Computing optimal sampling designs for two-stage studies



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

---------+
female I

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



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