FE/RE or xtlogit/xtprobit ?

[Farhad Mammadov]

Dear all,

I am working with panel data on the topic where my dependent variable is an 11-point scale ranging from 0 to 10.

I started with simple Fixed and Random Effects models (xtreg) but then realized that there is an option to use Logit or Probit in combination with Panel Data via xtlogit and xtprobit.

Now i do not know which direction i should stick with.

Waiting for your advices.

Thanks and BR

[Andrew Musau]

I am working with panel data on the topic where my dependent variable is an 11-point scale ranging from 0 to 10.

xtprobit and xtlogit are for binary dependent variables. Are you thinking about categorizing this variable? I would not advise it. But generally, to answer your question, there is no fixed effects option for xtprobit, so you will need to stick to xtlogit if estimating a fixed effects model. For random effects, empirically, there is not much to choose between both commands as is the case between logit and probit. Look at the marginal effects in the example below.

webuse union, clear
qui xtlogit union age grade i.not_smsa south##c.year
margins, dydx(*) predict(pr)
qui xtprobit union age grade i.not_smsa south##c.year
margins, dydx(*) predict(pr)

Res.:

. qui xtlogit union age grade i.not_smsa south##c.year

. margins, dydx(*) predict(pr)

Average marginal effects                        Number of obs     =     26,200
Model VCE    : OIM

Expression   : Pr(union=1), predict(pr)
dy/dx w.r.t. : age grade 1.not_smsa 1.south year

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |   .0014891   .0014248     1.05   0.296    -.0013036    .0042817
       grade |   .0082736   .0016735     4.94   0.000     .0049936    .0115537
  1.not_smsa |  -.0235051   .0075931    -3.10   0.002    -.0383872   -.0086229
     1.south |  -.0869896   .0072843   -11.94   0.000    -.1012665   -.0727127
        year |   .0001264   .0014638     0.09   0.931    -.0027426    .0029955
------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.

. qui xtprobit union age grade i.not_smsa south##c.year

. margins, dydx(*) predict(pr)

Average marginal effects                        Number of obs     =     26,200
Model VCE    : OIM

Expression   : Pr(union=1), predict(pr)
dy/dx w.r.t. : age grade 1.not_smsa 1.south year

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |   .0014041   .0014324     0.98   0.327    -.0014033    .0042115
       grade |   .0081695   .0016796     4.86   0.000     .0048776    .0114614
  1.not_smsa |  -.0233099   .0075834    -3.07   0.002    -.0381731   -.0084468
     1.south |  -.0856766   .0072877   -11.76   0.000    -.0999603    -.071393
        year |   .0001129   .0014716     0.08   0.939    -.0027714    .0029972
------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.

[Farhad Mammadov]

Dear Andrew, thank you for your reply. Can I know what you mean by categorizing? If you mean for example from 0 to 5 means 0 and from 6 to 10 means 1 then no, i will stick with all 11 points in my interpretation

[Andrew Musau]

Fine, but you cannot use xtlogit or xtprobit if your outcome is not binary. Maybe you are thinking about ordered logit or ordered probit? In which case, see

help xtologit
help xtoprobit

which fit random effects ordered logit and probit, respectively.

[Farhad Mammadov]

Sorry, yes i actually meant xtologit and xtoprobit by saying a combination of probit/logit with RE model. What would be more optimal in my case? To continue with basic FE/RE models or switch to xtologit/xtoprobit ? thanks

[Andrew Musau]

With an 11 point scale, I don't think that it makes much of a difference that you consider the outcome as continuous instead of ordinal. You can compare the results and if there are small differences, stick to the linear estimator and use a Hausman test to choose between fixed and random effects.

[Farhad Mammadov]

Understood, thank you for your help Andrew, greatly appreciated.