Generally-Altered, -Inflated and -Truncated Regression,
With Application to Heaped and Seeped Counts


Zero-altered, -inflated and -truncated count regression are now well
established, especially for Poisson and binomial parents.  Recently
these methods were extended to Generally-Altered, -Inflated and
-Truncated Regression (GAIT regression) and implemented in the VGAM
R package for three 1-parameter families.  In GAIT regression the
three operators apply to general sets rather than {0}.  Also, the
three operators may appear simultaneously in a single model.
Elements of the three mutually disjoint sets of support values are
called 'special'. Parametric and nonparametric variants are
proposed: the latter based on the multinomial logit model (MLM), and
the former on a finite mixture of the parent distribution on nested
or partitioned support.  The resultant "GAIT Mix-MLM combo" model
has five special value types. GAIT regression offers much potential
for the analysis of heaped (digit preference due to self-reporting)
and seeped data.

This project is consolidate the above and to investigate some
extensions. Some specific examples include:

1. Find new data sets from a wide range of fields exhibiting heaping
and seeping.  Perform some analyses.

2. Find any bugs in the software. Suggest any improvements (such as
initial values) and additions.

3. Marginal effects: extend margeff() to compute the first
derivatives of the MLM terms.

4. Find data sets that are underdispersed with respect to the
Poisson. Apply the GT-Expansion method of analysis.

Ideally, a student working on this project would have strong
computational skills and a solid understanding of generalized linear
models (GLMs; e.g., STATS 330 & 310).


Contact: Thomas Yee (t.yee@auckland.ac.nz)