LISREL summaries

[Guy Ashiri-Prossner]

Hello,

I am trying to follow a few examples of confirmatory FA presented in articles, but unfortunately the researchers just state "CFA was done using LISREL" and then provide the analyses summary (see below) with no further details. As my research field is statistics, this just isn't enough and I want to further investigate the methods used.

(Origin: Collins and Gleaves, 1998)

Is there any way of reproducing this table (or its results separately) using lavaan?

Thanks,

Guy

[Terrence Jorgensen]

Is there any way of reproducing this table (or its results separately) using lavaan?

These are tests of factorial invariance, and the authors hopefully cited some references you could read for more details on the fitted models.  Here is a good one:

Vandenberg, R. J., & Lance, C. E. (2000). A review and synthesis of the measurement invariance literature: Suggestions, practices, and recommendations for organizational research. Organizational Research Methods, 3(1), 4-70.

Collins and Gleaves fit some models that are rarely included in the sequence of tested models; namely, the top 2 rows.  But here are details about the models they fitted (find further details in the reference above).

1. a model estimating each element in each group's covariance matrix, constraining each estimates to equality across groups.
   
2. This is a configural invariance model, so an identically configured CFA model is freely estimated in each group, without equality constraints.
   
3. This is a metric/ weak nvariance model, which is the same CFA in 2 but with equality constraints on loadings.  You can specify equality constraints by using identical labels for loadings across groups, or with the argument group.equal = "loadings"
4. This model is like 3 but additionally imposes equality constraints on the factor (co)variances.  Again, you can use identical labels across groups, or specify the argument group.equal = c("loadings","latent.variances","latent.covariances")
5. This model is like 4 but additionally imposes equality constraints on the residual (co)variances.  Again, you can use identical labels across groups, or specify the argument group.equal = c("loadings","latent.variances","latent.covariances","residuals","residual.covariances")

This link shows details about multiple-group constraints:  http://lavaan.ugent.be/tutorial/groups.html

Terrence D. Jorgensen

Postdoctoral Researcher, Methods and Statistics

Research Institute for Child Development and Education, the University of Amsterdam

http://www.uva.nl/profile/t.d.jorgensen

[Guy Ashiri-Prossner]

Hi, thanks for replying.

Vandenberg states that omnibus tests of invariant observed variables’ covariance matrices is the basic step, but later on says only 26% of the observed papers have conducted them. I got this Collins and Gleaves paper as they are one of the papers who did conduct this kind of test. It's nice they note the chi-square statistic but I want to know which method has yielded it, in order to try and mimic it.

Generally speaking, my data has some 1800 observations with 45 variables. A previous research has found 10-factor model fitting the general data, now I want to add a gender variable and look for invariants in the factorial structure. I know 1800 over 45 isn't much (and lavaan::cfa doesn't even converge), but in order to replicate the methods used by Collins & Gleaves (or Byrne's 1988 SQD3 paper) I want to understand what's going on there - LISREL isn't open source so I need to find out in a different manner.

[Terrence Jorgensen]

I want to know which method has yielded it, in order to try and mimic it.

What is "it", what do you mean by "method"?  Are you asking how to specify their Model 1 in lavaan syntax?  Here is a toy example for specifying a saturated mean and covariance structure for 3 variables (easily scaled up by changing varnames), but with equality constraints across groups.

varnames <- paste0("x", 1:3)
covstruc <- outer(varnames, varnames, function(x, y) paste(x, "~~", y))
satMod <- covstruc[lower.tri(covstruc, diag = TRUE)] # cov structure
cat(satMod, sep = "\n")

When you fit the model to the data, you can constrain all observed-variable (co)variances to equality across groups using the argument

lavaan(satMod, data = ..., group.equal = c("residuals","residual.covariances"))

[Hugo Harada]

Vandenberg, R. J., & Lance, C. E. (2000). A review and synthesis of the measurement invariance literature: Suggestions, practices, and recommendations for organizational research. Organizational Research Methods, 3(1), 4-70. 

http://journals.sagepub.com/doi/abs/10.1177/109442810031002#articleCitationDownloadContainer

What a gem!!! Thank you for sharing!!

Hugo 

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[Guy Ashiri-Prossner]

A toy example is nice, but I try to understand what's behind.  Vandenberg defines it as " An omnibus test of the equality of covariance matrices across groups", there ought to be a named method behind this, a comparison method which yields a chi-square statistic - does it mean Box’s M-test? something else?

[Rönkkö, Mikko]

Hi,

The test is explained in the cited paper, but not as clearly as it could be. It is basically a multi group SEM, where you fit a saturated model where are variance and covariances are fee, but constrain these to be the same across groups.

The test is similar to Box’s M, but not equivalent because it is based on maximum likelihood estimates instead of calculated directly from the covariances.

Mikko

On 23 Sep 2018, at 15.38, Guy Ashiri-Prossner <guy.a...@gmail.com> wrote:

A toy example is nice, but I try to understand what's behind.  Vandenberg defines it as " An omnibus test of the equality of covariance matrices across groups", there ought to be a named method behind this, a comparison method which yields a chi-square statistic - does it mean Box’s M-test? something else?