Mean- and Variance-Adjusted Difference Test Statistic

[Jon]

Hi,

So I know that Satorra (2000) and Satorra & Bentler (2001, 2010) provide mean-scaled difference test statistics, and that I can get those using anova() and specifying the appropriate method. I have a bunch of models fit with estimator="MLM" so I can use this for those models. However, I have a whole bunch of other models fit using estimator="MLMVS" and another bunch fit using estimator="MLMV" and I want to get the respective difference test statistics within those two groups as well. In Mplus I would use the DIFFTEST method (at least for MLMVS... I don't recall if DIFFTEST can handle Asparouhov & Muthen's non-Satterthwaite mean- and variance-adjusted method), but is there something analogous to this in lavaan? Looking through the lavTestLRT code, it looks like any fit object marked as "mean-variance-adjusted" points right to the mean-scaled methods, ignoring the variance adjustment.

Thanks,

Jon

[Yves Rosseel]

On 07/06/2015 06:37 PM, Jon wrote:
> So I know that Satorra (2000) and Satorra & Bentler (2001, 2010) provide
> mean-scaled difference test statistics, and that I can get those using
> anova() and specifying the appropriate method. I have a bunch of models
> fit with estimator="MLM" so I can use this for those models.

So far, so good.

> have a whole bunch of other models fit using estimator="MLMVS" and
> another bunch fit using estimator="MLMV" and I want to get the
> respective difference test statistics within those two groups as well.

> In Mplus I would use the DIFFTEST method (at least for MLMVS... I don't
> recall if DIFFTEST can handle Asparouhov & Muthen's non-Satterthwaite
> mean- and variance-adjusted method),

It does. And theoretically (AFAIK), the results should be identical.

> this in lavaan? Looking through the lavTestLRT code, it looks like any
> fit object marked as "mean-variance-adjusted" points right to the
> mean-scaled methods, ignoring the variance adjustment.

I do not think this is correct. Any model marked as
"mean-variance-adjusted" will trigger the Satorra (2000) method:

library(lavaan)
example(cfa)
fit <- cfa(HS.model, data=HolzingerSwineford1939, estimator="MLMVS")
fit0 <- cfa(HS.model, data=HolzingerSwineford1939, estimator="MLMVS",
orthogonal = TRUE)
anova(fit, fit0)

# Scaled Chi Square Difference Test (method = "satorra.2000")
#
# Df AIC BIC Chisq Chisq diff Df diff Pr(>Chisq)
# fit 24 7535.5 7646.7 85.305
# fit0 27 7597.7 7697.8 153.527 60.977 2.8404 2.76e-13 ***

Or am I missing something?

Yves.