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| From | John Antonakis <John.Antonakis@unil.ch> |
| To | statalist@hsphsun2.harvard.edu |
| Subject | Re: st: Goodness-of-fit tests after -gsem- |
| Date | Sun, 14 Jul 2013 11:47:41 +0200 |
Hi Jenny: The following may be interesting to you:Rhemtulla, M., Brosseau-Liard, P. É., & Savalei, V. 2012. When can categorical variables be treated as continuous? A comparison of robust continuous and categorical SEM estimation methods under suboptimal conditions. Psychological Methods, 17(3): 354-373.
If your substantive results are similar I guess you could treat the variables as continuous, particularly if you have a nonsignificant chi-square test. Though, at this time, I would always double check my results with Mplus, which has a robust overid test.
That will be so cool when Stata adds the overid statistic for -gsem- and also for models estimated with vce(robust).
Best, J. __________________________________________ John Antonakis Professor of Organizational Behavior Director, Ph.D. Program in Management Faculty of Business and Economics University of Lausanne Internef #618 CH-1015 Lausanne-Dorigny Switzerland Tel ++41 (0)21 692-3438 Fax ++41 (0)21 692-3305 http://www.hec.unil.ch/people/jantonakis Associate Editor The Leadership Quarterly __________________________________________ On 13.07.2013 22:30, Bloomberg Jenny wrote:
Hi John, That is very informative and helpful indeed. Thank you so much. I liked the Karl Joreskög anecdote. I've always had an impression that a chi-square test of sem is actually of little practical use because it always gives significant results when the sample size is rather large. So I used to ignore chi-squares and rather look at other goodness-of-fit indexes when using sem. I will also look into your articles. In the meanwhile, could I ask you two more related questions?: (1) For now, chi-square statistics is not available with non-linear gsem. Then, to what extent do you think it makes sense to refer to the result of chi-square statistics of corresponding linear sem, that is to assume all the relevant variables are continuous (belonging to Gaussian family with Identity link) when they are actually not? Of course it depends on how the actual (g)sem model would look like, but let's now think of a very simple case, say, a measurement model with three binary outcomes x1-x3 and a latent variable L which measures x1-x3. If you use -gsem- and correctly specify -x1 x2 x3<-L, logit-, then you won't be able to obtain a chi-square statistics. However, if you "relax" the non-linearity and let x1-x3 pretend to be continuous variables, then you can obtain a chi-square statistics by using -sem-. My question is that what kind of implications on the actual non-linear (binary) model, if any, could we draw from thus obtained chi-square. (2) Suppose we submit to a journal a paper in which stata's gsem was developed. Then how do you think could/should the referee judge the paper, that is, judge if the model makes sense etc, without a chi-square test (or any other indexes)? (yes, I'm assuming that the Yuan-Bentler style chi-square test you mentioned is yet to be implemented at that time.) I guess researchers won't feel like using stata's gsem before this point is resolved. Best, Jenny 2013/7/13 John Antonakis <John.Antonakis@unil.ch>:Hi Jenny: At this time, and based on my asking the Tech. support people at Stata, the overidentification test (and here I mean the likelihood ratio test, or chi-square test) is not available for -gsem-, which is unfortunate, but understandable. This is only version 2 of -sem- and the program is really very advanced as compared to other programs when they were on version 2 (AMOS will is on version a zillion still can't do gsem, for example). From what tech. support told me, it is on the wishlist and hopefully we will have a Yuan-Bentler style chi-square test for models estimated by gsem, like Mplus does. As for assessing fit, you only need the chi-square test--indexes like RMSEA or CFI don't help at all. I elaborate below on an edited version of what I had written recently on SEMNET on this point (in particular see the anecdote about Karl Joreskog, who as you may know, was instrumental in developing SEM, about why approximate fit indexes were invented): "At the end of the day, science is self-correcting and with time, most researchers will gravitate towards some sort of consensus. I think that what will prevail are methods that are analytically derived (e.g., chi-square test and corrections to it for when it is not well behaved) and found to have support too via Monte Carlo. With respect to the latter, what is funny--well ironic and hypocritical too--is that measures of approximate fit are not analytically derived and the only support that they have is via what I would characterize as weak Monte Carlo's--which in turn are often summary dismissed---by the very people who use ignore the chi-square test--when the Monte Carlos provide evidence for the chi-square test. We have the following issues that need to be correctly dealt with to ensure the model passes the chi-square test (and also that inference is correct--i.e., with respect to standard errors): 1. low sample size to parameters estimated ratio (need to correct the chi-square) 2. non-multivariate normal data (need to correct the chi-square) 3. non-continuous measures (need to use appropriate estimator) 4. causal heterogeneity (need to control for sources of variance that render relations heterogenous)* 5. bad measures 6. incorrectly specified model (i.e., the causal structure reflects reality and all threats to endogeneity are dealt with). Any of these or a combination of these can make the chi-square test fail. Now, some researchers shrug, in a defeatist kind of way and say, "well I don't know why my model failed the chi-square test, but I will interpret it in any case because the approximate fit indexes [like RMSEA or CFI] say it is OK." Unfortunately, the researcher will not know to what extent these estimates may be misleading or completely wrong. And, reporting misleading estimates is, I think unethical and uneconomical for society. That is why all efforts should be made to develop measures and find models that fit. At this time the best test we have is the chi-square test; we can also localize misfit via score tests or modification indexes. I will rejoice the day we find better and stronger tests; however, inventing weaker tests is not going to help us. Again, here is a snippet from Cam McIntosh's (2012) recent paper on this point: "A telling anecdote in this regard comes from Dag Sorböm, a long-time collaborator of Karl Joreskög, one of the key pioneers of SEM and creator of the LISREL software package. In recounting a LISREL workshop that he jointly gave with Joreskög in 1985, Sorböm notes that: ‘‘In his lecture Karl would say that the Chi-square is all you really need. One participant then asked ‘Why have you then added GFI [goodness-of-fit index]?’ Whereupon Karl answered ‘Well, users threaten us saying they would stop using LISREL if it always produces such large Chi-squares. So we had to invent something to make people happy. GFI serves that purpose’ (p. 10)’’. With respect to the causal heterogeneity point, according to Mulaik and James (1995, p. 132), samples must be causally homogenous to ensure that ‘‘the relations among their variable attributes are accounted for by the same causal relations.’’ As we say in our causal claims paper (Antonakis et al, 2010), "causally homogenous samples are not infinite (thus, there is a limit to how large the sample can be). Thus, finding sources of population heterogeneity and controlling for it will improve model fit whether using multiple groups (moderator models) or multiple indicator, multiple causes (MIMIC) models" (p. 1103). This issues is something that many applied researchers fail to understand and completely ignore. References: *Antonakis J., Bendahan S., Jacquart P. & Lalive R. (2010). On making causal claims: A review and recommendations. The Leadership Quarterly, 21(6), 1086-1120. Bera, A. K., & Bilias, Y. (2001). Rao's score, Neyman's C(α) and Silvey's LM tests: an essay on historical developments and some new results. Journal of Statistical Planning and Inference, 97(1), 9-44. *Bollen, K. A. 1989. Structural equations with latent variables. New York: Wiley. *James, L. R., Mulaik, S. A., & Brett, J. M. 1982. Causal Analysis: Assumptions, Models, and Data. Beverly Hills: Sage Publications. *Joreskog, K. G., & Goldberger, A. S. 1975. Estimation of a model with multiple indicators and multiple causes of a single latent variable. Journal of the American Statistical Association, 70(351): 631-639. McIntosh, C. (2012). Improving the evaluation of model fit in confirmatory factor analysis: A commentary on Gundy, C.M., Fayers, P.M., Groenvold, M., Petersen, M. Aa., Scott, N.W., Sprangers, M.A.J., Velikov, G., Aaronson, N.K. (2011). Comparing higher-order models for the EORTC QLQ-C30. Quality of Life Research. Quality of Life Research, 21(9), 1619-1621. *Muthén, B. O. 1989. Latent variable modeling in heterogenous populations. Psychometrika, 54(4): 557-585. *Mulaik, S. A. & James, L. R. 1995. Objectivity and reasoning in science and structural equation modeling. In R. H. Hoyle (Ed.), Structural Equation Modeling: Concepts, Issues, and Applications: 118-137. Thousand Oaks, CA: Sage Publications. And, here are some examples from my work where the chi-square test was passed (and the first study had a rather large sample)--so I don't live in a theoretical statistical bubble: http://dx.doi.org/10.1177/0149206311436080 http://dx.doi.org/10.1016/j.paid.2010.10.010 Best, J. P.S. Take a look at the following posts too by me on these points on Statalist. http://www.stata.com/statalist/archive/2013-04/msg00733.html http://www.stata.com/statalist/archive/2013-04/msg00747.html http://www.stata.com/statalist/archive/2013-04/msg00765.html http://www.stata.com/statalist/archive/2013-04/msg00767.html __________________________________________ John Antonakis Professor of Organizational Behavior Director, Ph.D. Program in Management Faculty of Business and Economics University of Lausanne Internef #618 CH-1015 Lausanne-Dorigny Switzerland Tel ++41 (0)21 692-3438 Fax ++41 (0)21 692-3305 http://www.hec.unil.ch/people/jantonakis Associate Editor The Leadership Quarterly __________________________________________ On 13.07.2013 08:41, Bloomberg Jenny wrote:Hello, I have a question about goodness-of-fit tests with gsem. (I don't have any specific models in mind; it's a general question.) I'm now reading the Stata 13 manual, and noticed that postestimation commands such as -estat gof-, -estat ggof-, and -estat eqgof- can only be used after -sem-, and not after -gsem-. This means that goodness-of-fit statistics like RMSEA cannot be obtained when you use gsem. Then, how can I test goodness-of-fit if I use -gsem- to analyse a non-linear, generalized SEM with latent variables? I know that AIC and BIC are still available after -gsem- (by -ic- option), but they are not for judging fit in absolute terms but for comparing the fit of different models. What I'd like to know is if there are any practical ways to judge the goodness-of-fit of the model in absolute terms. Any suggestions will be greatly appreciated. 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