Reply to Freedman

Abstract

In our paper we proposed a general methodology for analyzing longitudinal data from several cohorts. This methodology is general and flexible and can accommodate many different models for this kind of data. The main purpose of the proposed methodology is to find a model which takes the intrinsic structure of the data collection design into account (i.e., the fact that repeated measurement on the same individuals are used and that comparable cohorts are used) and at the same time fits a given set of data reasonably well. We illustrated the general methodology using a small data set. We pointed out that this was merely an illustration. Freedman criticizes our analysis of these data and rejects essentially all assumptions on which this analysis was based. We admit (as we did in a footnote to our paper) that the assumptions (3) and (7) of independently and identically distributed observations and of multivariate normality, probably do not hold for these data. This will affect the interpretation of x 2 (more on this later) but will not necessarily severely bias the parameter estimates. Other assumptions considered by Freedman may bias parameter estimates but most such assumptions are in fact testable within the framework of our methodology, quite the contrary to what Freedman states. Freedman remarks "Why should a child's intelligence be representable as a single number?" Of course, we don't believe that intelligence in a general context is a single latent trait. And, of course, our general methodology is not restricted to a single latent variable but allows for several latent variables at each occasion. We point out "In this paper we assume that a single latent variable is measured at each occasion. The , Both authors are affiliated with the