Page 371 - Contributed Paper Session (CPS) - Volume 6

CPS1969 Janna M. De Veyra
3.3 Both y and z have 5 categories
Unlike in the first two sections, the size of the test when both y and z have 5
categories will be correctly sized even without the application of the bootstrap
procedure in the test when random error was included in the imputation.
Though the application of bootstrap procedure would still produce a correctly
sized test upon the inclusion of random error in the imputation, the test has a
higher power when bootstrap procedure was not applied. Similar as in the first
two sections, power in this case slightly increases when MCMC was applied in
the imputation.

Table 3. Average Size and Power of the Test when both y and z have 5 categories
Regression MCMC Regression Stochastic MCMC Stochastic

Imputation Imputation Imputation Imputation
Evaluation w/o Bootstrap Bootstrap within Bootstrap across w/o Bootstrap Bootstrap within Bootstrap across w/o Bootstrap Bootstrap within Bootstrap across w/o Bootstrap Bootstrap within Bootstrap across

Power 0.61 0.53 0.43 0.61 0.54 0.43 0.80 0.61 0.38 0.82 0.61 0.38
Size 0.55 0.39 0.16 0.54 0.39 0.16 0.03 0.00 0.00 0.03 0.00 0.00

4. Discussion and Conclusion
This paper analyzed the effect of matching categorical variables to test for
their independence using different simulation scenario on these matching
techniques (1) Logistic Regression, (2) MCMC on Logistic Regression, (3)
Logistic Regression with the inclusion of random error, and (4) MCMC on
Logistic Regression with the inclusion of random error. The test here is to be
obtained by (1) not resampling from the synthetic data (without bootstrap),
(2) resampling with replacement within the synthetic data (bootstrap within),
and (3) resampling with replacement across the synthetic data (bootstrap
across). These methods were evaluated by computing for the size and power
of the test.
Simulation shows that the use of MCMC slightly increases the power of the
test. The increase in power can evidently be seen when random error was
included in the imputation model. Bootstrap, on the other hand, produces a
correctly sized test when applied in an imputation procedure that has a
random error in the model. Among the two bootstrap approaches that were
considered, bootstrap within yields a higher power than bootstrap across.
However, when the variables of interest both have 5 categories, the test is
already correctly sized upon the inclusion random error in the model even
without applying the bootstrap procedure. Hence, it is safe to say that the
bootstrap procedure is more useful when the number of categories for both y
and z is small.

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