Dear Statalist,

I am using Stata 15.1 and I am estimating a three level model (time nested in firms nested in regions). My question is about how to interpret an empty model (with random intercepts for firms and regions) reporting that regional random intercept is not necessary (LR test confirm that random effect for region is not significant), but when including firms as well as regional predictors, the regional ones are highly significant.
Does this mean that the conclusion from the empty model is that I should not include any regional characteristic? Or does this mean that there is not regional random effect, and thus I should use xtlogit (my dependent is a dummy variable) and include regional predictors? With regard to the latest question: I imagine that standard errors should be corrected using cluster(region), but xtlogit does not allow this option (only xtreg), what to do then? I am very confused with respect to include or not regional predictors since they are very significant, even though the empty model says that the region (as a level) is not significant.

The other question is how to replicate in Stata a graph like the one below. As you can see, the "y" variable (aggregated trust) is captured in three time periods for different regions, and it is ordered (in the horizontal axis, even though it is not shown) by the variable "x" which is inequality in 1980. This show a negative association between regions with higher inequality showing lower trust. I give you a dataex example of my data below, for if you can help me with this, it will be much appreciated.


Array

Code:
* Example generated by -dataex-. To install: ssc install dataex
clear
input int year float(regionid x y) byte sample
2008 16  6.308918  .20467836 1
2011 16  6.308918   .1985294 1
2014 16  6.308918  .23333333 1
2008  7  .5649685  .19266056 1
2011  7  .5649685   .1632653 1
2014  7  .5649685  .16216215 1
2008 10  4.013527  .15384616 1
2011 10  4.013527  .18487395 1
2014 10  4.013527   .1625616 1
2008  1  4.319562  .13846155 1
2011  1  4.319562   .0886076 1
2014  1  4.319562  .13114753 1
2008 11  .1517857   .0967742 1
2011 11  .1517857   .0882353 1
2014 11  .1517857 .037037037 1
2008  4 .14693877  .04166667 1
2011  4 .14693877          0 1
2014  4 .14693877          0 1
2008  8  1.183995  .13913043 1
2011  8  1.183995  .14678898 1
2014  8  1.183995  .11881188 1
2008  9 16.033205  .25537634 1
2011  9 16.033205  .24547803 1
2014  9 16.033205   .2235294 1
2008  2  1.286149  .20689656 1
2011  2  1.286149   .1612903 1
2014  2  1.286149  .17857143 1
2008 13 18.833364    .154717 1
2011 13 18.833364   .1923077 1
2014 13 18.833364  .11904762 1
2008 15  .5725027  .25454545 1
2011 15  .5725027  .27272728 1
2014 15  .5725027  .14545454 1
2008 12 1.7787274       .192 1
2011 12 1.7787274  .11278196 1
2014 12 1.7787274   .0952381 1
2008  3  .5671447  .10638298 1
2011  3  .5671447        .18 1
2014  3  .5671447   .2162162 1
2008 17         0   .1904762 1
2011 17         0       .125 1
2014 17         0         .2 1
2008  6 1.0164384  .11538462 1
2011  6 1.0164384  .17391305 1
2014  6 1.0164384          0 1
2008 14  .8678223  .19148937 1
2011 14  .8678223   .2244898 1
2014 14  .8678223   .3170732 1
2008  5  .8506494  .06060606 1
2011  5  .8506494          0 1
2014  5  .8506494  .04761905 1
end