Hi everyone,
I am completely stumped on something and am hoping some of you might have helpful suggestions, or might identify something I am missing. I have estimated a linear latent growth model that measures change in a measure administered at multiple time points. I am testing a mediational model in which the slope of the LGM represents the proposed mediator. The script for my model is as follows:
model1 <- "INT =~ 1*M0 + 1*M1 + 1*M2 + 1*M3 + 1*M4 + 1*M5
SLP =~ 0*M0 + 1*M1 + 2*M2 + 3*M3 + 4*M4 + 5*M5
INT~~SLP
INT ~ IV + cov1
SLP ~ IV
DV ~ INT + SLP + IV + cov1 + cov2 + cov3"
growthmodel1 <- growth(model1, data=dat, estimator="MLM")
summary(growthmodel1, standardized=T, rsquare=T, fit.measures=T)
This model has good fit, as shown in the output below, χ2(80) = 118.35, robust CFI = .987, robust RMSEA = .053, SRMR = .041
It was recently suggested to me that I estimate the covariances between all exogenous predictors (beyond those that already have specified regression relationships). However, when I include them in the model, fit substantially worsens and df decrease by only one, as shown below:
model2 <- "INT =~ 1*M0 + 1*M1 + 1*M2 + 1*M3 + 1*M4 + 1*M5
SLP =~ 0*M0 + 1*M1 + 2*M2 + 3*M3 + 4*M4 + 5*M5
INT~~SLP
INT ~ IV + cov1
SLP ~ IV
DV ~ INT + SLP + IV + cov1 + cov2 + cov3
INT~~cov2
INT~~cov3
SLP~~cov1
SLP~~cov2
SLP~~cov3
IV~~cov1
IV~~cov2
IV~~cov3
cov1~~cov2
cov1~~cov3
cov2~~cov3"
growthmodel2 <- growth(model2, data=dat, estimator="MLM")
summary(growthmodel2, standardized=T, rsquare=T, fit.measures=T) #NOTE default was automatically changed to fixed.x=FALSE
χ2(79) = 1090.31, robust CFI = .672, robust RMSEA = .270, SRMR = 18.47
In fact, it seems that including any exogenous covariances has a strange effect, as model fit worsened and df increased when I replaced one regression (INT ~ IV + cov1) with the relevant covariances:
model3 <- "INT =~ 1*M0 + 1*M1 + 1*M2 + 1*M3 + 1*M4 + 1*M5
SLP =~ 0*M0 + 1*M1 + 2*M2 + 3*M3 + 4*M4 + 5*M5
INT~~SLP
SLP ~ IV
DV ~ INT + SLP + IV + cov1 + cov2 + cov3
INT~~IV
INT~~cov1”
growthmodel3 <- growth(model3, data=dat, estimator="MLM")
summary(growthmodel3, standardized=T, rsquare=T, fit.measures=T) #NOTE default was automatically changed to fixed.x=FALSE
χ2(89) = 2273.19, robust CFI = .434, robust RMSEA = .334, SRMR = 17.38
Can anyone help me identify why this might be happening, and how I might fix it? Thanks in advance!