Interpreting intercepts in a bivariate latent change score model

[Vibeke Nielsen]

I have a question about interpreting the direction/sign of intercepts of the change score factors. Below you can see the bivariate latent change score model I have analyzed (Imodel-fit was good). PB stands for prosocial behaviour, mPFC_CT stands for the cortical thickness of the medial prefrontal cortex, and T1 and T2 stand for the first and second measurement.

 

BLCS_PB_mPFC_CT<-'

T2_PB ~ 1*T1_PB     # This parameter regresses T2_PB perfectly on T1_PB
dPB1 =~ 1*T2_PB     # This defines the latent change score factor as measured perfectly by scores on T2_PB
dPB1 ~ 1             # This estimates the intercept (conditional mean)  of the change score
T1_PB ~  1           # This estimates the intercept (mean)  of T1_PB
T2_PB ~ 0*1          # This constrains the intercept of T2_PB to 0

T2_mPFC_CT ~ 1*T1_mPFC_CT     # This parameter regresses T2_mPFC_CT perfectly on T1_mPFC_CT
dmPFC_CT1 =~ 1*T2_mPFC_CT     # This defines the latent change score factor as measured perfectly by scores on T2_mPFC_CT
T2_mPFC_CT ~ 0*1          # This line constrains the intercept of T2_mPFC_CT to 0
T2_mPFC_CT ~~ 0*T2_mPFC_CT    # This fixes the variance of the T1_mPFC_CT to 0 

dPB1 ~~  dPB1       # This estimates the variance of the change scores
T1_PB ~~   T1_PB    # This estimates the variance of the T1_PB
T2_PB ~~ 0*T2_PB    # This fixes the variance of the T2_PB to 0 

dmPFC_CT1 ~ 1             # This estimates the intercept (conditional mean)  of the change score
T1_mPFC_CT ~ 1            # This estimates the intercept (mean)  of T1_mPFC_CT
dmPFC_CT1 ~~ dmPFC_CT1        # This estimates the variance of the change scores
T1_mPFC_CT ~~ T1_mPFC_CT      # This estimates the variance of T1_mPFC_CT

dmPFC_CT1~T1_PB+T1_mPFC_CT   # This estimates the PB to mPFC_CT coupling parameter and the PB to PB self-feedback
dPB1~T1_mPFC_CT+T1_PB   # This estimates the mPFC_CT to PB coupling parameter and the mPFC_CT to mPFC_CT self-feedback

T1_PB ~~  T1_mPFC_CT     # This estimates the T1_PB T1_mPFC_CT covariance
dPB1~~dmPFC_CT1          # This estimates the dPB and dmPFC_CT covariance
'

In my output all the intercepts are positive values. However, when calculating change in coritical thickness manually, I noticed that there is a decrease in change in cortical thickness. I do not understand why, according to the lavaan output, the intercept of the change in cortical thickness is positive when the change is actually negative. Notably, the within-domain coupling/self-feedback of cortical thickness (dmPFC_CT1 ~ T1_mPFC_CT) is significant and has a negative value. In addition, I read something about 'Note that if a regression parameter is included, the mean change should be interpreted conditional on the regression path' (kievit et al., 2018). I do not really understand what this 'interpreted conditional on the regression' means, but I guess this is somehow related to my question. 

[Terrence Jorgensen]

I have a question about interpreting the direction/sign of intercepts of the change score factors.

This is a forum for questions about the lavaan software.  You can post general SEM questions on SEMNET:

https://listserv.ua.edu/cgi-bin/wa?SUBED1=semnet&A=1

Terrence D. Jorgensen

Assistant Professor, Methods and Statistics

Research Institute for Child Development and Education, the University of Amsterdam

http://www.uva.nl/profile/t.d.jorgensen

 

[Mauricio Garnier-Villarreal]

Vibeke

The latent change point will be equivalent to the estimated mean difference that you are comparing when there are no regressions on it. That is the estimated change score.

One you included regressions on it (dPB1~T1_mPFC_CT+T1_PB), the change is the conditional mean as in regression. So, the interpretation of the intercept would be: the expected mean when all predictors are equal to 0