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st: Problem interpreting results from xttobit


From   Michael E Roettger <meroett@bgsu.edu>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   st: Problem interpreting results from xttobit
Date   Fri, 10 Oct 2008 09:58:23 -0400

Dear STATA list,

I am trying to determine if my (i) regression results are valid using xttobit and (ii) how to interpret my results due to
a major shift in likelihood functions.

I have been using a random effects tobit model to a measure left-censored variable [a propensity to commit
delinquent acts among a panel of respondents].  My initial model provides negative log-likehood with an individual-level random effect that seems reasonable:


>Random-effects tobit regression                 Number of obs      =      2401
>Group variable: aid                             Number of groups   =       804
>Random effects u_i ~ Gaussian                   Obs per group: min =         2
>                                                               avg =       3.0
>                                                               max =         3
>                                                Wald chi2(3)       =     91.53
>Log likelihood  = -4211.3782                    Prob > chi2        =    0.0000
.
.
.
>   /sigma_u |   2.079586   .2733142     7.61   0.000       1.5439    2.615272
>   /sigma_e |   5.835778   .1588994    36.73   0.000     5.524341    6.147215
>-------------+----------------------------------------------------------------
>         rho |   .1126776   .0284796                      .0662654    .1786233
>------------------------------------------------------------------------------


However, after adding several variables, the log-likelihood becomes highly positive and the
individual-level random effect that is of the order of E-39


>Random-effects tobit regression                 Number of obs      =      2294
>Group variable: aid                             Number of groups   =       768
>
>Random effects u_i ~ Gaussian                   Obs per group: min =         2
>                                                               avg =       3.0
>                                                               max =         3
>
>                                                Wald chi2(9)       =    300.30
>Log likelihood  =  52807.689                    Prob > chi2        =    0.0000
.
.
.
>   /sigma_u |   4.17e-39   1.06e-40    39.19   0.000     3.96e-39    4.38e-39
>    /sigma_e |   5.793114    .140685    41.18   0.000     5.517377    6.068852
>-------------+----------------------------------------------------------------
>         rho |   5.19e-79   3.65e-80                      4.52e-79    5.95e-79
>------------------------------------------------------------------------------


Both models converge to a concave solution and I am estimating about 35 quadrature points for the
Gauss-Hermite function.   Other than the random effects, the estimated coefficients for Beta's are
consistent with theory/prior research. Its just the change in likelihood and a highly significant random effect
near zero from the first to the second models above that leave me scratching my head.

Thanks for your time and help!

Mike Roettger

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