xtcloglog population averaged vs. random effects

[Tim Grünebaum]

Hi Statalist,

I would like to estimate a complementary loglog model with induvidual effects using Stata's xtcloglog command.

My dependent variabel is binary with rare events and I have a panel structure with small T and large N, so everything is fine for this kind of model.

I am now struggeling whether to use the pa (population averaged) or re (random effects) option for accounting for individual effects.
The general differences of thes two models are described e.g. here:
https://www.stata.com/support/faqs/s...tion-averaged/
and in more detail here:
http://journals.sfu.ca/llcs/index.ph...ewFile/249/238

The problem ist that I am interested in the marginal effects of a count variable (number of patents applied) on the dependent variable (the probability of bankruptcy of a firm) and that the results are very different for the pa and re model.
The second source I posted says (on page 155-156) that because of the non-llinearity of the assumed distribution the estimated coefficients differ and how they differ. However they also say that standard errors should vary proportionally and thus no serious effects on significant tests are to be expected. But in my case only one model delivers statistical significant results.
I estimate the marginal effects using the margins command at different values of my explanatory variable (say 0, 1 or 5 patents) and the atmeans option for the controls. I suppose no more information about my data is needed to understand the problem but I can offer later.

So beside the effects that it is obviously relevant to select the correct option (re or pa) for the research question, why do the marginal effects for point-estimates and standard errors differ quite substatially?

Thanks and best regards

Tim

[Phil Bromiley]

You'll increase your chances of a useful answer by following the FAQ on asking questions - provide Stata code in code delimiters, readable Stata output, and sample data using dataex.

The documentation for xtcloglog shows different parameters and standard errors for re and pa.

[Tim Grünebaum]

Ok, so here is an example using Stata's own dataset from the help xtcloglog postestimation so all can follow.
This highlights a similar problem as in my original dataset.

use http://www.stata-press.com/data/r15/union

then estimate random effects

quietly xtcloglog union age grade not_smsa south##c.year, re
margins, dydx(age) at(age=(20 30 40))
------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
age          |
         _at |
          1  |   .0014771   .0012951     1.14   0.254    -.0010612    .0040154
          2  |   .0015507   .0014322     1.08   0.279    -.0012564    .0043577
          3  |    .001622   .0015632     1.04   0.299    -.0014418    .0046857
------------------------------------------------------------------------------

and then the population averaged model

quietly xtcloglog union age grade not_smsa south##c.year, pa
margins, dydx(age) at(age=(20 30 40))
------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
age          |
         _at |
          1  |   .0025007   .0011564     2.16   0.031     .0002343    .0047672
          2  |   .0028129    .001479     1.90   0.057    -.0000859    .0057117
          3  |   .0031456   .0018338     1.72   0.086    -.0004486    .0067398
------------------------------------------------------------------------------

You can see that the marginal effects on the probability to be part of a union at the age of 20, 30 and 40 years are higher in the pa model and furthermore insignificant in the re model.
Similar issues arise already by looking at the bare coefficients of the baseline model (with or without robust standard errors). But I suppose marginal effects at different values of any explanatory variable can furthermore highlight the differences of the two models as described in the source from Szmaragd, Clarke and Steele (2013) from my original post.
Sometimes the effects are significant in the baseline model but the marginal effects become insignificant (no matter where I estimate them) what leave me even more confused.

So I simply wonder how to decide upon the model as the results are very different here.

Regards
Tim