ABSTRACT
The purpose of this study was to explore and compare several different methods for estimating unknown turning points in longitudinal data, employing the Bradway-McArdle longitudinal life-span data for crystallized (Gc) and fluid (Gf) intelligence scores (Cattell, 1998). Life-span studies are often designed to investigate age changes in characteristics (e.g., Nesselroade & Baltes, 1979). The focal data for life-span studies can be described as nested, repeatedly measured, multilevel, or longitudinal. Initial analyses may characterize the relationship among the occasions by the average change trajectory. At a second stage of analysis, the differences between the average group curve and the individual curves can be characterized in many different ways. A typical way to analyze both intraindividual change and variability and interindividual differences is to use mixed-effects models (Davidian & Giltinan, 1995; Diggle, Liang, & Zeger, 1994; McArdle, Ferrer-Caja, Hamagami, & Woodcock, 2002; Verbeke & Molenberghs, 2000). However, it is not always reasonable to use a single and simple dynamic function to capture the entire process. For example, in the processes of cognitive aging over the life span, some researchers suggest that cognitive development has several different stages (i.e., an infant development stage, a child development stage, an adolescent development stage, an adult development stage, an older adult decline stage, and a final decline toward death phase). If we take these substantive issues seriously, we need to investigate the age-based change points at which one trajectory stops and the next begins.
