path analyses: invariance

[Pascale Stephanie Petri]

Dear lavaan group,

I feel a bit lost in literature as well as in this great group (or I might simply missed it; please don't mind double-posting then), so I hope it is okay to ask this question here, despite this group focuses on analyses with *latent* variables: I am currently doing path analyses (not SEM; so no latent variables are encompassed in my model) and I would like to test the model's invariance across different groups.

I know about the 'measurementInvariance' function (semTools) and at first, I thought I could use it anyway (although I do not have a 'real' SEM), just implicitly 'accepting' that the first two models (configural versus metric) then have the same degrees of freedom as there are no 'loadings' from manifest to latent variables (due to not having latent variables at all). However, I wonder if I can simply do invariance testing for a path model this way, assuming that the level of metric invariance (if confirmed with acceptable fit indices) can be seen as indicating that path coefficients are equal across groups?

So please note that I am aware that this is not real *measurement* invariance testing but invariance testing in terms of examining if the paths are equal (or at least comparable ) across groups.

I would appreciate to be pointed to literature or even better to comparable analyses etc. in order to find a solution to this problem.

Thank you very much in advance,

Pascale

[Jošt Bartol]

Hi,

have you maybe tried searching youtube or google scholar for the terms "multi group path analysis"? I think you can find a bunch of relevant sources and examples. As for a good reference, I would suggest Kline's 2015 Principles and practices of structural equation modeling. It covers path analysis too, although I think that it only skims multi group path analysis ... Still, it might be helpful.

Anyway, this is how I did multi group path analysis across gender groups in R with lavaan:

fit.gender.difference= sem(model, data, estimator = "MLM", group = "gender")
summary(fit.gender.difference , fit.measures = T, standardized = T)

fit.gender.equal= sem(mod, dt1, estimator = "MLM", group = "gender", group.equal = "regressions")
summary(fit.gender.equal , fit.measures = T, standardized = T)

anova(fit.gender.difference, fit.gender.equal)

You also have to decide if you want correlations between independent variables to be equal or if you want error terms of dependent variables to be equal between groups. In the current case, I left both to be freely estimated across groups.

I also add two articles as examples of such analysis.

Hope this helps!

Regards,

Jošt

V V čet., 23. sep. 2021 ob 23:04 je oseba Pascale Stephanie Petri <pascale...@gmail.com> napisala:

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[Pascale Stephanie Petri]

Dear Jošt,

thank you very much for this elaborate response! I will try it this way and have a look into the respective papers.

Have a great day (as you made mine ;-)

best

Pascale

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[car...@web.de]

Two notes:
(1) You are using MLM. Because the data are not normally distributed? If so, are you sure that anova handles the results correctly? I would guess that lavTestLRT(..., method=''satorra.bentler.2001') is the better choice.
(2) The test is only useful if the chi square test is not significant and that is known to be rarely the case.

Am 29.09.21, 08:32 schrieb "Jošt Bartol" <barto...@gmail.com>:

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[Jošt Bartol]

Hi Carnold!

1.) Yes, however, the lavTestLRT uses the mentioned correction automatically.

2.) That is true, but in the current case it was not significant. One could also compare the change in CFI, RMSEA and SRMR, as suggested by Chen (2007) (although I am not 100% certain if this can be directly applied to path analysis).

Thanks for the notes!

Chen, F. F. (2007). Sensitivity of goodness of fit indexes to lack of measurement invariance. Structural equation modeling: a multidisciplinary journal, 14(3), 464-504.

Regards,

Jošt

V V sre., 29. sep. 2021 ob 08:42 je oseba <car...@web.de> napisala:

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[Alejandro Hermida]

Hi,

I would rather compare the models using differences > 2 in AIC as the main selection criteria as per Burnham & Anderson (2004). This is useful for both nested and non-nested models. I attach a paper using this aproach in the RSA setting in which some regression coefficients are constrained to equality within individuals. 

Hope this helps.

Best,

Alejandro