20231110 - interpretation of cross-lagged panel models

24-Repeated-Assessments.Rmd

@@ -241,14 +241,18 @@ Instead of difference scores, use autoregressive cross-lagged models, latent cha
 
 ##### Autoregressive Cross-Lagged Models {#clpm}
 
-Autoregressive cross-lagged models with random intercepts can be fit in [path analysis](#pathAnalysis-sem) or [SEM](#sem).\index{cross lagged!cross-lagged model}\index{path analysis}\index{structural equation modeling}
-An autoregressive cross-lagged model with random intercepts examines relative change in a variable, that is, change in individual differences in the variable, but not changes in level on the variable.\index{cross lagged!cross-lagged model}
+Autoregressive cross-lagged models (aka cross-lagged panel models) can be fit in [path analysis](#pathAnalysis-sem) or [SEM](#sem).\index{cross lagged!cross-lagged model}\index{path analysis}\index{structural equation modeling}
+Cross-lagged panel models examine relative change in a variable, that is, change in individual differences in the variable, but not changes in level on the variable.\index{cross lagged!cross-lagged model}
 Such a model allows examining whether one variable predicts *relative* change in another variable.\index{cross lagged!cross-lagged model}
-For example, I conducted a collaborative study that examined whether language ability predicts later behavior problems controlling for prior levels of behavior problems—that is, whether language ability predicts a person's change in behavior problems relative to the change among other people in the sample [@Petersen2013a; @PetersenLeBeau2021].\index{cross lagged!cross-lagged model}
+The cross-lagged panel model tests whether individuals with low levels of X *relative to others* experience subsequent *rank-order increases* in Y [@Orth2021; @Evans2023].\index{cross lagged!cross-lagged model}
+By contrast, the random-intercepts cross-lagged panel model tests whether, when individuals experience *lower-than-their-own usual levels* of X, they experience subsequent increases in Y *relative to their usual level* [@Orth2021; @Evans2023].\index{cross lagged!cross-lagged model}
+As an example of a cross-lagged panel model, I conducted a collaborative study that examined whether language ability predicts later behavior problems controlling for prior levels of behavior problems—that is, whether language ability predicts a person's change in behavior problems relative to the change among other people in the sample [@Petersen2013a; @PetersenLeBeau2021].\index{cross lagged!cross-lagged model}
+Cross-lagged panel models predict relative (rank-order) change, not absolute change in level.\index{cross lagged!cross-lagged model}
+For tests of absolute change, models such as [change score models](#lcsm) or [growth curve models](#gcm) are necessary.\index{cross lagged!cross-lagged model}\index{latent change score model}\index{growth curve model}
 
 ##### Latent Change Score Models {#lcsm}
 
-Latent change score models can be fit in [SEM](#sem).
+Latent change score models can be fit in [SEM](#sem).\index{latent change score model}
 Unlike autoregressive cross-lagged models, latent change score models examine *absolute* change—that is, people's changes in level.\index{latent change score model}\index{structural equation modeling}
 With latent change score models, you can examine change in latent variables that reflect the common variance among multiple measures.\index{latent change score model}
 Latent variables are theoretically error-free (at least of [random error](#randomError)), so latent change scores can be perfectly [reliable](#reliability), unlike traditional difference scores, whose [reliability](#reliability) is strongly influenced by the [measurement unreliability](#reliability) of the specific measures that compose them.\index{latent change score model}\index{latent variable}\index{measurement error}\index{measurement error!random error}