ABSTRACT
From one point of view, as we have seen, item response theory is an extension of factor analysis for binary items. The first phase of work on an item response model—fitting the model, estimating the item parameters, and assessing goodness of fit—parallels the concerns of factor analysis. In this phase, (a) we determine whether or not the data are unidimensional/homogeneous, and if not, how many latent traits are needed (see Chap. 14), and (b) we assess the items as relatively good or bad indicators of the factor attribute/latent trait they measure in common. Most applications of the common factor model have been multidimensional, that is, with multiple common factors, and the work is commonly considered to be finished when the factor structure is confirmed or discovered. Usually, the factor analysis of test- or Likert-item scores is followed up by grouping the variables into independent clusters—homogeneous subtests—and taking raw sum scores from these as simple measures of the factors. We seldom choose to obtain a better estimate of the factor score, partly because the simple sum is in practice nearly optimal anyway.
