Stata Technical Bulletin
21
requested any combination of tests by combining options or requested all possible tests with the single command: mlogtest,
all.
Tests of independent variables
We first conduct a LR test for each independent variable.
. mlogtest, Ir
**** Likelihood-ratio tests for independent variables
Ho: All coefficients associated with given variable(s) are 0.
|
kidvalue I |
chi2 |
df |
P>chi2 |
|
---------+— |
23.εεs |
3 |
— 0.000 |
|
black I |
7.231 |
3 |
o.oβε |
|
Othrrace I |
51.944 |
3 |
o.ooo |
|
degree I |
211.133 |
3 |
o.ooo |
|
anykids I |
2.323 |
3 |
o.εo8 |
For example, we can reject the hypothesis that gender does not affect the values considered important for children at the .01
level, or the effect of gender is significant (p < .01). Next, we conduct a Wald test for each independent variable. We also use
the set option to test the hypothesis that the coefficients for the two dummy variables indicating race are simultaneously equal
to zero.
. mlogtest, «aid set(black Othrrace)
**** Wald tests for independent variables
Ho: All coefficients associated with given variable(s) are 0.
|
kidvalue I |
chi2 |
df |
P>chi2 |
|
---------+— |
— | ||
|
female I |
23.431 |
3 |
0.000 |
|
black I |
7.317 |
3 |
0.062 |
|
Othrrace I |
34.177 |
3 |
0.000 |
|
degree I |
174.002 |
3 |
0.000 |
|
anykids I |
2.339 |
3 |
0.501 |
|
set_l: I |
60.988 |
6 |
0.000 |
black I
Othrrace I
Tests of IIA
Either the Hausman or Small-Hsiao tests can be used to test the IIA assumption. We begin with the Hausman test. The
base option specifies that all tests should be computed using the most frequently observed remaining category as the base value;
see Methods and formulas for details. We do not use the detail option, which provides all of the output from the successive
calls to Stata’s hausman command.
. mlogtest, hausman base
**** Hausman tests of IIA assumption
Ho: OddsCOutcome-J vs Outcome-К) are independent of other alternatives.
|
Omitted I |
chi2 |
df |
P>chi2 |
evidence |
|
— | ||||
|
obey I |
7.764 |
12 |
0.803 |
for Ho |
|
Workhard I |
-4.090 |
12 |
— |
for Ho |
|
helpoth I |
9.154 |
12 |
0.690 |
for Ho |
|
thnkself I |
884.043 |
12 |
0.000 |
against Ho |
Note: If chi2<0, the estimated model does not
meet asymptotic assumptions of the test.
Note the considerably different results depending on the category considered. In our experience, negative test statistics are very
common; Hausman and McFadden (1984, 1226) note this possibility and conclude that a negative result is evidence that IIA has
not been violated. When we run Small-Hsiao tests, we see that these results vary considerably from those of the Hausman tests.
. mlogtest, smhsiao base