An excellent book, Models for Discrete Data, Daniel Zelterman, Oxford Science Publications, ISBN 0-19-852436-6, addresses theory and applications. In keeping with this bolg’s software focus, the point of mentioning his book is the author’s contributed SAS examples. You will find standard and extended applications of SAS’s Proc Genmod in a variety of log-linear model settings using Binomial, Poisson, Hypergeometric and Negative Binomial response models.
Another excellent text is Alan Agresti’s Categorical Data Analysis, Wiley, ISBN 0-471-36093-7. His contributed SAS routines are quite extensive as well.
A careful study of these books and examples will help most any applied researcher with the discrete random variable setting.
Covariance matrices are a natural multivariate structure as input for various methods such as Structural Equations Modeling(SEM), Factor Analysis, Principle Components and Cluster Analysis to name a few. Almost all can be shown to be special cases of SEMs. Recently I came across the need to consider the question of Common Principle Components(CPC). The situation is a k-group setting involving questions about shared principle components among the k-groups. Note, this notion is not restricted to equality of covariance matrices. However this particular notion(CPC) is not directly estimated and tested within common statistical software such as SAS‘s Proc Calis or well known Lisrel. It turns out that this was the focus of statistican Bernhard Flury’s (1988) research. CPC software and references to Flury’s work can be found here.
Univariate Nonparametric tests have been available for some time. Exact Inference for these tests are also an option from software such as STatXact. However multivariate versions of univariate nonparametric tests are harder to come by in most standard statistical software. Oja and Randles’s 2004 paper, Multivariate Nonparametric Tests, Journal of Statistical Science, Vol.19, No. 4 Pg598, addresses the problem and offers an implementation as R routines. Author Oja’s website describes access to the following tests:
Multivariate sign test; Multivariate sign-rank test; Sign test of independence; Spearman’s rho -type test of independence; Kendall’s tau -type test of independence; Several-samples MANOVA multivariate sign test and a Several-samples MANOVA multivariate rank test.
I want to put a plug in for VUE. VUE is not a statistical package, but it can be useful to one’s modelling efforts interested in mapping the relationship between variables, for presentation needs, extensive anotation capabilities, sharing or just brainstorming. How about mapping relationships on competing theories and other complex structures?
The Visual Understanding Environment (VUE) is an Open Source project based at Tufts University. The VUE project is focused on creating flexible tools for managing and integrating digital resources in support of teaching, learning and research. VUE provides a flexible visual environment for structuring, presenting, and sharing digital information
This site is very useful for both research and teaching for all things statistical. What a nice resource. Enjoy.
The generality of Mixed Models(Linear or NonLinear) is well known and has found extensive use in just about every applied research setting in the Social Sciences, Medicine, Engineering and GIS applications. Variations of these methods have been implemented in most major statistical packages. A recent article in Journal of Agricultrural, Biological, and Environmental Statistics( Sept. 2007) by Heegaard and Nilsen discuss theory and application in a biological spatial setting. LLMM models can be thought of as complementary to GAMM models but with additional user control of the fixed and stochastic structures for purposes of spatial smoothing. An implementation of LLMM as a contributed R package can be found at: http://eecrg.uib.no/personal_pages/LLMM.htm
The Bias Project is an effort to produce research and software addressing Bayesian methods for combining individual and aggregate data sources as seen in Ecological Inference and Small Area Estimation problems. Many of the software contributions are available as either either Winbugs or R programs.
The Bias Project is one of several research efforts at ESRC where unique problems in Social Science research are addressed and explored with modern statistical methods.
MIXPREG, MIXOR, MIXREG, MIXGSUR and MIXNO are a collection of high quality generalized regression modeling tools that allows for mixed effects and various forms of censoring. Correlated, nested and hierarchical data structures are also addressed. Estimation and inference is based on a full-information maximum likelihood approach rather than a Taylor expansion to linearized the likelihood. The software is free and WinXp, Solaris and Mac versions are available.
SOLAR stands for Sequential Oligogenic Linkage Analysis Routines. SOLAR addresses genetic variance components analysis, including linkage analysis, quantitative genetic analysis, and covariate screening. Two basic types of linkage analysis are available, Twopoint and Multipoint. Maximum Likelihood estimation, Monte Carlo Simulations and Bayesian Model Averaging are some of the options available to address model formation and screening. SOLAR is available on Tufts Bioinformatic Server where larger computational intensive jobs may be run.
CSPro (Census and Survey Processing System) is a public-domain MS Windows software package for entering, editing, tabulating and mapping census and survey data. For those interested in a facility to capture and record new data, CsPro offers a simple interface to support this task. Support for survey Cross Tabulation is available but limited in scope. The other notable feature is the Mapping capability and viewer. Note, this package is not a complete statistical processing option nor an alternative to a GIS solution. Export of selected data/variables as ascii delimited files is available for input to other packages, such as SAS, SPSS.