Let us ignore discussion of preliminary item-level factor analysis, which are described elsewhere, and jump right into the IRT analysis. Given the response from this large and heterogeneous calibration sample, the first step is to estimate the parameters for an appropriate IRT model. For example, if a personality trait is being measured with dichotomous items, the 2PL model could be estimated. Alternatively, a competing model, such the 1PL could be estimated and the fit compared to the 2PL. Given the item parameter estimates from some model, the next step is to explore the issue of item fit as described in chapter 9. Specifically, a researcher may compute one or more chi-square item-fit statistics and inspect graphs of the empirical versus estimated IRCs. Items that display poor fit to the estimated model parameters are the first candidates for elimination from the scale.