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Abstract
Most novel analytic methods for longitudinal data are applicable to studies spanning three time-points of data at a minimum, whereas methods for two-occasion data have garnered comparatively little attention. Here, we address this limitation by introducing the two-wave latent change score (2W-LCS) model, a technique appropriate for preliminary detection of relations among dynamic processes with two-occasion data. The 2W-LCS model is well suited for the investigation of hypotheses in which changes in a construct are posited as predictors of changes in another construct. In an empirical illustration using data of elderly Hispanics from the Health and Retirement Study, we demonstrate how the 2W-LCS model provides the best match to theories rooted in changes, and highlight the advantages of this approach over other modeling alternatives (i.e., Little, Preacher, Selig, & Card, 2007; Selig & Preacher, 2009).
ACKNOWLEDGMENTS
We thank Dr. Daniel Bauer and Dr. Kevin Grimm for their helpful suggestions on previous versions of this article.
Notes
1 Some researchers have advocated for a departure from colloquial uses of the terms difference and change, where difference is used for interindividual phenomena and change is used to describe intraindividual patterns (see McArdle, Citation2009). This recommendation serves to clarify an important distinction. We make a concerted effort to follow these guidelines; however, to draw connections to previous literature we sometimes use the term difference when we are really referring to change.
2 As an illustration, consider three individuals with the following Time 1/Time 2 scores in a T-score metric (M = 50, SD = 10): 49/51, 48/50, 56/57. After computing the difference scores, we are now left with the following scores: 2, 2, 1. With raw scores, the standard deviation is 4.36 for Time 1 scores and 3.79 for Time 2 scores. The standard deviation of the difference scores is 0.58.
3 Lord (Citation1956, p. 435) made a compelling argument that although gains and differences tend to be larger for students who performed poorly on an assessment at Time 1, it could be the case that “a gain from an initial true score of 65 to a final true score of 70 may … be in every importance sense ‘greater’ than the numerically larger gain from 45 to 55[.] The former gain … may present more hours of study or more effort on the part of the teacher or perhaps a more insight than the latter, numerically larger, gain.” Another example incorporates clinical cutoffs. A change from 52 to 57 might still be within “average” depression, but a change from 66 to 71 could represent a clinically important transition from healthy to mentally ill.
4 The exception we make to recommendations set forth by Liker and colleagues (Citation1985) is to include fixed regression paths as a means of deriving the latent change score factor (i.e., an autoregression fixed at 1 from the latent variable at Time 1 to Time 2; a regression path fixed at 1 from the latent change score to the latent variable at Time 2). These “perfect” regressions are fundamentally different from those Liker and colleagues (Citation1985) cautioned against, as their purpose is to explicitly model change rather than make a causal prediction.
5 For cognitive health, the total mental status item had unequal intercepts across time. Results from these tests can be retrieved by contacting the first author.
6 This is in contrast to the univariate model of depression for which the mean of the latent change factor was nonsignificant. This discrepancy is likely due to the larger amount of missing data when the univariate model was fit.