Psychology 7291: Multivariate Statistics
Spring 1998
11:00 - 11:50 MWF
Muenzinger E311
Gregory Carey
D261B , Muenzinger
Phone: 303-492-1658
Fax: 303-492-2967
Home Page: http://ibgwww.colorado.edu/~carey
Office hours:
Official: 10:00 11:00 M, 1:00-2:00 Tu
Unofficial: 5:30 - ??, Friday at the Hungry Toad
Overview: This course will emphasize computer approaches to multivariate statistical analysis. We will discuss the three major goals of multivariate analysis and their associated techniques: (1) data reduction (principal components, factor analysis, and cluster analysis); (2) discrimination and classification (cluster analysis, discriminant analysis); and (3) hypothesis testing (multivariate regression, multivariate analysis of variance, logistic regression). Special topics of interest to a sufficient number of students may also be taught.
Toaccomplish the goals of the course two skills are required. First, we must learn fundamental matrix algebra. Second, we must have working knowledge of statistical packages that perform multivariate analysis.
Requirements: You will be required to turn in reports on problem sets over the semester. In the problem sets, you will be given data and must perform one or more analyses with them. You should write the reports as if they were the Methods and the Results section of a journal article, including relevant tables. The reports should not contain jargon from the statistical package that you used (e.g., "used the MANOVA option of the SAS GLM procedure"). The reports will vary with the topic, but in general should run about 2 typewritten pages excluding the tables. In lieu of a final exam, you will be required to do a major analysis of a data set of your choice and write the appropriate report. There will be no tests or exams. All reports and papers should be written in the style of a major journal in your field.
Statistical Packages: Course examples and illustrations will use SAS, the Statistical Analysis System. You are free to use any statistical package that you choose to perform the analyses. You may also use any computer that you choose (as long as you are responsible for the computing expenses). Arrangements have been made for each of you to have an account on the UNIX workstations located on the third floor of Muenzinger. The documentation for statistical packages is voluminous and can be very expensive. For that reason, we will rely on class notes to document the major features of the statistical packages.
Textbook.
Because students take this course for very different reasons, there is no mandatory text. You are, however, urged to purchase or borrow a text to read along with the class topics. Suggested texts are:
(1) Johnson, Dallas E. (1998). Applied multivariate methods for data analysis. Pacific Grove, CA: Duxbury Press. More theoretical than the other text.
(2) Tabachnick, B.G. & Fidell,L.S. (2000). Using Multivariate Statistics, 4th Ed. New York: Allyn & Bacon. A traditional text that emphasizes ³how to do it² over theory.
Some statistical software is available to purchase through CU site licenses. If you wish to see what is available, go to
http://www.colorado.edu/its/tpsitelic/
References
The following works are the more classic reference works (not textbooks) for multivariate analysis. A number of them are highly mathematical; others are more practical. Because many of the books are costly, it is always a good idea to examine a copy before making a purchase.
General Texts
Bock, R.D. (1975), Multivariate statistical methods in behavioral research. NY: McGraw-Hill.
Cooley, W.W. and Lohnes, P.R. (1971), Multivariate data analysis. NY: John Wiley & Sons
Dillon, W. R. and Goldstein, M. (1984). Multivariate Analysis, Methods and Applications. Wiley, New York.
Brian S. Everitt and Graham Dunn. Applied multivariate data analysis. New York : Oxford University Press, 1992.
Jobson, J. D. Applied multivariate data analysis. New York : Springer‑Verlag, c1991‑
Kleinbaum, Kupper, Muller 1988. Applied regression analysis and other multivariate analysis. PWS‑Kent Publishing Company, Boston.
Mardia, K. V., Kent, J. T. and Bibby, J. M. (1979). Multivariate Analysis. Academic Press, London.
Morrison, D.F. (1976), Multivariate Statistical Methods, 2nd edition. NY: McGraw-Hill.
Rao, C.R. (1973), Linear statistical inference and its applications. NY: John Wiley & Sons
Tabachnick, B.G. and Fidell, L.S. (2000). Using Multivariate Statistics, 4th Edition. New York, Allyn & Bacon.
Factor Analysis
Mulaik, S.A. (1972), The foundations of factor analysis. NY: McGraw-Hill
Harman, H.H. (1976), Modern factor analysis, 3rd edition. Chicago, University of Chicago Press.
Gorsuch,R.L. (1983). Factor Analysis, Second Edition. Hillsdale NJ: Lawrence Erlbaum Associates.
Lawley, D.N. and Maxwell, A.E. (1971). Factor analysis as a statistical method. NY: McMillan.
Cluster Analysis
Everitt, B.S. (1980). Cluster analysis, 2nd edition. London: Heineman Educational Books Ltd.
Generalized Linear Models
Hastie, T. and Tibshirani, R. (1990). Generalized Additive Models. Chapman and Hall, London.
McCullagh, P. and Nelder, J. A. (1983). Generalized Linear Models. Chapman and Hall, London.
Classical Regression and Modern Regression
Belsley, D. A., Kuh, E. and Welsch, R. E. (1980). Regression Diagnostics. Wiley, New York.
Breiman L., Friedman J.H., Olshen R.A., and Stone, C.J., (1984). Classification and Regression Trees. Wadsworth International Group, Belmont CA.
Cohen J. & Cohen, P. (1983). Applied multiple regression/correlation analysis for the behavioral sciences, 2nd edition. Hillsdale NJ: Lawrence Erlbaum Associates.
Draper, N. R. and Smith, H. (1981). Applied Regression Analysis. (second edition). Wiley, New York.
Myers, R. H. (1986). Classical and Modern Regression with Applications. Duxbury, Boston.
Raudenbush, S.W. & Bryk, A.S (2002) . Hierarchical Linear Models: Applications and Data Analysis Methods, 2nd Ed. Thousand Oaks CA: Sage.
Kreft, I.G.G & DeLeeuw, J. (1998) Introducing Multilevel Modeling. Thousand Oaks CA: Sage.
Bosker, R.J. & Snijders (1999) Multilevel Analysis: An Introduction to Basic and Advanced Multilevel Modeling. Thousand Oaks CA: Sage.
Others
Hampel, F. R., Ronchetti, E.M., Rousseeuw, P.J. and Stahel, W.A. (1986). Robust Statistics: The Approach Based on Influence Functions. Wiley, New York.
Hoaglin, D. C., Mosteller, F. and Tukey, J. W., (Eds.) (1983). Understanding Robust and Exploratory Data Analysis. Wiley, New York.
Johnson, N. L. and Kotz, S. (1970). Continuous Univariate Distributions, vols. 1,2. Houghton‑Mifflin, Boston.
Puri & Sen (1971), Nonparametric Methods in Multivariate Analysis, Wiley.
B.D. Bojanov, H.A. Hakopian, and A.A. Sahakian. Spline functions and multivariate interpolations. Dordrecht ; Boston : Kluwer Academic Publishers, 1993.
D.J. Hand and C.C. Taylor, Multivariate analysis of variance and repeated measures :
a practical approach to behavioural scientists. London ; New York : Chapman and Hall, 1987.
Agresti, Alan. Analysis of ordinal categorical data. New York : Wiley, 1984.
Stevens, James.
Agresti, Alan. Categorical data analysis. New York : Wiley, 1990.
Freeman, Daniel H. Applied categorical data analysis. New York: M. Dekker, 1987.
Manly, B.F. (1999) Randomization, Bootstrap and Monte Carlo Methods in Biology, 2nd Ed. CRC Press