22
Stata Technical Bulletin
STB-58
**** Small-Hsiao tests of IIA assumption
Ho: OddsCOutcome-J vs Outcome-К) are independent of other alternatives.
|
Omitted I |
InL(full) |
InL(omit) |
chi2 |
df |
P>chi2 |
evidence |
|
---------+- obey I |
-1041.535 |
-1039.193 |
4.683 |
6 |
0.585 |
for Ho |
|
workhard I |
-1107.167 |
-1103.476 |
7.381 |
6 |
0.287 |
for Ho |
|
helpoth I |
-1178.179 |
-1175.128 |
6.101 |
6 |
0.412 |
for Ho |
|
thnkself I |
-744.697 |
-740.162 |
9.069 |
6 |
0.170 |
for Ho |
Since the Small-Hsiao test is based on the creation of random half-samples from one’s data, the test may differ substantially
with successive calls of the command. For example, when we run the tests again, we obtain
. mlogtest, smhsiao base
**** Small-Hsiao tests of IIA assumption
Ho: OddsCOutcome-J vs Outcome-К) are independent of other alternatives.
|
Omitted I |
InL(full) |
InL(omit) |
chi2 |
df |
P>chi2 |
evidence |
|
obey I |
-1098.851 |
-1089.556 |
18.589 |
6 |
0.005 |
— against Ho |
|
workhard I |
-1164.440 |
-1153.210 |
22.459 |
6 |
0.001 |
against Ho |
|
helpoth I |
-1169.482 |
-1165.634 |
7.695 |
6 |
0.261 |
for Ho |
|
thnkself I |
-786.601 |
-774.531 |
24.141 |
6 |
0.000 |
against Ho |
The set seed command can be used before mlogtest in a do-file to have it produce the same results with each successive
run. For example, set seed 339487731.
Tests for combining dependent categories
Finally, we test whether the independent variables differentiate pairs of outcome categories using a Wald test. Note that all
pairs of outcomes have been evaluated.
. mlogtest, combine
**** Wald tests for combining outcome categories
Ho: All coefficients except intercepts associated with given pair
of outcomes are 0 (i.e., categories can be collapsed).
|
Categories tested I |
chi2 |
df |
P>chi2 |
|
——————————————————⅛-- Obey-Workhard I |
81.629 |
5 |
— 0.000 |
|
obey- helpoth I |
31.332 |
5 |
0.000 |
|
obey-thnkself I |
167.265 |
5 |
0.000 |
|
Workhard- helpoth I |
19.637 |
5 |
0.001 |
|
workhard-thnkself I |
79.317 |
5 |
0.000 |
|
helpoth-thnkself I |
65.716 |
5 |
0.000 |
Alternatively, LR tests can be computed with the Ircomb option as in the next example.
. mlogtest, Ircom
**** LR tests for combining outcome categories
Ho: All coefficients except intercepts associated with given pair
of outcomes are O (i.e., categories can be collapsed).
|
Categories tested I |
chi2 |
df |
P>chi2 |
|
—— — ——— — ——— — ——— ———-⅛-- Obey-Workhard I |
89.431 |
5 |
— 0.000 |
|
obey- helpoth I |
32.089 |
5 |
0.000 |
|
Obeythnkself I |
212.672 |
5 |
0.000 |
|
Workhard- helpoth I |
20.523 |
5 |
0.001 |
|
workhard-thnkself I |
80.259 |
5 |
0.000 |
|
helpoth-thnkself I |
70.485 |
5 |
0.000 |
As with the Wald and LR tests for each independent variable, the two tests for combining categories generally provide very
similar results, although many researchers prefer the LR test.
Overall, these examples illustrate that mlogtest makes it very simple to compute many tests. At the risk of repetition, we
note that it is not our intention to encourage researchers to combine categories or delete variables without careful consideration
of the substantive issues related to the research.