Charting change in behavior as a function of age and investigating longitudinal relations among constructs are primary goals of developmental research. Traditionally, researchers rely on a single measure (e.g., scale score) for a given construct for each person at each occasion of measurement, assuming that measure reflects the same construct at each occasion. With multiple indicators of a latent construct at each time of measurement, the researcher can evaluate whether factorial invariance holds. If factorial invariance constraints are satisfied, latent variable scores at each time of measurement are on the same metric and stronger conclusions are warranted. In this paper we discuss factorial invariance in longitudinal studies, contrasting analytic approaches and highlighting strengths of the multiple-indicator approach to modeling developmental processes. KeywordsLongitudinal designs; longitudinal models; growth curve models; factorial invariance Longitudinal design is a sine qua non for assessing change and factors that influence change, which are principal goals of developmental science. In longitudinal investigations, participants are assessed at two or more points in time, corresponding to different chronological ages. From these longitudinal assessments, mean levels of behavior, change in behavior, and individual differences in change can be estimated and modeled. Over three decades ago, Wohlwill (1970Wohlwill ( , 1973 formalized these aims as the study of the function relating behavior (B) to chronological age (A), or B = f (A), and the investigation of variables that influence this function. These dual aims are so entwined with the nature of developmental science that few would question the importance of longitudinal investigations, despite attendant problems or confounds.One of the more vexing problems in assessing development -and one that deserves greater attention -is the problem of measurement invariance. Researchers often use the same version of a scale for assessing a given construct at each time of measurement, so they can rest assured that the same construct is assessed, scale scores fall on the same metric, and thus change can be estimated unambiguously. But, just as often, researchers wonder whether to alter measuring instruments as participants get older, using developmentally appropriate measures so they can NIH-PA Author ManuscriptNIH-PA Author Manuscript NIH-PA Author Manuscript continue to assess "the same construct." If levels of performance of participants change so much that notable ceiling or floor effects occur at older age levels, measuring devices must change to enable proper estimation of behavioral change (Embretson, 2006(Embretson, , 2007May & Nicewander, 1998). More subtly, if the nature of the construct assessed by an instrument changes with age, an instrument might require alteration to ensure that the same underlying construct is still assessed (Widaman, 1991), although modeling such data requires dealing with changes in the scales, a topic for future investigation...

The ability to focus one’s attention underlies success in many everyday tasks, but voluntary attention cannot be sustained for extended periods of time. In the laboratory, sustained-attention failure is manifest as a decline in perceptual sensitivity with increasing time on task, known as the vigilance decrement. We investigated improvements in sustained attention with training (~5 hr/day for 3 months), which consisted of meditation practice that involved sustained selective attention on a chosen stimulus (e.g., the participant’s breath). Participants were randomly assigned either to receive training first (n = 30) or to serve as waiting-list controls and receive training second (n = 30). Training produced improvements in visual discrimination that were linked to increases in perceptual sensitivity and improved vigilance during sustained visual attention. Consistent with the resource model of vigilance, these results suggest that perceptual improvements can reduce the resource demand imposed by target discrimination and thus make it easier to sustain voluntary attention.

In this article we provide a review of recent advances in longitudinal models for multivariate change. We first claim the need for dynamic modeling approaches as a way to evaluate psychological theories. We then describe one such approach, latent change score (LCS) models, and illustrate their utility with a summary of research findings in various areas of psychological science. We then highlight the most prominent features of LCS models. We conclude the article with suggestions for future research on multivariate models of change that can enhance our understanding of psychological science.

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By modeling variables over time it is possible to investigate the Granger-causal cross-lagged associations between variables. By comparing the standardized cross-lagged coefficients, the relative strength of these associations can be evaluated in order to determine important driving forces in the dynamic system. The aim of this study was twofold: first, to illustrate the added value of a multilevel multivariate autoregressive modeling approach for investigating these associations over more traditional techniques; and second, to discuss how the coefficients of the multilevel autoregressive model should be standardized for comparing the strength of the cross-lagged associations. The hierarchical structure of multilevel multivariate autoregressive models complicates standardization, because subject-based statistics or group-based statistics can be used to standardize the coefficients, and each method may result in different conclusions. We argue that in order to make a meaningful comparison of the strength of the cross-lagged associations, the coefficients should be standardized within persons. We further illustrate the bivariate multilevel autoregressive model and the standardization of the coefficients, and we show that disregarding individual differences in dynamics can prove misleading, by means of an empirical example on experienced competence and exhaustion in persons diagnosed with burnout. (PsycINFO Database Record