness of fit assessment of item response theory (IRT) models can be performed based on three main underpinnings: (i) relying on a dichotomous decision strategy using chi-square tests; (ii) relying on indices that quantify the degree of fit along a continuum; and (iii) analyzing the eigenvalues of the manifest variables' polychoric correlation matrix. Despite a large stream of literature, there is currently no consensus on how to unequivocally establish whether an estimated model is sufficiently good for the data. A simulation study on large binary data sets with a common underlying generating process (major factor domain) was performed to address this gap. Three degrees of misspecifications were explored through a minor factor domain consisting of 50 orthogonal common factors accounting for three different fixed proportions of variance (0\%, 10\%, 30\%). Furthermore, two different sample sizes and three different levels of correlation among the major factors were considered. The results suggested that chi-square tests are well-calibrated only in the medium correlation specification with no variance accounted for by minor factors, while the fit indices strongly depend on the covariance structure of the major factor domain. The rules of thumb based on the eigenvalues tend to converge as the sample size increases. However, parallel analysis seemed to be more effective than counting eigenvalues greater than one for detecting the number of major factors.
