RE: st: multiple indirect effects with binary mediators

["Muehleck, Kai" <Muehleck@his.de>]

Dear Billy,

thank you for your thoughts! (And sorry for the late reply - was on sick leave.)

Thank you for hinting to moderated mediation (or rather mediated moderation, I think, in my case). I wasn't yet aware of this concept. I have examined that (with parental leave being the moderator and a managing position being the mediator). There is a small sig. interaction (parental leave*female) when considering all cases but not at all in the group models. Thus I think  the effect of parental leave does not differ that much between sexes. However, again the estimation of the interaction effect may get shaky due to the distribution of my variables as very few men take parental leave. 

Subordinates: Unfortunately we don't know the number of subordinates but just whether respondents have managerial function in their job.

I still think about alternative ways to estimate the model using Mplus. Yes, the manager variable is defined as categorical in Mplus. How could I estimate the reliability of this variable and what would be the benefit of treating it as a latent indicator? If I'm right, alternatively to WLSMV I could combine an ML estimator with bootstrapped standard errors. I have read that bootstrapped S.E. should be more efficient but have no experience with bootstrapping. Do you think it is worth exploring this option? 

Yes, the effect could be recursive. That's another problem. I expect the parental leave (if there is any) to mostly precede the managerial position as the former refers to the period between having left higher secondary education and now whereas the managerial position refers to the current job. But, yes, the current managerial position may have started before the parental leave for a certain number of respondents. I could explore if this is the case for many respondents and take this into account by a dummy variable. What do you think of this idea?

Thank's again and best regards,
Kai

HIS Hochschul-Informations-System GmbH
Goseriede 9 | 30159 Hannover | www.his.de
Dr. Kai Mühleck
HIS-Institut für Hochschulforschung
Arbeitsbereich Steuerung, Finanzierung, Evaluation
Internationale Studien & Projektakquise
Telefon +49 (0)511 1220-456 | Fax +49 (0)511 1220-431
E-Mail muehleck@his.de 
Registergericht: Amtsgericht Hannover, HRB 6489
Geschäftsführer: Dipl.-Phys. Wolfgang Körner
Vorsitzender des Aufsichtsrats: Prof. Dr. Andreas Geiger

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of William Buchanan
Sent: Wednesday, May 08, 2013 6:14 PM
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: multiple indirect effects with binary mediators

I'm not sure what addition data you can access, but it might be worth it to consider moderated mediation for your maternity/paternity variable.  Also, if you have information on the number of subordinates, you could do something similar with your second mediator since it is likely that people with a larger number of subordinates will earn a higher wage than those who have fewer subordinates.  

In Mplus you also need to specify parameters in the estimation commands to define the treatment of the binary indicator and how it would be estimated.  If you know the reliability you could always use a latent indicator (applying the necessary constraints on your observed variable).  

There seem to be quite a few methodological issues based on your variables/scaling and the model of interest.  There could be a recursive effect in the mediators if someone in a managerial position takes family leave vs the case where the same person takes family leave prior to taking a managerial position.  It might be more useful to consider fitting a simpler model or reconsidering how the mediators are measured and included in the model.  

HTH,
Billy

Sent from my iPhone

On May 8, 2013, at 1:23, "Muehleck, Kai" <Muehleck@his.de> wrote:

> Dear Billy,
> 
> thank you for your quick reply! The key variables in my model are: 
> 
> - gender (IV; female=1),
> - number of months on parental leave (MV1; 0 if not on parental 
> leave/no kid),
> - holding a management position (MV2; having any subordinates=1) and
> - income (DV; natural logarithm of current vocational gross income per hour).
> 
> My feeling is that the binary mediator (MV2) is not the main problem (I just realized I mixed up MV1 and MV2 in my previous post; sorry for that). In my view it captures quite well what it is supposed to measure and the distribution is quite ok as well (please let me know if you disagree; 40% of the respondents in the model do have any subordinates [the sample is persons holding an academic degree, that's why the proportion is so high]). Rather my hunch is that the distribution of MV1 is a key problem (75% of all respondents have a value of 0, i.e. have not been on parental leave or have no kid). 
> 
> What are the problems encountered in Mplus?
> 
> Now, there are several technical questions I have but the main problem is: most indirect effects are significant as long as I estimate the model with the maximum number of respondents (N=3720). However, I would also like to analyze subgroups (min. N= 168, max. N=502). Calculating models for the single groups (I have not done a group model yet as too many questions are still pending anyway) mostly yields ns direct and indirect effects. Of course this is related to the smaller N but still the sizes of the effects strike me as pretty big and I think the S.E. are surprisingly large. Effect sizes are reasonably stable in the models for the single groups as compared to the full model but for most variable S.E. increase considerably, sometimes by factor 5. Currently I'm using the WLSMV estimator as this seems the estimator of choice if at least one IV is categorical. I'm asking myself whether there's an alternative to WLSMV with more efficient estimates. 
> 
> Probably, it is like it is and the model simply doesn't work out for smaller groups. But I would like to check whether an alternative method in Stata (or in Mplus) yields the same results and large S.E. Or I would need to try setting up larger groups (groups are fields of subjects respondents studied) but from a substantial point of view that would clearly be suboptimal.
> 
> Any ideas very appreciated!
> 
> Best
> Kai
> 
> 
> 
> HIS Hochschul-Informations-System GmbH Goseriede 9 | 30159 Hannover | 
> www.his.de Dr. Kai Mühleck HIS-Institut für Hochschulforschung 
> Arbeitsbereich Steuerung, Finanzierung, Evaluation Internationale 
> Studien & Projektakquise Telefon +49 (0)511 1220-456 | Fax +49 (0)511 
> 1220-431 E-Mail muehleck@his.de
> Registergericht: Amtsgericht Hannover, HRB 6489
> Geschäftsführer: Dipl.-Phys. Wolfgang Körner Vorsitzender des 
> Aufsichtsrats: Prof. Dr. Andreas Geiger
> 
> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu 
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of William 
> Buchanan
> Sent: Tuesday, May 07, 2013 5:52 PM
> To: statalist@hsphsun2.harvard.edu
> Subject: Re: st: multiple indirect effects with binary mediators
> 
> What were the problems you encountered in Mplus?  Maybe they are indicative of a larger underlying problem with fitting the model you are interested in.  Do you know how reliably your binary indicator is measured and whether or not it is derived from some underlying continuous variable?
> 
> There could be other ways to address things, but given the complexity of your model it would be helpful to know more about your data.
> 
> HTH,
> Billy
> 
> Sent from my iPhone
> 
> On May 7, 2013, at 6:56, "Muehleck, Kai" <Muehleck@his.de> wrote:
> 
>> Dear all,
>> 
>> I would like to estimate the direct indirect effects of an independent variable. Some of the mediating variables are binary, some are continuous. The dependent variable is continuous (natural logarithm of income). There are some packages allowing for binary mediators (medeff, ldecomp), however as I understand none of them allow for specifying multiple indirect effects in the sense of subsequent mediating variables. 
>> 
>> What do I mean by that? Theoretical considerations suggest that one group of mediators influences the other group of mediators. Thus the MVs influence the DV subsequently: 
>> 
>> IV -> MV1 -> MV2 -> DV.
>> 
>> In this model the total effect of the IV would be made up of the direct effect (IV -> DV) and three indirect effects:
>> 
>> (1) IV -> MV1 -> DV;
>> (2) IV -> MV2 -> DV;
>> (3) IV -> MV1 -> MV2 -> DV;
>> 
>> MV1 is binary. MV2 is continous (but far from  normally distributed with 75% of all respondents on value 0 and the rest distributed across a long positively skewed tail). The DV is continous as well and close to normally distributed. 
>> 
>> My questions are:
>> 
>> (1) How can I estimate the direct and indirect effects of the IV?
>> 
>> (2) How can I estimate the different indirect effects of MV1 and MV2 and their total effects?
>> 
>> Obviously this asks for some kind of path analysis. However, Stata's sem command only allows for continuous DVs (and continuous MVs I suppose). I have also tried to do this using Mplus but ran into several other problems I couldn't yet solve. Thus I'm again trying to explore Stata's potential to do such an analysis.
>> 
>> Any help and hints highly appreciated!
>> 
>> Best regards,
>> Kai
>> 
>> 
>> 
>> HIS Hochschul-Informations-System GmbH Goseriede 9 | 30159 Hannover | 
>> www.his.de Dr. Kai Mühleck HIS-Institut für Hochschulforschung 
>> Arbeitsbereich Steuerung, Finanzierung, Evaluation Internationale 
>> Studien & Projektakquise Telefon +49 (0)511 1220-456 | Fax +49 (0)511
>> 1220-431 E-Mail muehleck@his.de
>> Registergericht: Amtsgericht Hannover, HRB 6489
>> Geschäftsführer: Dipl.-Phys. Wolfgang Körner Vorsitzender des
>> Aufsichtsrats: Prof. Dr. Andreas Geiger
>> 
>> 
>> 
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