[Jessica Thacker]

Thank you so much for your support Prof. Andrew Musau

[Jessica Thacker]

Dear Andrew Musau,

1. If you estimate a random effects model, at the foot of the table are results of a likelihood-ratio test which compares the pooled estimator (logit) with the panel estimator (xtlogit). This will tell you whether you can justify estimating a pooled model.

With respect to your comparison between logit re and pooled logit. I get the following results after running the command xtlogit status on various independent variables.

I would be grateful if you could help with interpreting the LR test of rho=0. In the xtlogit manual it is not given. On page 255 it is written "When rho is zero, the panel-level variance component is unimportant, and the panel estimator isno different from the pooled estimator. A likelihood-ratio test of this is included at the bottom of the output. This test formally compares the pooled estimator (logit) with the panel estimator". However, this test is not explained or interpreted in the manual.
I apologize for bothering you with elementary questions like these. I am using panel logit for the first time.
I would humbly request you to help me interpret LR test of rho=0. What is the null hypothesis and alternative?
I could not even understand what is chibar(01) represents and what prob>=chibar2=0.000 mean here?
Does prob>=chibar2=0.000 mean favoring pooled cross section over random effect panel?
I would also request if you could provide me with some reference of LR test of rho.

[Andrew Musau]

See

help lrtest

for details on likelihood ratio (LR) tests. The interpretation is provided in the manual entry of xtlogit

[rho] is the proportion of the total variance contributed by the panel-level variance component. When rho is zero, the panel-level variance component is unimportant, and the panel estimator is no different from the pooled estimator.

So the null hypothesis of the LR test is that rho=0 (or the pooled model and the panel model are equivalent). In your case, the test statistic is distributed as \(\bar{\chi}^{2}(1)\) and has a tail probability of less than 0.001. Therefore, you reject the null hypothesis and conclude that a panel model is warranted. Here is an example of how you implement the test using lrtest.

webuse union, clear
xtset idcode year
xtlogit union age grade i.not_smsa south##c.year, nolog
est sto panel
logit union age grade i.not_smsa south##c.year, nolog
est sto pooled
lrtest panel pooled, force

Res.:

. xtlogit union age grade i.not_smsa south##c.year, nolog

Random-effects logistic regression              Number of obs     =     26,200
Group variable: idcode                          Number of groups  =      4,434

Random effects u_i ~ Gaussian                   Obs per group:
                                                              min =          1
                                                              avg =        5.9
                                                              max =         12

Integration method: mvaghermite                 Integration pts.  =         12

                                                Wald chi2(6)      =     227.46
Log likelihood  = -10540.274                    Prob > chi2       =     0.0000

------------------------------------------------------------------------------
       union |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |   .0156732   .0149895     1.05   0.296    -.0137056     .045052
       grade |   .0870851   .0176476     4.93   0.000     .0524965    .1216738
  1.not_smsa |  -.2511884   .0823508    -3.05   0.002    -.4125929   -.0897839
     1.south |  -2.839112   .6413116    -4.43   0.000    -4.096059   -1.582164
        year |  -.0068604   .0156575    -0.44   0.661    -.0375486    .0238277
             |
south#c.year |
          1  |   .0238506   .0079732     2.99   0.003     .0082235    .0394777
             |
       _cons |  -3.009365   .8414963    -3.58   0.000    -4.658667   -1.360062
-------------+----------------------------------------------------------------
    /lnsig2u |   1.749366   .0470017                      1.657245    1.841488
-------------+----------------------------------------------------------------
     sigma_u |   2.398116   .0563577                      2.290162    2.511158
         rho |   .6361098   .0108797                      .6145307    .6571548
------------------------------------------------------------------------------
LR test of rho=0: chibar2(01) = 6004.43                Prob >= chibar2 = 0.000

.
. est sto panel

.
. logit union age grade i.not_smsa south##c.year, nolog

Logistic regression                             Number of obs     =     26,200
                                                LR chi2(6)        =     643.48
                                                Prob > chi2       =     0.0000
Log likelihood =  -13542.49                     Pseudo R2         =     0.0232

------------------------------------------------------------------------------
       union |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |   .0207656   .0050001     4.15   0.000     .0109655    .0305658
       grade |   .0489121   .0064308     7.61   0.000      .036308    .0615162
  1.not_smsa |  -.2195163   .0355977    -6.17   0.000    -.2892865   -.1497461
     1.south |  -1.530743   .4387964    -3.49   0.000    -2.390768   -.6707176
        year |  -.0145607   .0057128    -2.55   0.011    -.0257576   -.0033638
             |
south#c.year |
          1  |   .0110577   .0054775     2.02   0.044      .000322    .0217933
             |
       _cons |  -1.066526   .3414275    -3.12   0.002    -1.735711   -.3973401
------------------------------------------------------------------------------

.
. est sto pooled

.
. lrtest panel pooled, force

Likelihood-ratio test                                 LR chi2(1)  =   6004.43
(Assumption: pooled nested in panel)                  Prob > chi2 =    0.0000

[Carlo Lazzaro]

Jessica:
the LR outcome rejects the null that the pooled estimator is the way to go. Put differently, your dataset shows evidence of a panel-wise effect and you should go -xtlogit, re-.
In your future message, please post via CODE delimiters the code you typed and the complete outcome table. Thanks.

[Jessica Thacker]

Dear Prof. Andrew Musau. Thank you so much for your help.
Dear Carlo Lazzaro. I will always keep in mind to post via code delimiters with complete outcomes. Thank you so much for your help.

[Jessica Thacker]

Sorry to bother you again Prof. Andrew Musau and Carlo Lazzaro

I have some questions to ask:
(1)Is there a way to check for goodness of fit of the model? I ran fixed effect panel logistic model using the following code but, did not find R squared or pseudo R squared. I am attachinhg the output also

xtlogit status  creditors_turnover_w  ca_turnover_w quick_ratio_w npm_w log_sales age g_pat_w de_w icr_r cash_ca_w ca_ta_w i.dummy_sector  L.i.status , fe

(2)I checked for autocorrelation after running this command

xtserial status  creditors_turnover_w  ca_turnover_w quick_ratio_w npm_w log_sales age g_pat_w de_w icr_r cash_ca_w ca_ta_w

I am attaching the output also which clearly shows that the FE panel regression is serrially correlated. Is there a fix to it? Or as you suggested before that I do not have to worry for it.

[Carlo Lazzaro]

Jessica:
1) -xtlogit- returns -chi2-, not (pseudo) R_sq;
2) your residuals are autocorrelated but you cannot invoke -vce(cluster panelid)- under -xtlogit, fe-. On the other side, with >5000 groups, default standard errors seem way too optimistic; I'd go -bootstrap- standard error with 200 replications, as suggested in Efron B, Tibshirani R. An Introduction to the Bootstrap. Boca Raton, FL: CRC Press, 1993 (I don't remember the page).

[Jessica Thacker]

Hi Carlo Lazzaro and Andrew Musau
I wanted to ask if there is a way to find the marginal effects of the beta coefficients of fixed effects panel logistic regression. And does it give consistent estimates of beta coefficients of panel logistic regression?

[Carlo Lazzaro]

Jessica:
you may want to consider -margin- after -xtlogit-, provided that this is the gist of your question.

[Jessica Thacker]

Dear Carlo Lazzaro ,

(1) I had read somewhere that finding the odds ratio of the beta coefficients after xtlogit, fe gives an inconsistent odds ratio. I humbly wanted to confirm if that is true or not.
(2) Using xtlogit, or after xtlogit, fe would also give the odds ratio of the beta coefficients of panel logistic regression?

[Carlo Lazzaro]

Jessica:
I do not know if you refer to incidental parameters bias or else.
That said, you may want to take a look at: https://www.statalist.org/forums/for...n-logit-models.
As far as your last question is cosncerned, -xtlogit- has an -or- option.

[Jessica Thacker]

Thank you so much.

[Mehmet Serkan CALI]

Hi Andrew Musau & Carlo Lazzaro, I have a 41N32T panel data. My dep. var. not ordinary. İt is categorical. How I estimate paralel regression assumption after xtmlogit.

[Andrew Musau]

I assume that you are referring to the parallel regression assumption or proportional regression assumption. You test for this in an ordinal model. In multinomial logit, the categories do not have any natural ordering.

[Mehmet Serkan CALI]

Thanks sir @Andrew Musau. If I have a ordered dep. variable and try to run xtoprobit or xtologit. How I estimate parallel regression assumption or proportional regression assumption. Because I can't any postestimation command after these.