Modeling Life-Span Growth Curves of Cognition Using Longitudinal Data with Multiple Samples and Changing Scales of Measurement.

Classical research on cognitive abilities has provided information about the growth and decline of intellectual abilities over the lifespan (i.e. Cattell, 1941, 1998; Horn, 1988, 1998). Many recent analyses of this topic use some form of longitudinal mixed-effects, multi-level, latent curve models (Meredith & Tisak, 1990; McArdle, 1986, 1988; McArdle et al, 2002; McArdle & Nesselroade 2003). One of the basic measurement assumptions of all latent curve models is longitudinal measurement equivalence – i.e., the same unidimensional attribute is measured on the same persons using exactly the same scale of measurement at every occasion. Tests of these assumptions starts by measuring the same variables at each occasion and considering tests of factorial invariance (e.g., McArdle, 2007). However, the classical requirements of exactly equivalent scales of measurement is often impractical and not often achieved. These measurement issues have been raised in classic treatments of the analysis of change (e.g., Harris, 1961; Cattell, 1966; Wohwill, 1973), but have not fully been resolved (e.g., Burr & Nesselroade, 1991; Collins & Sayer, 2001). One creative solution to this problem of changing scales was illustrated in the work of Bayley (1956) in her analysis of data from the seminal Berkeley Growth Study. Individual growth curves of mental abilities from birth to age 26 were plotted for a selected set of males (Fig. 1a) and females (Fig. 1b). In the early stages of this data collection (circa 1929), Bayley (among many others) assumed any measurement occasion within each study should incorporate an “age-appropriate” intelligence test – i.e., a version of the Stanford-Binet (S-B) at ages 6 -17, then the Wechsler-Bellevue Intelligence Scale (W-B) at ages 16–26. While these tests measure specific intellectual abilities, they are not administered or scored in the same way and may measure different intellectual abilities at the same or different ages. However, Bayley was interested in using the statistical techniques applied to physical growth curves, so she created the individual growth curves represented in Figure 1 by adjusting the means and standard deviations of different mental ability tests at different ages into a common metric (based on z-scores formed at age 16). As Bayley suggested, “They are not in ‘absolute’ units, but they do give a general picture of growth relative to the status of this group at 16 years. These curves, too, are less regular than the height curves, but perhaps no less regular than the weight curves. One gets the impression both of differences in rates of maturing and of differences in inherent capacity.” (p. 66). She also noticed the striking gender differences in dispersion of the resulting curves. Figure 1 Growth curves of intellectual abilities from the Berkeley Growth Studies of Bayley (1956; Age 16 D scores). This classic study can be considered an early application of what is now termed linked or mapped measurement scaling of growth data. The practical scaling method used by Bayley permitted the analysis of fundamental features regarding growth curves of cognition, and appeared to put mental growth on the same scientific footing as physical growth. Nonetheless, not all researchers were convinced by the merits of this approach. In one important critique Wohlwill (1973, p.75) suggested, “Yet the pooling of data as conceptually diverse as Wechsler-Bellevue raw scores and Stanford-Binet mental age scores is surely suspect. For the reasons previously indicated growth functions based on the latter are altogether artifactual, so that pooling intelligence test scores from this scale together with other intelligence test scores can hardly be expected to yield useful information concerning the growth function” (p.75-76). These kinds of critiques highlight important technical concerns about the possible and most appropriate ways to examine these issues. In this paper we use concepts from Item Response Theory (IRT) to create measurement linkages for tests even though the same measurement device was not used on all occasions. We merge IRT with concepts from Latent Curve Modeling (LCM) for examining growth and change over age using data pooled from mmultiple longitudinal samples.