ABSTRACT
What it is now known as item response modeling [for an overview see van der Linden
and Hambleton (1997)] originated as an effort to overcome the limitations of the factor
model when applied to test items. Test items are most often categorical in nature, whereas
the factor model was designed for continuous data. Unfortunately, over the years item
response modeling and factor modeling have developed rather independently from one
another. One of the recurring topics in R.P.McDonald’s career has been establishing
bridges between these two fields (McDonald, 1967, 1980, 1981, 1982a, 1982b, 1985a,
1985b, 1986, 1999, 2001; McDonald & Mok, 1995). Two approaches can be used to
relate the nonlinear models used in item response theory (IRT) to the linear model used in
factor analysis. One approach is to use harmonic analysis (e.g., McDonald, 1967, 1982a).
The second approach is to use link functions (e.g., McDonald, 1999; Moustaki & Knott,
