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In change analyses (of any variable, from pre to post) we usually controll for the pre-score, as it may affect the rate of change. However, what if I am especially interested in the effect of the pre score on the rate of change, like

Diff(post - pre) = a + b*pre.

What if I am especially interested in b? Is the model above reasonable or are there any problems with that?

In multilevel-analysis of longitudinal data there is a correlation coefficient for the relation between the initial level (intercept) and the rate of change (slope). Thats the information I need, but in an ordinary regression model.

user405152
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  • Why not do a multilevel analysis? – Peter Flom Jan 17 '24 at 15:41
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    Take a look at latent difference scores, which is a SEM technique. In that framework, you can predict the latent difference/change from T0 to T1 by levels of T0. See https://doi.org./10.1177/0265407517718387 and https://stats.stackexchange.com/questions/595777/multilevel-model-with-two-timepoints – Erik Ruzek Jan 17 '24 at 16:46
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    As mentioned by @ErikRuzek, a latent difference score approach would be preferred because the observed difference (change) score variable typically contains a lot of measurement error variance (unreliability). This can lead to substantial bias in the estimated b coefficient. The latent change score approach corrects for error. See also: https://youtu.be/0QUuP2BoMlk – Christian Geiser Jan 17 '24 at 18:13
  • A problem is that the change score is necessarily correlated with the pre value. See this page and this page, for example. – EdM Jan 17 '24 at 18:49

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Here are some additional references for the latent change/latent difference score approach:

McArdle, J. J. (2009). Latent variable modeling of differences and changes with longitudinal data. Annual Review of Psychology, 60, 577-605.

Raykov, T. (1993). A structural equation model for measuring residualized change and discerning patterns of growth or decline. Applied Psychological Measurement, 17, 53-71.

Steyer, R., Eid, M., & Schwenkmezger, P. (1997). Modeling true intraindividual change: True change as a latent variable. Methods of Psychological Research - Online, 2, 21–33.

Steyer, R., Partchev, I., & Shanahan, M. (2000). Modeling true intra-individual change in structural equation models: The case of poverty and children's psychosocial adjustment. In T. D. Little, K. U. Schnabel & J. Baumert (Eds.), Modeling longitudinal and multiple-group data: Practical issues, applied approaches, and specific examples (pp. 109–126). Hillsdale, NJ: Erlbaum.

Christian Geiser
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