Computing optimal sampling designs for two-stage studies



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.



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