# Goodness of Fit indices & intervals.type="z" vs. "LB"

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Joined: 11/27/2016 - 22:30
Goodness of Fit indices & intervals.type="z" vs. "LB"

Hi Mike;

I have three questions regarding TSSEM for testing a fully mediated structural model. I will appreciate your advice.

(1) A problem I am facing now is that all goodness of fit indices are showing an acceptable fit for my model in tssem2() except SRMR, which is 0.109. I know that in your 2009 paper published in Structural Equation Modeling you have discussed that some of the goodness of fit indices such as CFI might be slightly inflated in tssem due to the two stages as well as the wls estimation method. Is this logic generalizable to SRMR as well? or is there any other reason for a higher SRMR estimate as compared to other goodness of fit indices?

(2) Do you have any suggestion for generating additional goodness of fit indices, besides the ones generated by tssem2(), such as GFI, AGFI, and IFI?

(3) When I test my fully mediated model using (diag.constraints=FALSE, intervals.type="z") the results make sense and they are very stable. However, changing it to (diag.constraints=TRUE, intervals.type="LB") results in OpenMx status1: 4 (and 6 after rerun()) and it generates many NA for lbound and ubound values. I was wondering whether it is safe to report the results based on (diag.constraints=FALSE, intervals.type="z"), given their stability and interpretability.

Hamed

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Joined: 10/08/2009 - 22:37
Hi Hamed,

Hi Hamed,

(1) I don't have an answer. Since WLS is used in the stage 2 analysis, you may start with Yuan and Chan (2005), who show some discrepancies in the fit indices with different estimation methods.
(2) I don't think that these indices are recommended nowadays. If you want to calculate them, what you need are the observed and model-implied correlation matrices. Please see the attached R code to get the observed and model-implied correlation matrices.
(3) It is usually easier to get the Wald CI to the LBCI. However, I always wonder how accurate the Wald CI is when the LBCI does not work. A good topic for future simulations?

Best,
Mike

Yuan, K.-H., & Chan, W. (2005). On nonequivalence of several procedures of structural equation modeling. Psychometrika, 70(4), 791–798. https://doi.org/10.1007/s11336-001-0930-9

model <- "## Factor loadings
Alpha=~A+C+ES
Beta=~E+I
## Factor correlation
Alpha~~Beta"

RAM <- lavaan2RAM(model, obs.variables=c("A","C","ES","E","I"),
A.notation="on", S.notation="with")

#### Random-effects TSSEM with random effects on the diagonals
random1 <- tssem1(Digman97$data, Digman97$n, method="REM",
RE.type="Diag")

random2 <- tssem2(random1, Amatrix=RAM$A, Smatrix=RAM$S, Fmatrix=RAM$F) summary(random2) ## Model implied correlation matrix mxEval(impliedS, random2$mx.fit)

## Sample correlation matrix
mxEval(sampleS, random2\$mx.fit)
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Joined: 11/27/2016 - 22:30
Thank you, Mike! The R code

Thank you, Mike! The R code and the reference were very helpful.

Regarding Wald CI vs LBCI, a simulation study seems in order. It is interesting that sometimes while LBCI is not generated properly (many NA in the lbounds and ubounds of estimates), Wald CI seem very stable and make theoretical sense. It has happened to me in more than one case.

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Joined: 10/08/2009 - 22:37
BTW, have you tried to rerun

BTW, have you tried to rerun the models with LBCI? It usually helps.

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Joined: 11/27/2016 - 22:30
Yes, I have. I did it twice

Yes, I have. I did it twice (rerun and rerun of rerun). It does help; some of the NAs are estimated but not all. Therefore, some relations still remains unknown.