Hello,

I have some questions regarding (dis)advantages of using melogit vs logit, vce(cluster) vs xtlogit when you have multilevel data. Are there any theoretical (or practical) reasons to prefer one or the other?
I specified some alternatives (see code and results below): in this case the results are pretty robust, but in some other cases, coefficients and standard errors may be quite different according to the specification.


Code:
use http://www.stata-press.com/data/r15/bangladesh
eststo clear
* Basic multilevel logit
melogit c_use urban age child* || district:
eststo melogit
* Multilevel logit with clusterd standard errors
melogit c_use urban age child* || district:, vce(cluster district)
eststo melogit_cl
* 'Normal' logit with clustered standard errors 
logit c_use urban age child*, vce(cluster district)
eststo logit_cl
* declare panel data (xtset district)
xtset district
* Random intercepts logit (panel data)
xtlogit c_use urban age child*, re
eststo xtlogit_re
* Fixed intercepts logit (panel data)
xtlogit c_use urban age child*, fe
eststo xtlogit_fe
* Manually created fixed intercepts logit (because vce(cluster) is not possible using xtlogit, fe
logit c_use urban age child* i.district
eststo logit_man_fe
* Manually created fixed intercepts logit with clustered s.e. (because vce(cluster) is not possible using xtlogit, fe
logit c_use urban age child* i.district, vce(cluster district)
eststo logit_man_fe_cl
* consolidate output in 1 table
esttab, mtit keep(urban age child*)


Code:
----------------------------------------------------------------------------------------------------------------------------
                      (1)             (2)             (3)             (4)             (5)             (6)             (7)   
                  melogit      melogit_cl        logit_cl      xtlogit_re      xtlogit_fe    logit_man_fe    logit_man_~l   
----------------------------------------------------------------------------------------------------------------------------
c_use                                                                                                                       
urban               0.732***        0.732***        0.797***        0.732***        0.644***        0.662***        0.662***
                   (6.13)          (4.39)          (4.21)          (6.13)          (5.12)          (5.19)          (3.58)   

age               -0.0265***      -0.0265***      -0.0239***      -0.0265***      -0.0266***      -0.0274***      -0.0274***
                  (-3.36)         (-3.70)         (-3.49)         (-3.36)         (-3.31)         (-3.36)         (-3.62)   

child1              1.116***        1.116***        1.067***        1.116***        1.123***        1.154***        1.154***
                   (7.06)          (5.73)          (5.82)          (7.06)          (7.01)          (7.10)          (5.59)   

child2              1.366***        1.366***        1.276***        1.366***        1.359***        1.398***        1.398***
                   (7.82)          (8.13)          (7.51)          (7.82)          (7.69)          (7.79)          (7.91)   

child3              1.344***        1.344***        1.214***        1.344***        1.364***        1.404***        1.404***
                   (7.48)          (6.60)          (6.05)          (7.48)          (7.48)          (7.58)          (6.57)   
----------------------------------------------------------------------------------------------------------------------------
N                    1934            1934            1934            1934            1907            1907            1907   
----------------------------------------------------------------------------------------------------------------------------

t statistics in parentheses
* p<0.05, ** p<0.01, *** p<0.001
Thanks a lot for any comments of valuable suggestions,
Mike