Understanding correlates of change by modeling individual differences in growth

Abstract

longitudinal analysis, measurement of change,

Evaluating Value-Added Models for Teacher Accountability

“…the choice of an appropriate analysis method is highly sensitive to assumptions about the nature of individual growth." Because both approaches can perform poorly for some models of growth, Weisberg (1976 and1977) and others (see Rogosa and Willett, 1982) suggest modeling growth rather than using these two more common approaches. We do not advocate one method over the other as a means of estimating teacher effects, but rather list the relative advantages and disadvantages of each method later in this section.…”

“…It has an additional intuitive appeal because it can be interpreted as all students starting at the same initial level of achievement. However, the estimates will be sensitive to the year chosen as the starting value (see Bryk and Weisberg [1977] and Rogosa and Willett [1982]). In addition, the regression function E( y t y t −1 ) can be thought of as predicting the student's achievement with the average teacher (see Chapter Two), as opposed to his or her actual teacher, even if test scores from successive years are not on a single developmental scale.…”

“…In addition, the regression function E( y t y t −1 ) can be thought of as predicting the student's achievement with the average teacher (see Chapter Two), as opposed to his or her actual teacher, even if test scores from successive years are not on a single developmental scale. One of the greatest strengths of the covariate adjustment approach is its ability to be extended naturally, via higher-order polynomial terms, to models where scores from successive years are nonlinearly related (although, as noted in Rogosa and Willett [1982], the form of the nonlinear models will be sensitive to the year of testing).…”

On the power of multivariate latent growth curve models to detect correlated change.

“…When developmental change can be characterized as progressive or cumulative (e.g., cognitive development from childhood to early maturity or cognitive aging in older adults), latent growth curve models (LGCMs) provide an attractive means of assessing both average developmental function and individual differences in rates of developmental change (Bryk & Raudenbush, 1987;Duncan, Duncan, Strycker, Li, & Alpert, 1999;Laird & Ware, 1982;McArdle & Epstein, 1987;Raykov, 1993;Rogosa & Willett, 1985).…”

Multivariate Modeling of Age and Retest in Longitudinal Studies of Cognitive Abilities.

“…This approach seems more appropriate to make inferences about correlations between variables, especially when examining whether the correlations depend on the within-or between-person variation. Moreover, a multivariate approach is more powerful than the univariate analyses to examine the age and retest effects for the various cognitive abilities, particularly when they are correlated and have different patterns of missing data (e.g., see Raudenbush & Bryk, 2002;Snijders & Bosker, 1999).Examining relations among the growth of two or more variables is possible with multivariate models of change (Goldstein, 1995; MacCalum, Kim, Malarkey, & KielcoltGlasser, 1997;McArdle, 1988;Rogosa & Willett, 1985;Tisak & Meredith, 1990;Willett & Sayer, 1994, 1995. In fact, since the appearance of these models, researchers have been interested in understanding correlates of change between the growth of variables.…”