Testing latent mean differences

[Marija Dzida]

Hi, I was wondering what steps are necessary to test latent mean differences between two groups?

I conducted multi-group measurement invariance with group.equal  (I have tested configural, metric and scalar invariance). When I set equality of intercepts in addition to loadings, the latent mean in the first group is 0, and in the second group is some value with its p-value. I wondered whether that standardized value in the other group represents the latent mean difference between two groups, or do I have to make some additional step to test latent mean difference explicitly?

Also if I use marker indicator approach for factor variance, is it necessary to use marker indicator for factor mean as well?

I have pasted the part of the output with intercepts for my latent variables in scalar model (strong invariance). 

> fit.panas.scal.raz<-cfa(model=panas,data=first, estimator= "MLR",missing= "fiml", group="raz_bin", group.equal=c("loadings","intercepts"))

Warning message:

In lav_data_full(data = data, group = group, cluster = cluster,  :

  lavaan WARNING: group variable ‘raz_bin’ contains missing values

 

> summary(fit.panas.scal.raz, fit.measures = TRUE, standardized = TRUE)

Group 1 [0]:

Intercepts:

                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all

  

    fpa               0.000                               0.000    0.000

    fna               0.000                               0.000    0.000

 

 Group 2 [1]:

Intercepts:

                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all

  

    fpa              -0.238    0.037   -6.471    0.000   -0.349   -0.349

    fna               0.026    0.030    0.855    0.393    0.053    0.053

[Terrence Jorgensen]

I was wondering what steps are necessary to test latent mean differences between two groups?

You need to establish at least partial scalar invariance across groups for the latent means to be comparable.

the latent mean in the first group is 0, and in the second group is some value with its p-value

And because the first group is fixed to 0, the second group's mean is by definition also the mean difference between groups.

 

I wondered whether that standardized value in the other group represents the latent mean difference between two groups, or do I have to make some additional step to test latent mean difference explicitly?

You are conflating 2 issues: test statistic and effect size.  The standardized group-2 mean is equivalent to Glass' delta (if Group 1 could be considered the "control" or reference group).

 

Also if I use marker indicator approach for factor variance, is it necessary to use marker indicator for factor mean as well?

No.

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

[Brian Peña Calero]

Hello Professor Terrence

I have some doubts, I would greatly appreciate your guidance:

1. i am intrigued as to why lavaan defaults to Glass's Delta instead of Cohen's D which is more common. is the assumption made that the variances between the groups could have wide difference? or because the variance in the first group is fixed at 1, this value could not be used?

2. In the example in this publication, it is noted that for glass's delta in fpa (-0.238) to be -0.349, his variance should have been 0.465. With this information in mind, could I calculate his Cohen's D value?
(-0.238 - 0) / sqrt((0.465 + 1)/2) = -0.278

In some cases I observe a wide difference between the standardized value (delta of glass) and that of Cohen's D (e.g., from 0.27 to 0.51, respectively), which completely changes the interpretation of the magnitude of their differences.

Thank you very much for your time

[Terrence Jorgensen]

why lavaan defaults to Glass's Delta instead of Cohen's D

lavaan doesn't provide either.  lavaan provides a standardized solution, in which the mean/intercept of each variable is expressed in units of that variable's SD (in that particular group or level, for multigroup or multilevel SEMs).  I only pointed out that in some situations, that parameter would be equivalent to Glass' delta.  You can calculate whatever standardized mean (difference) you are interested in.  It is not a lavaan issue.

[Brian Peña Calero]

Okay, I understand. That makes a lot of sense to me. Thank you very much for your clarification!