Data in the form of counts or proportions often exhibit more
variability than that predicted by a Poisson or binomial
distribution. Many different models have been proposed to account
for extra-Poisson or extra-binomial variation. A simple model
includes a single heterogeneity factor (dispersion parameter) in the
variance. Other models that allow the dispersion parameter to vary
between groups or according to a continuous covariate also exist but
require a more complicated analysis. This thesis is concerned with
(1) understanding the consequences of using an oversimplified model
for overdispersion, (2) presenting diagnostic tools for detecting the
dependence of overdispersion on covariates in regression settings for
counts and proportions and (3) presenting diagnostic tools for
distinguishing between some commonly used models for overdispersed
data.
The double exponential family of distributions is used as a
foundation for this work. A double binomial or double Poisson
density is constructed from a binomial or Poisson density and an
additional dispersion parameter. This provides a completely
parametric framework for modeling overdispersed counts and
proportions.
The first issue above is addressed by exploring the properties
of maximum likelihood estimates obtained from incorrectly specified
likelihoods. The diagnostic tools are based on a score test in the
double exponential family. An attractive feature of this test is
that it can be computed from the components of the deviance in the
standard generalized linear model fit. A graphical display is
suggested by the score test. For the normal linear model, which is a
special case of the double exponential family, the diagnostics reduce
to those for heteroscedasticity presented by Cook and Weisberg
(1983). / Graduation date: 1990
| Identifer | oai:union.ndltd.org:ORGSU/oai:ir.library.oregonstate.edu:1957/38199 |
| Date | 18 August 1989 |
| Creators | Ganio-Gibbons, Lisa M. |
| Contributors | Schafer, Daniel W. |
| Source Sets | Oregon State University |
| Language | en_US |
| Detected Language | English |
| Type | Thesis/Dissertation |
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