fixed effects and and vce(robust) in poisson regression

[Christopher Weber]

Hello everyone,
I am aware that this is more of a statistical quuestino than a question on Stata but maybe someone here can help me regardless:

In a poisson regression model, does it always make sense to include "fe" as well as vce(robust)? If i add "fe" to my regression, the model all of a sudden lacks degrees of freedom, if i further add vce(robust), the values become nonsignificant. Does this tell me i have created a weak model that needs to be changed? Or does it not make sence in certain cases, to add "fe" and "vce(robust)"?

Best regards

Chris

[Joao Santos Silva]

Dear Christopher Weber,

Whether or not to include fixed effects is a modelling decision, so it is up to you to decide whether you want to condition on them. If your variables have little time variation, they are likely to become less significant but that is because they only explain what is not explained by the fixed effects that mop up the effect of anything that is constant over time. Robust (clustered) standard errors are a must.

Best wishes,

Joao

[Andrew Musau]

You should read an econometrics textbook on panel data models. Fixed effects models allow you to account for unobserved individual effects that may be correlated with covariates in the model. -vce(robust)- on the other hand corrects the standard errors for some forms of misspecification. In linear models and Poisson regression, I would always advise that you calculate robust standard errors. Whether your results turn out to be significant or not should not affect the estimation method. You should focus on whether your model is appropriate and whether you have quality data.

Note: Crossed with #2.

[Carlo Lazzaro]

Cristopher:
Joao and Andrew gave excellent advice.
As you're surely aware of, -xtposson,fe- gives back conditional -fe- (which differs from -fe- we're used to in -xtreg-) due to incidental parameter bias (see http://www.econ.brown.edu/Faculty/To...meters1948.pdf).

[Andrew Musau]

I will add to Carlo's advice that there is no incidental parameters bias in Poisson regression, unlike other nonlinear models like probit or logit. Therefore, conditional fixed effects and unconditional fixed effects will result in the same coefficient estimates for the time-varying regressors. The difficulty here is that unconditional fixed effects are computationally burdensome.

webuse ships
xtset ship
xtpoisson accident op_75_79 co_65_69 co_70_74 co_75_79, exposure(service) fe nolog
poisson accident op_75_79 co_65_69 co_70_74 co_75_79 i.ship, exposure(service) nolog

Res.:

. xtpoisson accident op_75_79 co_65_69 co_70_74 co_75_79, exposure(service) fe nolog

Conditional fixed-effects Poisson regression    Number of obs     =         34
Group variable: ship                            Number of groups  =          5

                                                Obs per group:
                                                              min =          6
                                                              avg =        6.8
                                                              max =          7

                                                Wald chi2(4)      =      48.44
Log likelihood  = -54.641859                    Prob > chi2       =     0.0000

------------------------------------------------------------------------------
    accident |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
    op_75_79 |    .384467   .1182722     3.25   0.001     .1526578    .6162761
    co_65_69 |   .6971404   .1496414     4.66   0.000     .4038487    .9904322
    co_70_74 |   .8184266   .1697736     4.82   0.000     .4856763    1.151177
    co_75_79 |   .4534266   .2331705     1.94   0.052    -.0035791    .9104324
 ln(service) |          1  (exposure)
------------------------------------------------------------------------------

.
. poisson accident op_75_79 co_65_69 co_70_74 co_75_79 i.ship, exposure(service) nolog

Poisson regression                              Number of obs     =         34
                                                LR chi2(8)        =     107.63
                                                Prob > chi2       =     0.0000
Log likelihood = -68.280771                     Pseudo R2         =     0.4408

------------------------------------------------------------------------------
    accident |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
   op_75_79 |    .384467   .1182722     3.25   0.001     .1526578    .6162761
    co_65_69 |   .6971404   .1496414     4.66   0.000     .4038487    .9904322
    co_70_74 |   .8184266   .1697736     4.82   0.000     .4856763    1.151177
    co_75_79 |   .4534266   .2331705     1.94   0.052    -.0035791    .9104324
             |
        ship |
          2  |  -.5433443   .1775899    -3.06   0.002    -.8914141   -.1952745
          3  |  -.6874016   .3290472    -2.09   0.037    -1.332322    -.042481
          4  |  -.0759614   .2905787    -0.26   0.794    -.6454851    .4935623
          5  |   .3255795   .2358794     1.38   0.168    -.1367357    .7878946
             |
       _cons |  -6.405902   .2174441   -29.46   0.000    -6.832084   -5.979719
 ln(service) |          1  (exposure)
------------------------------------------------------------------------------

.

[Carlo Lazzaro]

Andrew is correct:
THe OP correctly wrote Poisson, but I read -probit-.
Hence, only the part concerning the conditional -fe- holds.
Sorry for the confusion and thanks to Andrew for pointing this out and elaborating on the issue with an interesting comparison.

[Christopher Weber]

Thank you to everyone for the answers. You guys are awsome!

[Fei Wang]

A footnote to Andrew's comment in #5. Incidental parameter problems could be ignored in several models, including poisson, logit, and nbreg (not recommended though).

[Joao Santos Silva]

Dear Fei Wang,

Can you please clarify in what sence the IPP problem an be ignored in the logit and nb?

Best wishes

Joao

[Fei Wang]

Joao Santos Silva , In the estimation of non-linear models with FEs, the density of DV, used to construct the ML function, is a function of regressors and FEs. If the FEs have to be estimated, then IPP arises particularly when T is fixed. In very specific cases, FEs can be cancelled out from the likelihood and one may consistently estimate parameters of interest without bothering to estimate FEs. For each subject i, define a variable, say z_i, to be the sum of DV of i along t. FEs magically disappear when the density function is conditional on z_i (in other words, z_i serves as sufficient statistics of FEs) -- and this math transformation holds for poisson, logit (multinomial logit as well) and nbreg (I haven't checked that for nbreg, but it should be similar to the transformation of poisson). I'm not sure if I have listed all cases, but any Stata command doing a conditional FE estimation for a non-linear model should share the same merits.

[Joao Santos Silva]

Dear Fei Wang,

Thanks for clarifying. I guess that in #8 what you meant was that in these models the IPP can be by-passed, not ignored.

Best wishes,

Joao