Page 318 - Contributed Paper Session (CPS) - Volume 7

CPS2110 Johann Sebastian B. C. et al.
An issue with the regression-based test is how the extra-Poisson variation
will be modelled.An overdispersed count distribution is often assumed prior
to formally testing for overdispersion because the variance is not directly
observed. This makes the variance model in (3) prone to misspecification
because () can be made arbitrary for as long as the variance remains
positive – a misspecified variance model also has negative effects on the
Poisson model regression model where, similar to the consequences of
overdispersion, the standard errors might also be incorrect, leading to
erroneous inferences.

2. Methodology
Primarily, the variance can be misspecified in the model; consequently, the
test statistic may also be affected, as well as the testing procedure itself.
Moreover, there are multiple scenarios leading to misspecification of the
variance. Thus, to answer the research questions, given these scenarios, this
research was designed as a simulation study on the current methodology of
Cameron and Trivedi’s test for overdispersion (1990) by:

Four forms of the variance models will be used:
 Constant: ( )=

 Linear: ( )=

2
 Quadratic: ( )=

 Polynomial: ( ) =

To facilitate the simulation of overdispersed counts whose variance follows the
form in Equation (2), the Functional Negative Binomial (NB-F) distribution,
proposed by Claveria (2016) as a generalization of the Polynomial Negative
Binomial (NB-P) model (Greene, 2008), was used for simulating :

For the different scenarios of the variance, the following forms of () are
used:
 Equidispersed: ( ) = 0

 Weakly overdispersed: ( ) = 0.25 + 0.2 0.5

 Strongly overdispersed:( )= 2.75 + 2.75 2.5

 Transcendental overdispersion: ( ) = ln(1 + )

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