### Test Statistics for Dispersion Parameter in Poisson Regression and Generalized Poisson Regression Models

*Veeranun Pongsapukdee, Pairoj Khawsittiwong, Maysiya Yamjaroenkit*

#### Abstract

Two symmetrical distributed test statistics, called Zm and Z0_New are proposed and their goodness-of-fit tests are

compared with other available five test statistics: Wald-t, Score test, Z μ, ZY, and Z0, for overdispersion in Poisson

regression model versus generalized Poisson model. Five thousand data sets in each condition of overdispersion

parameters and sample sizes are simulated to perform the assessment of the models’ fits using those statistics, concerning

the coverage probability and power of tests. Results show that the Zm test performs closely as good a Zμ and ZYtests

but it tend to be better than the others when the sample size is large. Even if the Z0_New test has the largest power;

however, in consideration for coverage probability and power of tests, the Zm test probably be more reliable. The Zm

test statistic is interesting not only in its simplest form, with the reasonable coverage probability and power but also

in its robust property of using median that needs fewer assumptions for its parent distribution.

Key Words: Goodness-of-fit statistics; Coverage probability; Power of tests; Generalized linear models

compared with other available five test statistics: Wald-t, Score test, Z μ, ZY, and Z0, for overdispersion in Poisson

regression model versus generalized Poisson model. Five thousand data sets in each condition of overdispersion

parameters and sample sizes are simulated to perform the assessment of the models’ fits using those statistics, concerning

the coverage probability and power of tests. Results show that the Zm test performs closely as good a Zμ and ZYtests

but it tend to be better than the others when the sample size is large. Even if the Z0_New test has the largest power;

however, in consideration for coverage probability and power of tests, the Zm test probably be more reliable. The Zm

test statistic is interesting not only in its simplest form, with the reasonable coverage probability and power but also

in its robust property of using median that needs fewer assumptions for its parent distribution.

Key Words: Goodness-of-fit statistics; Coverage probability; Power of tests; Generalized linear models

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