SCS Short Courses, Winter 2004

SCS Courses Data Analysis Using SAS Introduction to SPSS for Windows Introduction to Structural Equation Modeling Introduction to Geographic Information Systems (GIS) Statistics, Geometry and Brain Mapping An Introduction to R and S-Plus

Data Analysis Using SAS for Windows

This short course provides a basic introduction to the Statistical Analysis System (SAS). Sessions One and Two provide an overview of SAS and its underlying logic; an explanation of the use of the Display Manager System to run a SAS job; an introduction to the SAS Data step for reading, transforming, and storing data; and a demonstration of how statistical analyses may be performed in SAS Insight.

Sessions Three and Four will concentrate on SAS programming techniques to modify data and enhance SAS output. More statistical procedures will be introduced for general linear models.

Introduction to SPSS for Windows

This course presents the basics of the Statistical Package for the Social Sciences (SPSS). Session One will introduce the computing concepts of SPSS, the different facilities for reading data into an SPSS spreadsheet, and saving SPSS data files for future use. At the end of the first session, participants should be able to run simple programs, including some statistical procedures.

Sessions Two and Three will cover basic data modifications, transformations and other functions including the uses of SPSS system files. More statistical procedures will also be introduced, with an emphasis on the use of graphical methods for examining univariate and bivariate relationships. Session Four will cover Analysis of Variance and Least Squares Regression. As with previous sessions, graphical techniques will be demonstrated.

Introduction to Structural Equation Modeling

This course will provide a general introduction to the methods of structural equation modeling (SEM), including a discussion of developing models, evaluating the fit of models to data, evaluating the significance of model parameters and performing model modification. The primary objectives of this class will be to provide:

1. the ability to recognize situations where these techniques may be useful in research;
2. an appreciation for the roles of sound theory in making these techniques useful;
3. an understanding of the limitations of these methods; and
4. the ability to use available software for analyzing data.

Introduction to Geographic Information Systems (GIS)

Geographic Information System (GIS) is a computer tool for visualizing, processing and analyzing data with a spatial dimension such as population distribution and facility location. This course provides hands-on experience with ArcView 3.2 and participants will learn how to construct, plot and edit maps, perform queries and basic spatial analyses. Examples will be drawn from Canadian census and other social science data. The class will be convened in the GIS computer lab.

The four three-hour sessions in this short course will cover:

1. introducing basic GIS concepts and getting started with ArcView
2. mapping census data
3. working with attribute table and spatial queries
4. geocoding street addresses

Statistics, Geometry and Brain Mapping

This full-day workshop is a special, SCS presentation by an invited lecturer.

Overview

A course on the intersection of statistics, geometry and brain mapping, illustrated with 3D graphics demonstrations using IRIS Explorer, and finishing with a demonstration of the analysis of fMRI data using the FMRISTAT package written in Matlab.

Abstract

The geometry in the title is not the geometry of lines and angles but the geometry of topology, shape and knots. For example, galaxies are not distributed randomly in the universe, but they tend to form clusters, or sometimes strings, or even sheets of high galaxy density. How can this be handled statistically?

The Euler characteristic (EC) of the set of high density regions has been used to measure the topology of such shapes; it counts the number of connected components of the set, minus the number of `holes', plus the number of `hollows'. Despite its complex definition, the exact expectation of the EC can be found for some simple models, so that observed EC can be compared with expected EC to check the model. A similar problem arises in functional magnetic resonance imaging (fMRI), where the EC is used to detect local increases in brain activity due to an external stimulus.

We are also interested the analysis of brain shape: does brain shape change with disease, age or gender? Three types of data are now available: 3D binary masks, 2D triangulated surfaces, and trivariate 3D vector displacement data from the non-linear deformations required to align the structure with an atlas standard. Again the Euler characteristic of the excursion set of a random field is used to test for localised shape changes. We extend these ideas to scale space, where the scale of the smoothing kernel is added as an extra dimension to the random field. Extending this further still, we look at fields of correlations between all pairs of voxels, which can be used to assess brain connectivity. Shape data is highly non-isotropic, that is, the effective smoothness is not constant across the image, so the usual random field theory does not apply. We propose a solution that warps the data to isotropy using local multidimensional scaling. We then show that the subsequent corrections to the random field theory can be done without actually doing the warping -- a result guaranteed in part by the famous Nash Embedding Theorem.

Finally we shall look in some detail at the statistical analysis of fMRI data. Our proposed method seeks a compromise between validity, generality, simplicity and execution speed. The method is based on linear models with local AR(p) errors fitted via the Yule-Walker equations with a simple bias correction that is similar to the first step in the Fisher scoring algorithm for finding ReML estimates. The resulting effects are then combined across runs in the same session, across sessions in the same subject, and across subjects within a population by a simple mixed effects model. The model is fitted by ReML using the EM algorithm after re- parameterization to reduce bias, at the expense of negative variance components. The residual degrees of freedom are boosted using a form of pooling by spatial smoothing. Activation is detected using Bonferroni, False Discovery Rate, and non-isotropic random field methods for local maxima and spatial extent. We conclude with some suggestions for the optimal design of fMRI experiments.

An Introduction to R and S-Plus

The statistical programming language and computing environment S has become the de-facto standard among statisticians. The S language has two major implementations: the commercial product S-PLUS, and the free, open-source R. Both are available for Windows and Unix/Linux systems; R, in addition, runs on Macintoshes. Although I will briefly introduce S-PLUS, the major emphasis will be on R. (A slightly longer abstract is available as a Word document.)

While some statistical packages make it difficult to undertake analyses that are non-standard or to add to the built-in capabilities of the package, S supports innovative programming; in this regard, statisticians have contributed literally dozens of freely available statistical "libraries" of R and S-PLUS programs. S is also particularly capable in the area of statistical graphics.

The purpose of this short course is to show participants how to accomplish a variety of tasks in S, including the tasks of writing programs and constructing non-standard graphs. The statistical content is assumed known or taught in other courses.

The seven sessions in this short course will cover (with chapter references to Fox, 2002): There is also a web site for the course: http://socserv.socsci.mcmaster.ca/jfox/Courses/S-course/.

• 1. Getting started with R and S-PLUS (Ch. 1)
• 2. Reading and manipulating data (Ch. 2 & 3)
• 3. Linear regression and linear models in S (Ch. 4)
• 4-5. An introduction to programming in S (Ch. 8)
• 6. S graphics (Ch. 7)
• 7. Generalized linear models in S (Ch. 5)

It is recommended that you buy one of:

1. J. Fox, An R and S-PLUS Companion to Applied Regression. Sage, 2002. Additional materials are available at http://socserv.socsci.mcmaster.ca/jfox/Books/Companion/index.html.
2. W. N. Venables and B. D. Ripley, Modern Applied Statistics with S-PLUS, Third Edition. New York: Springer, 1999.

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