There are about 200 men and 800 women in my sample (an online survey). I would like to run a structural equation model with sex as one of the predictors. The model is a three-step mediation: PREDICTORS (including SEX) --> MEDIATORS --> MEDIATORS --> OUTCOMES.
I would be very grateful if you might suggest how to handle this man/woman ratio and preferably provide me with a reference that might back-up your strategy. Thank you!
Hi Lukasz
Mplus handles binary data easily. So does LISREL - so you could model gender as an IV using DWLS estimation. Actually, ML estimation is pretty robust to deviations from normality, so you could try with ML too...
If you try ML, the following snip from an old paper I wrote (Cadogan et al. 2001, p. 272) might be useful:
"there is growing evidence that ML estimates are reasonably well behaved when the multivariate normality assumption has been violated (Jaccard and Wan, 1996). In particular, West et al. (1995) have noted that the CFI is robust even under severely nonnormal conditions see also Ping, (1995)."
The full text is available here (see p 19 on this version:
https://www.researchgate.net/publication/236003967_Key_Antecedents_to_Export_Market-Oriented_Behaviors_A_Cross-National_Empirical_Examination?ev=prf_pub
Best
John
Article Key Antecedents to Export Market-Oriented Behaviors: A Cross...
Thank you John for your answer and your useful citation. Please let me clarify that I do not find using gender as a binary predictor problematic. My doubt is whether I should use gender as the predictor of EVERY dependent variable? More specifically:
Consider my mPlus model is:
Case1:
y ON m1;
m1 ON m2;
m2 ON x1 x2 gender;
Should I also control for gender on each step towards the y? Consider this:
Case2:
y ON m1 gender;
m1 ON m2 gender;
m2 ON x1 x2 gender;
This would seem a bit odd, but it seems that Case1 controls for gender only in the prediction of m2, and the remaining steps of mediation are biased by prevelance of female participants. Please help!
Hmmm.... okay - got it now.
In Case 1, you are explicitly modeling gender with two sharp hypotheses that say "Gender has a precise value of zero as a predictor of m1 and of y".
Fit for Case 1 has a good chance of being quite bad – worse than the fit for Case 2 anyway (where you allow Gender to take on any value as a predictor of both m1 and y - including a value of zero). That is, Case 2 is a model that estimates values for Gender’s relationship with m1 and y, and the value estimated might be 0, but it might be any other value too. Case 1 on the other hand forces the value for Gender’s direct relationship with m1 and y to be exactly zero, and probably, those values are not exactly zero in the sample (although they might be close).
Your options? I suspect that you might need to report findings for Case 2, and explain that you are controlling for possible effects of Gender on m1 and y. Ideally, Case 2 does not change the substantive relations you are really interested in (Gender’s impact on m2, for instance), and does not harm model testing in any other way. References for this kind of approach? Nothing comes to mind this second. However, one strategy for justifying running Case 2 is to cite papers that have reported direct relationships between Gender and m1 and y as justification for including Gender as a control in the model. Another option is to develop plausible reasons / arguments why one might expect to see direct links between Gender and m1 and y, over and above any indirect effect that Gender may have through m2.
I guess I’m suggesting that your theory development section would contain only Case 1 model. However, in the methods / analysis section of the work, you would explain that in order to provide evidence on Case 1 model, you must run Case 2 model to control for Gender’s potential indirect effects on m1 and y, etc… You can then also compare nested models to see whether, over and above the control paths, your Case 1 model paths (ie the hypothesized paths) are viable additions (to a model containing only control paths). Lots of options. Hope I’m dealing with the correct issue this time!
John
Thank you John Cadogan. I used the approach you suggested, regressed meditors on gender and the results are pretty awesome and consistent :D Simple solutions are sometimes the best. Thank you!
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