Developmental psychology is concerned with intrain-dividual change over time. Therefore longitudinal methods (Khoo, West, Wu, & Kwok, chap. 21, this volume), which involve assessments of the same group of people over time, are well suited to the goals of developmental psychology. Because developmental psychologists are particularly interested in pathways and trajectories, designs that are able to capture the progression of time and the course of a phenomenon are especially valuable. Longitudinal methods are most appropriate when the researcher is interested in the processes underlying a phenomenon, rather than merely the status of that phenomenon.

There are many advantages to longitudinal methods. First, longitudinal designs allow one to assess change, and the processes proceeding, cooc-curring with, or following change within an individual. Second, they allow an individual to be compared to other individuals over the same period of time, so that issues of interindividual consistency over time can be examined. Third, they allow for a mapping of normative age trends, as well as alternative patterns of development that may occur for different groups of children. Fourth, longitudinal methods provide the opportunity for researchers to pinpoint the time of onset of a behavior. Additionally, longitudinal methods are extremely useful when interventions are used because they allow the researcher to view change in trajectories as a result of the intervention.

Despite the valuable information longitudinal studies provide, there are many disadvantages to this method. Disadvantages include the length of time needed to collect and analyze the data, the costs associated with the amount of data collection and analysis, and incentives for continued participation. Moreover, subject attrition is a major problem in longitudinal studies because the same subjects are needed to participate year after year, and it is often difficult to locate participants and to motivate them to continue participation. In addition, longitudinal designs pose specific threats to study validity because of cohort effects (e.g., wherein the effect is a reflection of the time period and not the experimental manipulation) and repeated exposure effects (wherein the participant learns how to answer questions or respond to other assessments because he or she has been exposed to them year after year). Additionally, longitudinal studies sacrifice depth for breadth, and therefore the results may only be generalizable to populations similar to those studied.

Because longitudinal methods produce data points over a period of time, certain statistical analyses are optimalâ€”those that allow change to be observed over time. Structural equation modeling (SEM) is the term used to describe a category of multivariate statistical models used to estimate the relationship between observed variables and latent constructs, as well as relations among latent constructs. One type of SEM, latent growth curve modeling, is a particularly promising technique for the study of development (Duncan, Duncan, & Hops, 1996). Latent growth curve modeling (LGM)

includes observed variables that constitute the latent construct, estimates growth trajectories (patterns of change) across time, and can be used to assess the degree to which other variables (e.g., regulation) predict various trajectories for another variable (e.g., aggression). The latent slope and intercept on average define trajectories. Similar to LGM in its consideration of change as a function of time, the person-centered approach of individual growth modeling, such as Hierarchical Linear Modeling (HLM), represents individual change over time; this is done by determining the functional form (linear, cubic, quadratic) that best fits the data, in addition to the individual values of the trajectories. HLM can be used for assessing the rate of growth or change, the status of an individual at a given point in time, the rate of acceleration, and individual variation around the growth curve (Rau-denbush & Chan, 1993). Therefore, this statistical technique allows for comparison of individual trajectories.

LGM and HLM differ in several ways. The LGM approach is multivariate; that is, growth curves for two variables can be estimated at the same time, and intercept and slope for one variable can be used as a predictor or explanatory variable for the intercept and slope of another variable. The LGM approach also can cluster trajectories that are similar. LGM has two restrictions as compared to HLM. Time, or a time-related variable such as age, on which growth is defined, has the same value for each subject at each time point (HLM allows the actual time or age for each subject if the measurements are not taken on exactly the same day.) Second, in LGM time-varying covariates have the same regression coefficient across subjects, whereas HLM allows for coefficients to vary across subjects.

Another statistical procedure that is sensitive to change over time is Repeated Measures Analysis of Variance (ANOVA). This statistic can be used to assess time-specific change and is similar to individual growth curve modeling in that it determines the functional form (e.g., linear, quadratic, cubic) that best fits the data. Unlike LGM and HLM, Repeated Measures ANOVA does not estimate individual trajectories; rather, the variability between subjects is completely removed through blocking, and only overall trends are constructed.

We illustrate the use of a longitudinal design through the study of the construct of antisocial behavior. Many large longitudinal studies have focused on the development of antisocial behavior (Farrington, 1983; Loeber et al., 2002; Moffit, Caspi, Dickson, Silva, & Stanton, 1996). Longitudinal methods are well suited for this topic because they allow for the investigation of when delinquency starts, its longevity, and the link between juvenile and adult behaviors and provide timelines for the specific types of behaviors (Farrington, 1983). Because outcomes tend to differ as a function of the age of onset of the antisocial behaviors, longitudinal methods are especially important for understanding this aspect of social behavior.

One of the largest studies on aggression, the Pittsburgh Youth Study, is based on 1,517 inner-city boys. Assessment began when the boys were in elementary or middle school, and the investigators traced the development of antisocial behavior from childhood to adolescence (Loeber et al., 2002). Key findings included identification of types of delinquency pathways, long-term risk factors for delinquency, outcome differences by age of onset of antisocial behavior, and changes in alcohol and drug use as it relates to delinquencyâ€”as analyzed using growth curve modeling (Loeber et al., 2002). As is evident by this example, longitudinal designs are often the ideal method for studying developmental issues; however, these designs are not always feasible. For these reasons and others, cross-sectional designs are probably the most widely used design in developmental research (Lerner, 2002).

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