Latent growth curve modeling with a cohort sequential design

Abstract

The measurement change over time permeates much of social work research. Within this rubric are investigations on the effectiveness of interventions, research on the emotional sequelae of disorders, and explorations of the pathways that lead to risk, resilience, prevention, and amelioration. In all these areas a common focus is change on some attribute that is functionally related to time. Moreover, many areas of social work are concerned with change as a process. This process view requires than an index of the amount of change between arbitrary time points because underlying dynamic pathways often are proposed to generate chronometric change (Burchinal & Appelbaum, 1991). The shifting dynamics of these pathways suggest the need for longitudinal studies that can capture both inter- and intraindividual change as well as the predictors of this change. This research note addreses the study of change over time by the use of a cohort sequential design (CSD), and data analysis using latent growth curve modeling (LGM). The Cohort Sequential Design In the CSD researchers conduct several short-term longitudinal studies to simulate a much longer longitudinal study (Duncan, Duncan, & Hops, 1996; Nesselroade & Baltes, 1979). Participants of varying ages are sampled at a single time point and then followed for several years. The age of the participants defines a cohort, and the overlapping measurements of these cohorts are linked together to determine a common growth curve or developmental trend. Figure 1 is a pictorial representation of the combination of the CSD with a latent growth curve model. The figure depicts the generation of a five-year growth trajectory (grades 6 through 10) from three years of data (wave 1 = sixth, seventh, eighth; wave 2 = seventh, eighth, ninth; wave 3 = eighth, ninth, 10th). [Figure 1 ILLUSTRATION OMITTED] There are several advantages to the CSD. First, the follow-up period for data collection is shorter (for example, three years versus five years), thus reducing expenses and attrition. Second, unlike panel data that confound age effects (those related to maturation) and period effects (those due to historical events), observations between same-age participants at time 1, time 2, and time 3 can be contrasted. (Note: The example shown in Figure 1 displays seventh graders at waves 1 and 2; eighth graders at waves 1, 2, and 3; and ninth graders at waves 2 and 3.) Comparison of seventh, eighth, and ninth graders at two and three different points in time is not possible in a standard longitudinal design that follows only one age group. There are disadvantages to the CSD. One disadvantage is that age-cohort interaction effects may be confounded, and important information about intervening variables that influence the course of development or change may be lost (Raudenbush & Chan, 1992). Therefore, it is important to consider the type of change process being investigated and whether the CSD, notwithstanding its limitations, adequately addresses the research questions and the behavior of interest (Duncan et al., 1996). Also, as noted by Raudenbush and Chan accelerated longitudinal designs such as the CSD are most credible when adjacent cohorts share more rather than fewer points of overlap' (p. 391). Latent Growth Curve Modeling Latent growth curve modeling (LGM) resembles classic confirmatory factor analysis. LGM uses repeated measures raw-score data as indicators of the latent factors that are interpreted as chronometric common factors representing individual differences over time (McArdle, 1988). LGM combines elements of MANOVA and structural equation modeling (SEM) to capture aspects of longitudinal change. Unlike MANOVA, LGM takes into account variance in the latent variable (Duncan et al., 1996; Meredith & Tisak, 1990) and differs from traditional SEM in that it computes a mean for the latent variable (Willett & Sayer, 1994). …