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

[Marine Lemaire]

Dear all,

I came across this discussion because I am facing the same issue as Vibeke Nielsen. I am trying to interpret the intercept of a univariate latent change score to determine if there is a significant change between a pre-test and a post-test.

Due to an inconsistency between the observed change (mean change = mean post - mean pre = -0.05) and the intercept of the latent change score in the model (1.43, p<0.001), I am wondering how to interpret this latent change score considering that the baseline pre-test regresses on the latent variable. This change of 1.43 corresponds to the change when the pre-test equals 0, if I understand correctly, which is not theoretically interpretable. I find an intercept b0 = 1.43 when testing the following model in simple linear regression: change = b0 + b1*pretest, where b0 = 1.43, p<0.001. To understand my change for an average level of the baseline (pre-test), I need to center my pre-test variable (0 corresponding to the mean of my pre-test variable). The equation then becomes: change = b0 + b1*centered pre-test, where b0 = -0.05, p<0.001 (which aligns with my descriptive data). I applied this to my SEM model by centering my pre-test and post-test variables (centered relative to the pre-test), and the intercept of my latent change becomes -0.05, p<0.001.

However I have noticed that few recommend centering variables in SEM, advocating for the use of raw scores instead. However, doesn't this make the interpretation of the latent change score challenging?

Thank you for your insights.

Best regards,

Marine

PhD student in psychology

Univerité Paris Cité - LaPsyDE

[Terrence Jorgensen]

To understand my change for an average level of the baseline (pre-test), I need to center my pre-test variable (0 corresponding to the mean of my pre-test variable). The equation then becomes: change = b0 + b1*centered pre-test, where b0 = -0.05, p<0.001 (which aligns with my descriptive data). I applied this to my SEM model by centering my pre-test and post-test variables (centered relative to the pre-test), and the intercept of my latent change becomes -0.05, p<0.001.

I don’t see anything wrong with centering both the pre and posttest at the pretest mean. The interpretation makes sense. 

[Marine Lemaire]

Thank you very much for clarifying this !