R-squared for mixed models

[Victoria Rogers]

If I would use -xtmixed- to control for all fixed effects while still being able to see the effect of the time-invariant variable Male, would this be the code?

mixed alpha Male MRP SMB HML MOM       I  I alpha: Male MRP SMB HML MOM

How can I get the correspondng R-squared? (I assume that reporting e(R2) isn't correct in this case...)

[daniel klein]

The term "fixed-effects" used with these models has nothing in common with the the concepts in xtreg ,fe, but the name. Therefore the model you show does not control for any fixed-effects, in the sense of (unobserved) individual heterogeneity, but those specified in the model, namely Male (and maybe some of the other specified variables,that I do not know the meaning).

I think you would be (much) better off trying to understand the concepts (not just the syntax) of one of the various models you proposed in countless threads you started within the past 24 hours, than trying to learn everything at once and in a forum. Read some literature about the models you are trying to fit. Introductory books might be a better approach than surfing the net for hours, as you cannot even cite the latter when explaining your model to others.

I understand you are in a hurry, but your current strategy will likely get you into more trouble than doing one thing at a time and do that correct.

Best
Daniel

[Victoria Rogers]

I don't know what I should have cited, however, thank you for telling me that the fixed effects of mixed models do not control for all fixed effects like -xtreg, fe- does. However, can this model still be used to take care of omitted variable bias? If so, please tell me how because my main concern is getting rid off the omitted variable bias.

I never saw that difference of fixed effects on the Internet, even though I researched it quite a lot. By the way, if -xtmixed- only controls for fixed effects of Male, then it would be the same as using -xtreg, re- because it controls for the fixed effects of the panelvar ID (person fund combination in my case). Why doesn't -xtmixed- control for all fixed effects even though it includes using -xtreg, fe- (and -xtreg, re-)

Unfortunately, based on that, I don't which model I should focus on because -xtreg, fe- cannot be used due to the time-invariant variable Male. There should be another model like the useful one of Sebastian which controls for all fixed effects.

Could you tell me what the use is of -xtmixed-?

[daniel klein]

What exactly is your understanding of "fixed-effects"? What do you mean by "control for all fixed-effects"?

What exactly is your understanding of an "omitted variable bias"?

[Victoria Rogers]

Fixed effects: for example, if someone is trying to test the effect of age on returns.....reg returns age.....then you could control for fixed effects like gender due to the fact that gender is time-invariant and if you use -xtreg, fe- for example then you control for those time-invariant variables which are considered to be omitted variables. However, there are often a lot of unknown variables which have an effect on the independent variable, therefore you cannot simply add all those variables as control variables.

Does my understanding correspond with your understanding?

Maybe, it sounds like I don't know anything Daniel, but I'm kinda tired of working literally 48 hours in 3 days in a row.
It's not like I'm not investigating the mixed and simply asking for help. If you want I can start spamming all the websites I've read the next time I start a new thread.

[daniel klein]

Maybe, it sounds like I don't know anything Daniel, [...]

Sorry if my question offended you. I just wanted to make sure we are talking about the same thing. Especially because the term fixed-effects is used to describe very different things in otherwise closely related models.

Let me add to your description a very important fact. In order to estimate an unbiased coefficient for a predictor/independent variable, it is not necessary to include every variable that influences the response/outcome/dependent variable.This is why we add error-terms to our equations. They capture any effects that are not explicitly modeled. The important thing for unbiased estimation is, that what we omit from the model does not correlate with the predictors in the model. Only if what we omit correlates with the response and with one of the predictors, will we have biased estimates. At least in linear models. Now, there are basically three things we can do about omitted variable bias.

1. We can explicitly control for the variables. This requires that we have measured these variables, which we rarely have.
2. We can try and wipe the unmeasured causes out of our equations. This is what the within-transformation implemented in xtreg ,fe does and this works for variables that do not vary within units.
3. We can find instruments for the variables that are correlated with the error. The basic rational behind is to use only part that of the variance in the predictor that is uncorrelated with the error. These models require additional assumptions and this has been discussed elsewhere.

The mixed-model you present in this thread does neither of these three things, and is capable of doing the first. The term fixed-effects in these models merely state that one parameter/slope is to be estimated for the respective predictor. xtmixed allows you to estimate random intercepts and random-slopes and the latter is the advantage over xtreg ,mle, which is otherwise exactly the same model. To sum up, the model you describe here controls for what you call "fixed-effects" only insofar as you have measured them and put them in the model.

Let me clarify one more thing.

There should be another model like the useful one of Sebastian which controls for all fixed effects.

The model you refer to here is the correlated random effects model. Contrary to your belief it does not control for all fixed-effects. While it is true that the coefficients for predictors that vary within units resemble the within-estimator (xtreg ,fe) this does by no means hold for the predictors that do not vary within units. These coefficients resemble more a between-estimator (in the case of varying predictors the coefficients estimate the difference between the within and between effects) and therefore are controlled for only those "fixed-effects" that are explicitly added to the model.

I will not go to deep into discussing why invariant predictors. like gender, cannot possibly be causes of anything within the counterfactual causal model, but it might be useful to think about what we mean by stating that gender has an "effect" on a given response. The basic point is that we cannot possibly change gender without changing the unit of observation. Therefore differences in a given outcome according to gender are actually caused by something else.

Please do not start yet another thread, as this will make things even more difficult to follow - for you and for others.

Best
Daniel