Help with Latent Difference Score Model Syntax

[Matt Graham]

I'm trying to fit a latent difference score model (e.g. McArdle, 2009) to look at cross-lagged and auto-regressive effects on change with multiple indicators for two-wave dyadic data. I am looking at the relation of two factors - Utility Value (UV) with three measures and Perceptions of Instrumentality (PI) with four measures. Each was measured twice, once on a pre-test (time 0) and once on a post-test (time 1). I believe that they hypothesized model should look something like this:

If this is correct, then I believe the model syntax should be as follows:

ChngUVxPI <-

'

#Create UV Latent Variables - Fix latent variable to be equal across timepoints

#Utility Value (UV)

UV0 =~ l1*UV0_2 + l2*UV0_3 + l3*UV0_4

UV1 =~ l1*UV1_2 + l2*UV1_3 + l3*UV1_4

#Perceptions of Instrumentality (PI)

PI0 =~ l4*PI0_1 + l5*PI0_2 + l6*PI0_3 + l7*PI0_4

PI1 =~ l4*PI1_1 + l5*PI1_2 + l6*PI1_3 + l7*PI1_4

#constrain residuals to be the same across timepoints

#Utility Value

UV0_2 ~~ r1*UV0_2

UV1_2 ~~ r1*UV1_2

UV0_3 ~~ r2*UV0_3

UV1_3 ~~ r2*UV1_3

UV0_4 ~~ r3*UV0_4

UV1_4 ~~ r3*UV1_4

#Perceptions of Instrumentality (PI)

PI0_1 ~~ r4*PI0_1

PI1_1 ~~ r4*PI1_1

PI0_2 ~~ r5*PI0_2

PI1_2 ~~ r5*PI1_2

PI0_3 ~~ r6*PI0_3

PI1_3 ~~ r6*PI1_3

PI0_4 ~~ r7*PI0_4

PI1_4 ~~ r7*PI1_4

#create Latent Difference Score

#Utility Value

chg_UV =~ 1*UV1

chg_UV ~ b1*UV0

UV1 ~ 1*UV0

UV1 ~~ 0*UV1

UV0 ~~ 1*UV0

chg_UV ~~ r8*chg_UV

UV1 ~ 0*1

UV0 ~ 0*1

#Percpetions of Instrumentality (PI)

chg_PI =~ 1*PI1

chg_PI ~ b2*PI0

PI1 ~ 1*PI0

PI0 ~~ 1*PI0

PI1 ~~ 0*PI1

chg_PI ~~ r9*chg_PI

PI1 ~ 0*1

PI0 ~ 0*1

#cross-lagged parameters

chg_UV ~ g1*PI0

chg_PI ~ g2*UV0

#covariances

UV0 ~~ cov1*PI0

chg_UV ~~ cov2*chg_PI

#Mean Structure

chg_UV ~ a1*1

chg_PI ~ a2*1

'

ChngUVxPIFit <- sem(ChngUVxPI, data=JulieData, missing = "ml", se = "robust")

summary(ChngUVxPIFit, standardized=TRUE, fit.measures = TRUE)

inspect(ChngUVxPIFit, 'r2')

Does this syntax match the model? I am getting some unusual/surprising parameter estimates and I want to make sure that the issue is not in my code.

Thank you all for your help.

MCG

[Christy Starr]

Hi Matt,

I am about to embark in writing syntax for a Latent Difference Score Model (also using motivational beliefs). I know this was written 2 years ago, but just curious, did you find out if your syntax worked correctly?

Thanks!

Christy Starr

cst...@uci.edu

Postdoctoral Scholar at University of California, Irvine