Matlab offers a variety of Optimization functions in the Optimization and Statistics Toolboxes. One useful application for students is the Gui interface to nlinfit, called nlintool. This interactive graphical tool can be used for nonlinear least squares regression fitting and prediction for functions of one or more variables and parameters. As with all such tools, your mileage will vary depending on needs and data formats. The strength of this tool and interface is the relative ease of use and default outputs. The typical workflow setting is in the support of lab data analysis. You can investigate the nlinfit and nlintool documentation via the DEMOs help browser.
Spatial statistics is a large collections of tools with different historical developemental settings and results. History aside, one area that has been exploited recently is the class of models for univariate and multivariate hierarchical point-referenced spatial regression models for gaussian and non-guassian responses. The approach taken in spBayes is through generalized hierarchical random effects models estimated via Monte Carlo Markov Chain(MCMC) sampling. Spatial effects are captured via a zero centered multivariate guassian process where a variety of spatial covariance structures can be specified. A new R package http://www.r-project.org called spBayes addresses this area with more success than previous attempts. One advantage of the MCMC approach is the ability to estimate functionals. In particular, a recent entropy based measure call DIC, Deviance Information Criterion, is available to help consider the viability of competing nested or non nested models conditional on the same set of data.
SAS is known as a large and powerful statistical program. Recently SAS offers access to an add-on PROC called Glimmix. Many years ago this toolset was developed as a user macro and it evolved to the point that SAS has turned it into a SAS/STAT PROC. However, it is not yet included in the STAT product under version 9.1. You must register and download this into your installed version of SAS. Also note that the 256 page documentation needs to be downloaded as well. From the SAS docs: The GLIMMIX procedure fits statistical models to data with correlations or nonconstant variability and where the response is not necessarily normally distributed. These models are known as generalized linear mixed models (GLMM). The GLMMs, like linear mixed models, assume normal (Gaussian) random effects. Conditional on these random effects, data can have any distribution in the exponential family. The exponential family comprises many of the elementary discrete and continuous distributions. The binary, binomial, Poisson, and negative binomial distributions, for example, are discrete members of this family. The normal, beta, gamma, and chi-square distributions are representatives of the continuous distributions in this family. In the absence of random effects, the GLIMMIX procedure fits generalized linear models (fit by the GENMOD procedure). Pratically speaking GLIMMIX is a cross between Proc GENMOD and Proc MIXED functionality. This is a huge plus to researchers needing to deal explicitly with the nature of their data instead of the more likely outcome of approximating a modeling effort with something not quite right for the problem at hand. For example, choosing a response distribution more closely aligned with your setting, exploring covariance structures for correlated data and nesting. In addition, thin plate spline modeling is available to address NonParametric Smoothing of covariate effects when in fact they may be nonlinear. Despite the additional capabilities, you may view this as a blessing or a curse.
Often researchers will need access to functionality that isn’t found in commercial statistics packages. This problem varies quite a bit and is meet with specialized solutions by the statistical community. These solutions are often cutting edge, reflecting new statistical research. Most stats packages allow some form of macro authorship. This works to a point and often provides a just in time solution. Well known examples include Matlab’s scripting language, SAS IML, GAUSS, Stata, Splus and R. Yet others will seek stand alone solutions in one form or another. These range from public domain C, C++, Fortran, and Java research subrountines to stand-alone programs with various user interfaces.
The goal of this blog is to list references and short descriptions of various solutions that may offer additional insights into your research and the statistical methods, and maybe even save you some time. About a dozen or so topics some to mind and I hope to address them shortly.
These posts are not intended as statistical guidance nor endorsment. Most problems are best addressed by the advice of an experienced practioner in the relevant field.