Logistic Regression and Item Response Theory: Estimation Item and Ability Parameters by Using Logistic Regression in IRT.

The purpose of this study was to investigate the utility of logistic regression procedures as a means of estimating item and ability parameters in unidimensional and multidimensional item response theory models for dichotomous and polytomous data instead of IRT models. Unlike the IRT models, single logistic regression model can be easily extended from unidimensional models to multidimensional models, from dichotomous response data to polytomous response data and the assumptions such as all slopes are the same and intercept is zero are unnecessary. Based on the findings of this study, the following preliminary conclusions can be drawn: Item and ability parameters in IRT can be estimated by using the logistic regression models instead of IRT model currently used. Item characteristic curve, probability of correct answer, and related concepts can be interpreted the same in the framework of the logistic regression as in the framework of the IRT. Correlation coefficients between item and ability parameter estimates obtained from the logistic regression models and item and ability parameter estimates obtained from the IRT models are almost perfect. That means item and ability parameters can be equivalently estimated by using logistic regression models instead of IRT models currently used. Item and ability parameter estimates of the Rasch model can be equivalently estimated by the logistic regression model, assuming all $\beta$s are 1. Item and ability parameter estimates of the Rasch model can be equivalently estimated by the logistic regression model with intercept only model. Item difficulty in IRT is equal to median effect level in the logistic regression model. Sample size effect in the logistic regression parameter estimates can be investigated the same as the IRT models. When sample size increases, invariance properties of the logistic regression models increase and goodness of fit statistics becomes consistent. Test length in the logistic regression parameter estimates can be investigated the same as the IRT models. When test length increases, invariance properties of the logistic regression models increase and goodness of fit statistics becomes consistent. The logistic regression models are more flexible than IRT models. They can be easily extended from the dichotomous data to polytomous data.