96JCGS03\P0209-------------------------------------------------
Exact Tests for Interaction in Several $2\times 2$ T
Karim F. Hirji, Stein E. Vollset, Isildinha M. Reis,
and Abdelmonem A. Afifi
The investigation of interaction in a series of $2 \times 2$ tables
is warranted in a variety of research endeavors. Though many
large-sample approaches for such investigations are available, the
exact analysis of the problem has been formulated for the
probability statistic only. We present several alternative
statistics applicable in this context. We also give an efficient
polynomial multiplication algorithm to compute exact distributions
and tail areas for the family of stratum-additive statistics.
Besides the probability statistic, these include the score,
likelihood ratio, and other statistics. In addition to comparing,
in empirical terms, the diverse computational strategies for exact
interaction analysis, we also explore the theoretical linkages
between them. Data from published papers are used for illustration.
Key Words: Exact inference; Fast Fourier transform; Network algorithm;
Polynomial multiplication algorithm; Test of homogeneity.
96JCGS03\P0225---------------------------------------------------
An Algorithm for Isotonic Regression on Ordered Rectangular Grids
Shixian Qian and William F. Eddy
In this article, we give an algorithm for isotonic regressions on
ordered rectangular grids. The running time of the algorithm is no
more than cubic in the number of grid points. This algorithm makes
bivariate isotonic regression a practical choice for some data
analysis.
Key Words: Block class algorithm; Monotone regression; Recursive
partitioning; Sandwich algorithm.
96JCGS03\P0236---------------------------------------------------
Randomized Quantile Residuals
Peter K. Dunn and Gordon K. Smyth
In this article we give a general definition of residuals for
regression models with independent responses. Our definition
produces residuals that are exactly normal, apart from sampling
variability in the estimated parameters, by inverting the fitted
distribution function for each response value and finding the
equivalent standard normal quantile. Our definition includes
some randomization to achieve continuous residuals when the
response variable is discrete. Quantile residuals are easily
computed in computer packages such as SAS, S-Plus, GLIM, or
LispStat, and allow residual analyses to be carried out in
many commonly occurring situations in which the customary
definitions of residuals fail. Quantile residuals are applied
in this article to three example data sets.
Key Words: Deviance residual; Exponential regression; Generalized
linear model; Logistic regression; Normal probability plot;
Pearson residual.
96JCGS03\P0245----------------------------------------------------
Risks of Using Improper Priors with Gibbs Sampling and
Autocorrelated Errors
Judy L. Palmer and Lawrence I. Pettit
In this article we examine the use of Gibbs sampling to estimate the
autocorrelation coefficient in a linear regression model.
Researchers had previously experienced difficulty with
moderate-to-high positive autocorrelated errors; estimates could be
unstable and sometimes failed to converge. We show that the cause
of this problem is that the use of an improper prior leads to an
improper posterior, although the conditionals are proper, and hence
a formal Gibbs sampler can be constructed. The problem is solved by
the use of a vague but proper prior. In this simple case many of
the calculations can be done analytically and it serves as a warning
as to the uncritical use of improper priors with Gibbs sampling.
Key Words: Autocorrelation; Noninformative prior; Vague prior.
96JCGS03\P0250----------------------------------------------------
Recent Developments and Future Directions in LispStat
Luke Tierney
Lisp\_Stat is an extensible statistical computing environment based
on the Lisp language. The system is currently being revised on the
basis of experience gained from several years of use. This article
outlines some of the changes that have been completed and others
that are under consideration.
96JCGS03\P0263------------------------------------------------------
Extensible Statistical Software: On a Voyage to Oberon
G\"{u}nther Sawitzki
Recent changes in software technology have opened new possibilities
for statistical computing. Conditions for creating efficient and
reliable extensible systems have been largely improved by
programming languages and systems that provide dynamic loading
and type-safety across module boundaries, even at run time. We
introduce Voyager, an extensible data analysis system based on
Oberon, which tries to exploit some of these possibilities.
Key Words: Extensibility; Object-oriented programming; Software portability;
Statistical software.
96JCGS03\P0284-------------------------------------------------------
Extensible Software Systems in Oberon
Johannes L. Marais
Extensible software systems play an important role in prototyping
environments where a fast compile-and-test turnaround is required.
Typically, extensible software systems combine ways to reuse code,
an approach to object-oriented programming, and ways to preserve
state from one session to another. In this article we introduce
the Oberon system from the perspective of an extensible system.
In Oberon, the stated requirements manifest themselves as separate
hierarchies related to modularity, the type system, run-time
system organization, and persistency. We discuss issues related
to these hierarchies and the approaches selected in Oberon for their
implementation. The article is mainly a short introduction to
Oberon and a summary of what has been accomplished with this system.
Key Words: Extensible software systems; Oberon; Object-oriented
programming; Software components; User interfaces.
96JCGS03\P0299---------------------------------------------------
R: A Language for Data Analysis and Graphics
Ross Ihaka and Robert Gentleman
In this article we discuss our experience designing and implementing
a statistical computing language. In developing this new language,
we sought to combine what we felt were useful features from two
existing computer languages. We feel that the new language provides
advantages in the areas of portability, computational efficiency,
memory management, and scoping.
Key Words: Computer language; Statistical computing.