xtprobit random effects negative variance

[Max Resende]

Dear all stata users,

I have several variables that explains the state (approved (aprov)=1; not approved (aprov)=0) for a student i in grade (1or 2) at time t.

Because the way of my dataset is set, I cannot run fixed effects once I have students that only appears once (one year). So, I am running a xtprobit random effect model in order to identify the presence of unexplained heterogeneity between students.

My estimation is giving me a negative variance random effects model and I don't know why. As I read on Stata forun one reason of that, may be because I have regression disturbances are serially correlated.

So, I have a few questions in order to understand my results:

1) Is negative variance possible? It dosen't make sense to me.
2) How can I fix it?
3) How can i interpretate the /lnsig2u values and signal?

I have posted bellow my codes and data.

Thank you all

Max

* Define panel data

xtset i t

* Teste para efeitos aleatórios LM

* Estimar efeito aleatório

*FS1

xtprobit aprov menino branco rural bolsa lnpib_pc e_biblio i_funcionarios_razao prof_idade alunos_turma

*FS2

xtprobit aprov menino branco rural bolsa lnpib_pc e_biblio i_funcionarios_razao prof_idade alunos_turma e_preescolar e_fundamental

----------------------- copy starting from the next line -----------------------

* Example generated by -dataex-. To install: ssc install dataex
clear
input double(t i serie) float(aprov menino branco rural bolsa lnpib_pc) double e_biblio float i_funcionarios_razao double(prof_idade alunos_turma e_preescolar e_fundamental)
2009  1 1 1 1 1 1 0  9.625462 0 2.1891892 37.71 12 1 1
2010  1 2 1 1 1 1 0 10.060905 0 2.5135136 37.71 30 1 1
2008  2 1 1 0 1 0 0  9.437439 1   6.66129  42.3 23 1 1
2009  2 2 1 0 1 0 0  9.574466 1  7.709677  42.3 33 1 1
2009  3 1 . 1 1 1 0  9.625462 1  5.391304 39.25 23 1 1
2010  4 1 1 0 1 0 0 10.060905 1  5.565217 39.25 30 1 1
2011  4 2 1 0 1 0 0  9.949522 1  5.652174 39.25 30 1 1
2011  5 1 . 1 1 0 0 10.373494 1 10.588235  43.8 26 1 1
2009  6 1 0 0 0 0 0  10.15323 1 10.255555 49.04 29 1 0
2010  6 1 1 0 0 0 0 10.373487 1      10.8 49.04 31 1 0
2011  6 2 0 0 0 0 0  10.41702 1 11.055555 49.04 29 1 0
2012  6 2 . 0 0 0 0  10.37931 1  10.82353  43.8 16 1 1
2009  7 1 1 1 1 0 0 10.176663 1 14.724638 43.12 34 1 1
2010  7 2 . 1 1 0 0  10.27858 1 16.144928 43.12 15 1 1
2009  8 1 1 0 1 0 0 10.204742 1      10.3 42.15 20 1 0
2010  8 2 1 0 1 0 0  9.868883 1 3.9411764 43.96 27 1 1
2009  9 1 1 1 1 0 0 10.176663 1   3.40625  41.3 17 1 1
2010  9 2 1 1 1 0 0  10.27858 1    4.1875  41.3 17 1 1
2009 10 1 1 1 1 0 0 10.176663 1         9  43.8 24 1 1
2010 10 2 1 1 1 0 0  10.27858 1  11.82353  43.8 31 1 1
2009 11 1 1 0 1 0 0 10.176663 1         9  43.8 24 1 1
2010 11 2 1 0 1 0 0  10.27858 1  11.82353  43.8 24 1 1
2009 12 1 1 0 1 0 0 10.176663 1  7.057471 43.93 19 1 1
2010 12 2 1 0 1 0 0  10.27858 1  8.678161 43.93 24 1 1
2009 13 1 1 1 1 0 0 10.176663 1         9  43.8 19 1 1
2010 13 2 1 1 1 0 0  10.27858 1  11.82353  43.8 31 1 1
2010 14 1 1 1 1 0 0  10.27858 1  11.82353  43.8 21 1 1
2011 14 2 1 1 1 0 0 10.373494 1 10.588235  43.8 28 1 1
2009 15 1 1 1 1 0 0 10.198914 1  11.72549 40.32 28 1 1
2010 15 2 1 1 1 0 0  9.927378 0  4.129032 41.83 27 1 1
2012 16 1 . 1 1 0 0  10.37931 1         9 43.93 37 1 1
2008 17 1 1 0 1 0 0 10.207653 1  10.47059  43.8 18 1 1
2009 17 2 1 0 1 0 0 10.176663 1         9  43.8 18 1 1
2008 18 1 1 1 1 0 0 10.207653 1  10.47059  43.8 19 1 1
2009 18 2 1 1 1 0 0 10.176663 1  7.057471 43.93 15 1 1
2008 19 1 1 1 1 0 0 10.207653 1  10.47059  43.8 34 1 1
2009 19 2 1 1 1 0 0 10.176663 1         9  43.8 14 1 1
2008 20 2 1 1 1 0 0 10.207653 1  6.965517 43.93 28 1 1
2012 21 1 . 0 1 0 0 10.173985 1 2.1754386    52 22 1 1
2009 22 2 1 1 1 0 0  9.970919 1 10.941176 43.45 17 1 0
2008 23 1 . 1 1 0 0  9.621763 1 15.790322 41.74 21 1 1
2008 24 1 1 0 1 0 0 10.207653 1  10.47059  43.8 34 1 1
2009 24 2 1 0 1 0 0 10.176663 1         9  43.8 14 1 1
2008 25 1 1 0 1 0 0 10.207653 1  10.47059  43.8 19 1 1
2009 25 2 1 0 1 0 0 10.176663 1         9  43.8 18 1 1
2008 26 1 1 0 1 0 0 10.190008 1 10.644444 49.04 24 1 0
2009 26 2 1 0 1 0 0  10.15323 1 10.255555 49.04 27 1 0
2008 27 1 1 1 1 0 0 10.207653 1   3.09375  41.3 19 1 1
2009 27 2 1 1 1 0 0 10.176663 1   3.40625  41.3 17 1 1
2009 28 2 1 1 1 0 0 10.176663 1   3.40625  41.3 35 1 1
2008 29 1 1 0 1 0 0 10.207653 1  10.47059  43.8 19 1 1
2009 29 2 1 0 1 0 0 10.176663 1         9  43.8 18 1 1
2012 30 1 . 0 1 0 0 10.430882 1 4.7073865 42.75 36 1 1
2008 31 1 1 1 1 0 0   9.82471 0  8.173077 42.74 33 1 1
2009 31 2 1 1 1 0 0  9.856041 0  7.884615 42.74 37 1 1
2009 32 1 1 0 1 0 0  10.14595 1  4.159091 40.21 27 1 1
2010 32 2 1 0 1 0 0    10.166 1       4.5 40.21 22 1 1
2009 33 1 1 0 1 0 0 10.176663 1 4.4693875 45.74 27 1 1
2010 33 2 . 0 1 0 0  10.27858 1  5.979592 45.74 41 1 1
2008 34 1 . 1 1 0 0 10.207653 1  6.965517 43.93 16 1 1
2009 35 1 1 0 1 0 0  10.15323 1  2.953488 43.54 17 1 1
2010 35 2 . 0 1 0 0 10.373487 1  3.744186 43.54 21 1 1
2008 36 1 0 0 1 0 0  9.621763 1 15.790322 41.74 20 1 1
2009 36 1 1 0 1 0 0  9.699168 1 14.887096 41.74 19 1 1
2010 36 2 1 0 1 0 0 10.051065 1 19.096775 41.74 33 1 1
2010 37 1 0 1 1 0 0  10.27858 1  11.82353  43.8 21 1 1
2011 37 1 . 1 1 0 0 10.373494 1 10.588235  43.8 26 1 1
2008 38 1 . 0 1 0 0 10.207653 1  10.47059  43.8 18 1 1
2010 39 2 0 0 1 0 0 10.206867 1  3.090909 42.86 28 1 1
2011 39 2 1 0 1 0 0 10.220284 1   2.69697 42.86 28 1 1
2011 40 1 . 1 1 0 0 10.220284 1   2.69697 42.86 16 1 1
2008 41 2 1 0 1 0 0   11.5715 1 13.346154 43.54 27 1 1
2009 42 1 1 0 1 0 0  9.699168 1      8.29 44.08 20 0 0
2010 42 2 1 0 1 0 0 10.051065 1 19.096775 41.74 29 1 1
2009 43 1 1 0 1 1 0 10.361177 0  5.085714  39.8 12 1 1
2010 43 2 . 0 1 1 0 10.724752 0  5.057143  39.8 22 1 1
2010 44 1 0 1 1 0 0  10.99051 1  12.76923 43.54 37 1 1
2011 44 1 . 1 1 0 0 11.143866 1  5.139535 40.89 12 1 1
2010 45 2 1 0 1 1 0 10.373487 1      10.8 49.04  1 1 0
2009 46 1 0 0 1 0 0  9.739263 1  3.030303 42.86 18 1 1
2010 46 1 1 0 1 0 0 10.206867 1  3.090909 42.86 26 1 1
2011 46 2 1 0 1 0 0 10.220284 1   2.69697 42.86 28 1 1
2009 47 1 1 0 1 0 0  9.739263 1  3.030303 42.86 18 1 1
2010 47 2 0 0 1 0 0 10.206867 1  3.090909 42.86 28 1 1
2011 47 2 1 0 1 0 0 10.220284 1   2.69697 42.86 28 1 1
2009 48 1 1 1 1 1 0  9.739263 1  3.030303 42.86 18 1 1
2010 48 2 1 1 1 1 0 10.206867 1  3.090909 42.86 28 1 1
2010 49 1 . 0 1 0 0 10.373487 1      10.8 49.04 27 1 0
2009 50 1 0 1 0 0 0  10.15323 1 10.255555 49.04 23 1 0
2010 50 1 0 1 0 0 0 10.373487 1      10.8 49.04 28 1 0
2011 50 1 1 1 0 0 0  10.41702 1 11.055555 49.04 24 1 0
2012 50 2 . 1 0 0 0 10.430882 1  10.21111 49.04 31 1 0
2008 51 2 1 0 1 0 0 10.190008 1 10.644444 49.04 24 1 0
2010 52 2 0 1 1 0 0 10.373487 1      10.8 49.04 25 1 0
2011 52 2 1 1 1 0 0  10.41702 1 11.055555 49.04 28 1 0
2009 53 1 1 0 1 0 0  10.15323 1 10.255555 49.04 23 1 0
2010 53 2 1 0 1 0 0 10.373487 1      10.8 49.04 21 1 0
2008 54 1 . 1 1 0 0 10.207653 1 2.4158416 46.14 16 1 1
2009 55 1 1 0 1 0 0  10.15323 1 10.255555 49.04 24 1 0
2010 55 2 . 0 1 0 0 10.373487 1      10.8 49.04 30 1 0
end

[Phil Bromiley]

While negative variances are possible in some ml estimators (termed heywood cases in SEM), I suspect your problem is misinterpreting the output.

When I run your data and program, I see a positive estimate of sigma_u and a negative estimate of the log of the variance (/lnsign2u). That's fine - logs of numbers below 1 are negative. However, in the data you sent, the LR test suggests you don't need the panel effects anyway - the test is quite insignificant, which is consistent with an estimate of sigma_u that is very close to 0 (.000787).