Two-step estimation of latent trait models

We consider two-step estimation of latent variable models, in which just the measurement model is estimated in the first step and the measurement parameters are then fixed at their estimated values in the second step where the structural model is estimated. We show how this approach can be implemented for latent trait models (item response theory models) where the latent variables are continuous and their measurement indicators are categorical variables. The properties of two-step estimators are examined using simulation studies and applied examples. They perform well, and have attractive practical and conceptual properties compared to the alternative one-step and three-step approaches. These results are in line with previous findings for other families of latent variable models. This provides strong evidence that two-step estimation is a flexible and useful general method of estimation for different types of latent variable models.