Relationships Among Classical Test Theory and Item Response Theory Frameworks via Factor Analytic Models

There are well-defined theoretical differences between the classical test theory (CTT) and item response theory (IRT) frameworks. It is understood that in the CTT framework, person and item statistics are test- and sample-dependent. This is not the perception with IRT. For this reason, the IRT framework is considered to be theoretically superior to the CTT framework for the purpose of estimating person and item parameters. In previous simulation studies, IRT models were used both as generating and as fitting models. Hence, results favoring the IRT framework could be attributed to IRT being the data-generation framework. Moreover, previous studies only considered the traditional CTT framework for the comparison, yet there is considerable literature suggesting that it may be more appropriate to use CTT statistics based on an underlying normal variable (UNV) assumption. The current study relates the class of CTT-based models with the UNV assumption to that of IRT, using confirmatory factor analysis to delineate the connections. A small Monte Carlo study was carried out to assess the comparability between the item and person statistics obtained from the frameworks of IRT and CTT with UNV assumption. Results show the frameworks of IRT and CTT with UNV assumption to be quite comparable, with neither framework showing an advantage over the other.