* Philip Paolino, "Maximum Likelihood Estimation of Models with
*    Beta-Distributed Dependent Variables", Political Analysis,
*    Vol. 9, 2001, pp. 325-346.
* Table 5 - OLS vs. Beta estimation, page 340.
SAMPLE 1 140
READ (soss.txt) year scostfam sbvalue sdemgovt secon sflabor &
   swash sgcfound sapps year1991 year1992 id sort

GENR Y=sgcfound/100
* OLS estimation - Column 1 of Paolino, Table 5, page 340.
* The GF option reports tests for normality.
OLS Y scostfam sbvalue sapps sflabor secon sdemgovt &
   year1991 year1992 / GF
* Test for heteroskedasticity
DIAGNOS / HET NOWHITE
* Calculate the mean squared error
GEN1 MSE=$SSE/$N
PRINT MSE

* Proportions data - bounded by 0 and 1.
GENR sgcfs=sgcfound*100/10001

* MLE estimation - beta distribution with the mean and variance
* specified as functions of the X variables.
* Column 3 of Paolino, Table 5, page 340.
MLE sgcfs scostfam sbvalue sapps sflabor secon sdemgovt &
   year1991 year1992 / TYPE=MBETA NUMERIC

* The independent variables for the variance function are
* specified in brackets.
* Column 5 of Paolino, Table 5, page 340.
MLE sgcfs scostfam sbvalue sapps sflabor secon sdemgovt &
   year1991 year1992 (sbvalue sapps) / TYPE=MBETA NUMERIC
* Note: The start of the estimation output gives the warning:
*    ...MATRIX INVERSION FAILED IN ROW   10
*    ...RESULTS MAY BE UNRELIABLE
* In any nonlinear estimation, the matrix inversion could
* fail at one of the iterations. As long as it does not
* fail at the final iteration, the results should be reliable.
STOP