Professor: Aaron Moody

Lectures: MWF 9:00 - 9:50 in Saunders 204

Office Hours: MW 1:00 - 2:00

E-mail: aaronm@email.unc.edu

Office Phone: 962-5303

Outline of Course:

This course will focus on a set of common, advanced methods for analyzing a variety of data types and their combinations. Most procedures that are discussed will be put into practice through lab exercises. We will begin with a review of basic concepts, methods, and theory. This section will quickly cover distributions, parameters and estimates, significance tests, point-pattern-analysis, and the background and theory to understand the well. The review section will lead us into common advanced statistical procedures, with an emphasis on estimation, hypothesis testing, model construction, interpretation, and residual analysis. This section will include simple- and multiple regression, one-way- and two-way ANOVA, dummy-variable regression, logistic regression, weighted (spatial) regression, and spatial interpolation. We will then turn to two methods that are powerful exploratory tools, but that do not explicitly allow significance tests of parameter estimates or hypotheses. Data transformations will begin with Principle Components Analysis and progress through a set of Ordination methods frequently used for community classification and gradient analysis in community ecology. Classification and Regression Trees (CART) will be the last scheduled topic for the course.

Most of the Labs will be conducted in S-Plus, which is a high level statistical and graphical programming language. S-Plus already has programs to do most of what you will need, but you will be asked to write functions for many of the homework assignments. As such, I strongly encourage learning how to use S-Plus at the command line, as well as the use of scripts to run your analyses. We will use PC-ORD for the ordination section of the course. Datasets will include animal and plant morphology, soil properties, plant species composition, species richness, terrain data, and a number of other environmental variables.

Your lab write-ups should take the form of short papers, either nicely handwritten or wordprocessed, in complete sentences, and with the following sections.

• Identify the Question or Problem
  
• Describe the Data
  
• Describe the Method, Why its Appropriate, and its Assumptions
  
• Present the Results of Analysis (Tables & Figures Imbedded in Text)
  
• Discuss the Results
  
• Identify One Analogous Question in Your Own Field of Research
  

Requirements and Evaluation:

Grading will be based largely (75%) on the labs and homework assignments. In addition, each student is required to provide 1 hour of consultation time per week. This is time during which other students in the class can come to you for help with course material or labs. Finally, there will be a unified course project (25%) that will require participation from all students in the course.

Texts:

Chambers, J. M. and T. J. Hastie (Eds.). 1992. Statistical Models in S. Wadsworth and Brooks/Cole. Pacific Grove, CA (Recommended).

Kent, M. & Coker, P. 1995. Vegetation Description and Analysis: A Practical Approach, Wiley (Recommended).

Kleinbaum, D. G., L. L. Kupper, K. E. Muller, and A. Nizam. 1998. Applied Regression Analysis and Other Multivariable Methods, 3rd Ed. Duxbury Press, Pacific Grove, CA (Required).

Important Dates:

September 2: Labor Day, No Class
October 16 - 18: Fall Break, No Class
November 27 - 29: Thanksgiving Break, No Class
Wednesday December 4: Last Day of Class
Friday December 13, 12:00: Final Exam Period

Course Topics: Expanded Outline

I. Introduction & Elemental Building Blocks:

• Basic Terms, Definitions & Notation
  
• Deterministic vs. Stochastic Models
  
• Theory of the Stochastic Variable (Random Process) & PDFs
  
• Probability Distributions: Their Properties, Parameters & Utility
  
• Parameters & Their Properties
  
• Degrees of Freedom and the '60s
  
• The Sample: Murky Depths of Representation

II. Estimation, Hypothesis Testing, & Exploration

• Confidence: Probabilities, Standard Errors
  
• Special Distributions (t, F) & Their Utility
  
• Hypotheses & Testing Them
  
• The t-Test & Life Out on the Tails

III. Spatial Data:

• Point Distributions - Tests for Randomness & Sampling Issues
  
• Spatial Association & Spatial Dependence - Friends & Foe
  
• Neighborhood Matrices
  
• Tests for Spatial Dependence - I, C

IV. Linear Regression:

• Assumptions & Theoretical Basis
  
• Least Squares Parameter Estimation vs. Eyeball Approach
  
• Assessing the Model: t, F, & Some Error Terms
  
• Confidence & Prediction Bands & Other Distinctive Markings
  
• SCP, r, r-square, Tests & Revisiting Assumptions
  
• ANOVA Regression Set Up: F & Its Distributions

V. Multiple Regression:

• Hypothesis Testing with the Conditional Model
  
• Full & Reduced Model: ANOVA for Multiple Regression
  
• Sums of Squares . . . Circles . . . Triangles . . .
  
• Overall, Partial, & Multiple-Partial Tests
  
• Variables Added in Order vs. Variables Added Last
  
• Correlation Revisited: Multiples, Partials, Multiple Partials
  
• Forward, Backward, & Exhausting Stepwise Models

VI. Residual Analysis:

• Residuals, Leverage, & the Internal Combustion Engine
  
• Residual Analysis: Standardized, Studentized, Jacknifed
  
• PRESS Statistic, PUSH Statistic
  
• Cook's D

VII. Higher Order & Expanded Models:

• Interaction - Formulation & Tests
  
• Confounding - Formulation & Tests
  
• Utter Bafflement - Formulation & Tests
  
• Dummy Variables & Their Utility - Formulation & Tests

VIII. Analysis of Variance:

• Sums of Squares & F Tests
  
• Fixed Effects, Random Effects, Mixed Effects
  
• One-Way - Factor Level Effects
  
• Post hoc Tests & Ipso facto Procedures
  
• Two-Way - Factor Level Effects, Interaction Effects

IX. Logistic Regression:

• Basic Model
  
• Souped-up Model
  
• Transforms
  
• Interpretation of Results

X. Spatial Interpolation:

• Taxonomy of Methods
  
• Thiessen Polygons, Splines, Trend Surface Analysis
  
• Inverse Distance Weighted Average
  
• Regionalized Variable Theory
  
• Semivariance & The Scariogram
  
• Kriging

XI. Spatial Regression (Weighted Regression):

• Discrete Space Autoregressive Model
  
• Spatial Dependence, Spatial Weights Matrix, Moran's I
  
• Null Model, Spatial Model & Chi-Square Test

XII. Ordination:

• PCA - Principal Components Analysis
  
• CA - Correspondence Analysis
  
• DCA - Detrended Correspondence Analysis
  
• CCA - Canonical Correspondence Analysis
  
• NMMDS - Nonmetric Multidimensional Scaling

XIII. Classification & Regression Trees:

• Basic Algorithm, Its Strengths & Weaknesses
  
• Basic Structure & Interpretation
  
• Presentation

Homeworks & Labs:

     Homework 1: Due 8/30/2
     Homework 2: Due 9/9/2
     Homework 3: Due 9/18/02
     Homework 4: Due 9/25/2
     Homework 5: Due 10/4/2
     Homework 6: Due 10/16/2
     Homework 7: Due 10/28/2
     Homework 8: Due 11/6/2
     Homework 9: Due 11/15/2
     Homework 10: Due 11/22/2
     Homework 11: Due 12/13/2