difference between mixed and hybrid models in analyzing panel data

[Jung-soo Kim]

I have been confused between hybrid model(xthybrid) and mixed model(xtmixed) in analyzing panel data. Both models seem to be very useful in analyzing panel data where unbiasedness needs to be pursued based on hausman test result but time-invariant variables are also main variables for the analysis. Is my understanding correct? What is the difference between the two models?

[Clyde Schechter]

Yes, both are useful for analyzing panel data when estimating the effects of time-invariant variables is necessary.

Relevant to this situation, the difference between them is this:

-xthybrid- disentangles the between-panel and within-panel effects of all the explanatory variables and presents separate estimates of the between- and within- effects.
-mixed- (formerly called -xtmixed- before version 13) constrains the within- and between- effects of the explanatory variables to be equal and estimates this common effect. This constraint is a strong assumption and is one reason that in some disciplines the use of mixed-effects models is discouraged, or sanctioned only with the blessing of Hausman. (Hausman tests this constraint.)

More generally, however, -mixed- is a general command for multi-level linear models with random intercepts and slopes and any number of levvels. -xthybrid- is restricted to 2-levels, does not support random slopes (at least not in the version I have), and can do generalized linear models (e.g. logistic, Poisson...), not just linear.

[Jung-soo Kim]

Clyde Schechter Thanks very much for your helpful explanation. You mentioned about hausman test for using the mixed model. How does the test work in STATA then? I know how to test it between Fixed and Random Effects(store each estimate and implement hausman test), and I tried the same way with ME and FE model but it does not work...below are the commands that I used and the error message.

. xtmixed y x1 x2 ...
. estimates store ME
. xtreg y x1 x2 ..., fe
. estimates store FE
. hausman ME FE
no coefficients in common; specify equations(matchlist)
for problems with different equation names.

[Clyde Schechter]

No, you can't use -mixed- with Hausman. The way it names the coefficients is different from -xtreg, fe- so Hausman doesn't recognize the two models as related. You have to use -xtreg, re-, which, for a model with only 2 levels and no random slopes is equivalent to -mixed- as a model but uses the same coefficient names as -xtreg, fe-.

[Sapna Goel]

Hello
I have some doubts in understanding the hybrid model.

The hybrid model divides an effect into two parts: in-between effect and within effect.

I will ask my doubt with an example:

I am working with a panel data set with monthly observations.
My dependent variable is farm days spent by women in a month.

My independent variable is household level monthly migration status. We say a household is migrant household if any male member of the household migrated in a given month.

now, my understanding is that the within effect captures: if in a given household migration happens, then how does it affect the days spent by women compared to if migration didn't happen.

For the in-between effect: we are comparing the difference in farm days spent by women between a migrant and non-migrant family.

However, the household level monthly migration status obviously changes on a month -to-month basis.
So in the in-between effect, what exactly are we getting.
Is it a comparison between families that were migrant families some months and families that didn't have any migrant member during the entire study period ?

Or is it this:
Suppose family A migrates in January. Family B doesn't migrate in January. Family C doesn't migrate in January. So for January, it's like we have two groups. Family A is one group. Family B and C is another group. So we compare the difference in farm days between these two groups.
Now Suppose Family A doesn't migrate in February. Family B migrates. Family C migrates. So, now, we treat family A and family B as one group. And family C is another group. And we compare the difference in farm days spent by women in these two groups.


Also, if I add with-in and in-between effect, do I get a meaningful coefficient?

Kindly clarify.
Thank you

[Daniel Geiter]

Sapna Goel to my understanding, your first intuition is right. You are measuring the effect of a person migrating in a given month on farm days. You are analyzing the effect between different households. But since you also have multiple observations per household over time, you are also measuring the effect within households, which could differ from the in-between effect, because of household specific characteristics. By accounting for both kinds of effects in your model you control for these household specifics.

Besides, I also have a question regarding the hausman test for mixed commands: I have a similar problem as described by Jung-Soo Kim. But my model does include random slopes. Therefore, I cannot simply use ,re but I have to use mixed. Do you know any solution for this issue, Clyde Schechter ?
Thanks a lot in advance!