Leona Aiken
Psychology
Spring, 2004
Psychology 531
Multiple Regression in Psychological Research
B139, M W 8:30-10:30
syllab04.doc
What is Multiple Regression Analysis?
"Multiple regression analysis (MR) is a general system for examining the
relationship of a collection of independent variables to a single dependent
variable. It is among the most extensively used statistical analyses in the
behavioral sciences. Multiple regression is highly flexible and lends itself
to the investigation of a wide variety of questions. The independent variables
may be quantitative measures such as personality traits, abilities, or family
income; or they may be categorical measures such as gender, ethnic group, or
treatment condition in an experiment. In the most common form of multiple
regression analysis, which we will consider here, the dependent variable is
continuous. The basic ideas of multiple regression can be extended to consider
other types of dependent variables such as categories or counts or even
multiple dependent variables. The relationship between an independent variable
and the dependent variable may be linear, curvilinear, or may depend on the
value of another independent variable1."
Instructor: Leona Aiken
Office: Psychology 249A
Phone: 965-3494
email:
Leona.Aiken@asu.edu
Teaching Assistant: Nick Schweitzer
Office:
Office hours in
statistics lab,
Psychology B153
email:
njs@asu.edu
Office Hours
The following are my office hours; they are close to being certain and will be
confirmed within the next week. Nick Schweitzer's office hours will be set
when we create the schedule of hours in the Psychology Computing Laboratory
within the next week. I will inform you as soon as the permanent schedule is
set.
Leona Aiken,
Monday
Monday
Wednesday
Office Hours
10:45AM-12:00 PM
1:45PM- 4:00 PM
10:45AM-12:15 PM
Nick Schweitzer, Office Hours
Office hours will be held in
the Statistics Lab, PSYB153,
to be arranged first week of
class
If your schedule conflicts with office hours, please contact me or Nick
Schweitzer to make an appointment. I prefer that you make an appointment if
you can, so that we insure the time is set aside.
Text
The text for the course is the third edition of the now classic Cohen and
Cohen regression analysis text. The book should serve you as a reference text
for many topics in multiple regression beyond what we will cover in this
semester.
Cohen, J., Cohen, P., West, S. G., & Aiken, L. S. (2003).
1Aiken,
Multiple
L. S., West, S. G., & Pitts, S.C. (2003). Multiple regression
analysis. In Schinka, J. A., & Velicer, W. F., (Eds) Comprehensive Handbook of
Psychology, Volume 2, Research Methods in Psychology. New York: Wiley.
Leona Aiken, Psychology 531, Multiple Regression, Spring 2004
2
regression/correlation analysis for the behavioral sciences
(3rd Ed.) Mahwah, NJ: Lawrence Erlbaum.
Supplemental Source
Tests
Aiken, L. S., & West, S. G. (1991). Multiple regression:
Testing and interpreting interactions. Newbury Park, CA: Sage.
There will be three noncumulative tests. No tests will be dropped. The
dates of the tests are as follows (Test 1 and 2 dates are approximate; Test 3,
certain)
Test 1
Wednesday, February 25
Test 2
Wednesday, April 5
Test 3
Monday, May 10, 7:40AM-9:30AM.
Homework
There will be approximately 6 or 7 homework assignments. They will be graded
on a four-point scale: Excellent = 4; Good = 3; Fair = 2; and Poor = 1.
Please turn these in on time. Please note that all problem sets must be turned
in for you to receive a grade in the course.
Final Grade
The final grade will based on the three tests plus the homework. The three
tests will count equally. Total points on the problem sets will be counted as
half a test.
Computer Usage
We will be using both SPSS for Windows and SAS PC for class examples and
homework. We will be using the statistical and graphical capabilities of
these two computer packages. My goal is that you become familiar with both SAS
and SPSS for regression analysis.
All the software is available in the Psychology Computing Lab, Room 153.
and SAS are available at other computing sites around campus as well,
including the Goldwater Center, across from Noble Library.
SPSS
I am assuming that most of you have used SPSS for Windows with syntax (not
just "point and click".) I am assuming that most of you have no familiarity
with SAS PC. You will receive fully documented examples of data analyses in
both SPSS and SAS that will serve as models for your homework. We will also
have training sessions in the statistics lab for those of you who are not
familiar with a software package. Nick Schweitzer is preparing a series of
handouts on SPSS 12 graphics (As I prepare this syllabus, we are at the outset
of transition from SPSS 11.5 to SPSS 12. The SPSS materials you will receive
this semester cover both versions of SPSS. The differences are in the graphics
between the two versions.)
Nick Schweitzer, the teaching assistant, is remarkable at statistical
computing. He is also a saint of a teacher. Computing should go well for you
all.
We will make available the information you need for problem sets (the data
plus initial SPSS and SAS syntax) will be stored on my Website,
http://www.public.asu.edu/~atlsa/PSY531
In addition, the information will be stored on the server in the Psychology
Statistics Lab, Psy B. 153.
Leona Aiken, Psychology 531, Multiple Regression, Spring 2004
3
Schedule Issues
This semester we are short one class from the usual semester. The usual
semester contains 29 class sessions. This semester contains 28 class sessions.
We need 29 sessions to complete the course content. Thus I will schedule an
additional class session at a time everyone can attend.
Handouts
I will be giving a full set of handouts covering lecture material throughout
the course. In addition, we will be distributing computer output with
documentation, which will run into many pages. We need to reimburse the
Psychology Department for all this xeroxing. Later in the semester, I will
collect funds for the Department in the amount of 30.00 per person. I will
collect money from all those who are registered for the course and who are
informally sitting in the course as well.
Class Study Strategy
Please read the assigned material before coming to class; note that I will
make more explicit reading assignments for daily lectures. I will be giving
handouts as well. The strategy I used when I was taking graduate statistics
courses was to copy over my notes after class. I would use this strategy to
force myself to determine whether I could follow all the notes I had taken. If
something was unclear, I would leave space for clarification and ask the
instructor. This is an easy way to keep up. Please keep up with the class,
because the material is cumulative.
Don't worry about the course. I'll do whatever I can to make everything
clear, and Nick Schweitzer is a highly competent teacher of things to do with
computing and statistics. I would be delighted if you would enjoy this course
and want to continue to study quantitative methods.
Course Content:
The course is devoted to the study of multiple regression as a general
system for assessing the relationship of a dependent variable Y to a set of
independent variables Xs, i.e. a "general data analytic system" (J. Cohen,
1968). During the course of the semester we will first examine the prediction
of a dependent variable from a single independent variable (bivariate
regression) and then quickly move to the case of multiple independent
variables (multiple regression). Our focus will be on linear regression, with
the general form of the multiple regression equation with which we work as
follows:
Yˆ =
bo + b1 X1 + b2 X2 + ...+ bp Xp
where X1...Xp are a set of independent variables,
Yˆ is a predicted score on the dependent variable based on
the set of independent variables, and
b1...bp
are a set of "regression coefficients" that indicate
the relationship of the independent variables to
the dependent variable.
Multiple regression analysis is a completely general approach to data
analysis. Your work from last semester on the Analysis of Variance (ANOVA)
can be subsumed as a special case of multiple regression. The independent
variables in the above equation can be factors and their interactions from
ANOVA, or a combination of factors and covariates from the Analysis of
Covariance (ANCOVA). Thus the analytic approaches we consider this semester
are applicable both to "experimental" research in which factors (Xs) are
Leona Aiken, Psychology 531, Multiple Regression, Spring 2004
4
manipulated and outcomes observed and to "correlational" research in which
cases are selected along the X variable dependent variables (Ys) are observed.
Linear regression, it will turn out, is not confined only to individual
independent variables linearly related to some dependent variable. We will
examine how curvilinear relationships and interactions among independent
variables are included in multiple regression. The outcomes of multiple
regression analysis are affected by violations of assumptions of the analysis.
We will explore how graphical methods help to surface the nature of data and
violations of assumptions. In addition, statistical methods of detecting
violations of assumptions and problematic data points that may grossly affect
outcomes will be examined, and remedies will be explored. If time permits, I
will provide an introduction to missing data imputation.
Topics and Readings
Reading abbreviations: Cohen, Cohen, West, & Aiken (CCWA), Aiken & West (A&W)
Topic
Reading
1.
Overview of multiple regression analysis
CCWA chap. 1
2.
Bivariate Regression
CCWA chap. 2
CCWA chap. 4, pp110-116
3.
Two-predictor regression, multiple regression
CCWA chap. 3
4.
Multiple prediction in matrix form
CCWA chap. 3a
5.
Sets of predictors and variable selection
CCWA chap. 5
6.
Curvilinear relationships
CCWA chap. 6
Leona Aiken, Psychology 531, Multiple Regression, Spring 2004
7.
Interactions among continuous variables
CCWA chap. 7
A&W chap. 2,3
8.
Regression Assumptions
CCWA chap. 4
9.
Regression Graphics Introduction
CCWA chap. 4
10.
Regression Diagnostics and Model Fixes
(transformations)
CCWA chap.10
CCWA chap. 6
5
11. Categorical Independent Variables and
ANOVA (design matrices)
CCWA chap. 8
12. Categorical by continuous variable
interactions, ANCOVA
CCWA chap. 9
A&W chap. 7
West, Aiken,
Krull (1996)b
13. Measurement error, power,
how many subjects?
CCWA, pp. 51-53, 92-95,
176-182, 297
Maxwell (2000)c,e
14. Missing data imputation
Allison (2001)a,d
CCWA, chap. 11
aTime
permitting.
bWest,
S.G., Aiken, L. S., & Krull, J. L. (1996). Experimental
personaltiy designs: Analyzing categorical by continuous variable
interactions. Journal of Personality, 64(1), 1-48.
cMaxwell,
S. E. (2000). Sample size and multiple regression analysis.
Psychological Methods, 5, 434-458.
dAllison,
eKelly,
D. (2001). Missing Data. Thousand Oaks, CA: Sage.
K., & Maxwell, S. E. (2003). Sample size for multiple regression:
obtaining regression coefficients that are accurate, not simply
significant. Psychological Methods, 8(3), 305-321.