Two-level random-slope model

[Dan Murphy]

Dear Statalist community,

I am using a two-level random-slope model and using the Bangladesh dataset as an example for my question.

use http://www.stata-press.com/data/r15/bangladesh
melogit c_use i.urban || district: urban

I am looking for advice on how to extract the estimate (that incorporates the fixed and random effects) and standard error of urban for each district.

Many thanks.

[Clyde Schechter]

predict u*, reffects reses(v*)
des u* v*
gen urban_effect = _b[c_use:1.urban] + u1
// AND THE STANDARD ERROR IS IN v1

[Erik Ruzek]

Clyde's solution is spot on. Stepping back a bit, when estimating models with random slopes, analysts often allow the random effects to covary. Whether this is appropriate for the data can be evaluated by the use of a likelihood ratio test. In this case, the model fit of the model with an unstructured variance-covariance matrix for the random effects provides a better fit to the data.

melogit c_use i.urban || district: urban
est sto no_cov

predict u*, reffects reses(v*)
des u* v*
gen urban_effect = _b[c_use:1.urban] + u1

melogit c_use i.urban || district: urban, cov(un)
est sto cov

predict uc*, reffects reses(vc*)
des uc* vc*
gen urban_effect_c = _b[c_use:1.urban] + uc1

*test of model fit
lrtest cov no_cov, stats 

Likelihood-ratio test                                 LR chi2(1)  =     12.29
(Assumption: no_cov nested in cov)                    Prob > chi2 =    0.0005

Akaike's information criterion and Bayesian information criterion

-----------------------------------------------------------------------------
       Model |          N   ll(null)  ll(model)      df        AIC        BIC
-------------+---------------------------------------------------------------
      no_cov |      1,934          .  -1249.223       4   2506.446   2528.716
         cov |      1,934          .  -1243.079       5   2496.158   2523.994
-----------------------------------------------------------------------------

Comparing the estimates of the two different urban_effect variables, the distribution of predictions varies non-trivially. Accordingly, think carefully about which set of predictions are more relevant for your situation.

sum urban_effect*

    Variable |        Obs        Mean    Std. Dev.       Min        Max
-------------+---------------------------------------------------------
urban_effect |      1,934     .665147    .2960627   -.117348   1.376067
urban_effe~c |      1,934    .7398765    .5705939  -.8973983   1.991332

[Dan Murphy]

Thank you very much, Clyde and Erik.