Week 1 / Jan. 8-10 :
Class 1 will (1) introduce everyone to each other, (2) introduce
everyone to the class' requirements (including the term project),
objectives and style, (3) provide a brief general overview of regression,
and (4) survey students to learn about their familiarity with statistical
analysis and with SPSS.
Class 2 (R) will begin our study of bivariate regression, starting
with a review of standardized scores, correlation coefficients,
and regression coefficients.
Required Reading (for class 2): Sections 2.1-2.5.
Key concepts: linear transformation; x = X - Mx; covariance; Pearson
product-moment correlation coefficient; point-biserial correlation;
phi coefficient; z distribution; regression coefficient.
Week 2 / Jan. 15-17:
I will miss our Jan. 17 session (I'll be at an academic administrator
seminar--wheee). We'll pick a date to make up the session.
Class 3 (T) will deal with confidence intervals, hypothesis testing
and power in bivariate regression. The first homework will be assigned.
Required Reading: 2.6-2.10.
Key concepts: r(y, yhat) = r(yx); variance decomposition of y;
variance of a linear composite; coefficient of alienation; standard
error of estimate; standard error of B(yx); extrapolation vs interpolation;
confidence interval Vs NHST; margin of error; t distribution Vs
z distribution.; Fisher's z' transformation; significance of r Vs
significance of B; regression toward the mean; assumptions of the
fixed regression model.
Week 3 / Jan. 22-24:
Class 4-5 extends the basic regression concepts from 1 predictor
to 2 predictors, and then to k predictors. Class 4 (M) addresses
estimation, and Class 5 (W) addresses standard errors, confidence
intervals and hypothesis testing. Multiple predictors introduce
the issue of covariance among predictors and the possibility of
indirect effects and spurious relationships.
Required Reading: (T) 3.1-3.4; (R) 3.5-3.7.
Key concepts: (T-R)
Ch. 2 Fisher's z' transformation; significance of r Vs significance
of B; correlation/regression artifacts (item-total correlations,
regression toward the mean, range restrictions, unreliability, similarity
of distributions); assumptions of the fixed regression model; Ch.
3 direct and indirect effects; spurious correlation; requirements
for causal reasoning; partial Vs zero-order coefiicients; excluded
predictor problem; suppression.
Week 4 / Jan. 29-31:
Class 6 (T) will conclude our introducing to regression with k
predictors. Class 7 (R) will introduce graphical approaches to representing
data--an invaluable tool in data analysis--and introduce the assumptions
underlying the ordinary least squares (OLS) method of estimation.
Required Reading: (T) 3.7-3.9; (R) 4.1-4.3.
Key concepts: (T) Multiple R; multiple R square; adjusted R square;
significance of R square, unstandardized beta, and standardized
beta; F. (R) Power in multivariate regression; choosing sample size
for a study; cautions about prediction; Rozeboom's cross-validation
R square; graphing concepts.
Week 5/ Feb. 5-7:
Class 8 (T) will
look at how to look for evidence of violations of the assumptions
underlying OLS methods, and some purported remedies for such violations.
In Class 9 (R), we will begin a broad look at the kinds of research
questions that we can address using regression. We will also introduce
the idea of hierarchical regression, where some predictors are of
more research interest than others.
Required Reading:
(T) 4.4-4.6; (R) 5.1-5.3.
Key concepts: (T)
Violation of assumptions (consequences / detection / remedies);
correctness of the model; distribution of residuals. (R) Prediction
Vs explanation; elasticity; hierarchical regression; order of entry.
Week 6 / Feb 12-14:
Classes 10-11 will extend the idea of a hierarchy of predictors
to a hierarchy of *sets* of predictors. There is a fair amount of
complexity here, and we need to take our time.
Required Reading: (TR) 5.4-5.8.
Key concepts: (TR) Research factors; R square for sets of predictors
in hierarchical regression; controlling Type I error and Type II
error with complex investigations; Fisher's "protected"
t test.
Week 7 / Feb. 19-21:
Class 12 (T) introduces the use of polynomial terms as predictors.
Class 13 (R) focuses on transformations to meet assumptions and/or
aid interpretability.
Required Reading: (T) 6.1-6.3; (R) 6.4-6.7.
Key concepts: (T) Linear in the variables Vs linear in the coefficients;
linearizable by transformation Vs inherently nonlinear; powers of
X as aspects of X; order of the polynomial; centering predictors;
essential collinearity Vs nonessential collinearity; simple slope;
orthogonal polynomials. (R) Logarithms; started logs and started
powers; ladder of re-expression; bulging rule; one-bend transformations
Vs two-bend transformations.
Week 8 / Feb.
26-28:
Class 14 (T) is a review session--bring your questions. Class 15
(R) is our midterm exam, which will focus on concepts
and interpretation of results.
Required Reading: none.
Key concepts: See Weeks 1-7.
Mar. 4-6: SPRING BREAK / NO CLASSES
Week 9 / Mar. 11-13:
In Class 16 (T) we will briefly review the midterm, and start talking
about interactions with continuous predictors. We'll continue that
discussion in Class 17 (R).
Required Reading: (T) 7.1-7.3; (R) 7.4-7.12.
Key concepts: (T) Interaction; regression plane; simple regression
line; centering and collinearity; effects of reliability and research
design on power to detect interactions. (R) Significance of simple
slopes; why this significance is equation-dependent; cautions on
using standardized estimates; ordinal Vs disordinal interactions;
finding the crossing point; higher order interactions; interactions
with sets of predictors.
Week 10 / Mar.
18-20:
In Classes 18-19
(TR) we'll make a careful study of non-continuous (categorical or
nominal) predictors. We need to make careful coding choices in order
to get the most out of a regression using these predictors.
Required Reading:
(T) 8.1-8.3; (R) 8.4-8.8.
Key concepts: (T)
Dummy codes; reference group; interpreting dummy code B,
R and R square; standardization and nominal predictors; power and
nominal predictors; "dummy-like" codes; (R) Unweighted
effects codes; weighted effects codes; base group; contrast codes;
choosing a coding system.
Week 11 / Mar.
25-27:
In Classes 20-21
(TR) we'll look at interactions involving categorical predictors.
As we've seen before, categorical variables simplify regression
in many ways, and that is certainly true of interactions. Still,
we may find ourselves a bit behind at this point, so let's no take
this too fast.
Required Reading:
(T) 9.1-9.2; (R) 9.3-9.4.
Key concepts: (TR)
Interpretation of nominal interactions; balanced Vs unbalanced designs;
full representation; sums of squares Type I, II, III; impact of
different coding schemes.
Week 12 / Apr.
1-3:
This week we'll struggle with two common problems in regression.
In Class 22 (T), we'll talk about outliers (or influential cases).
In Class 23 (R), we'll talk about collinearity, one of the primary
drawbacks to nonexperimental research.
Required Reading:
(T) 10.1-10.4; (R) 10.5-10.7.
Key concepts: (T)
Outliers; leverage; hat values; discrepancy; internally studentized
residuals (SRESID); externally studentized residuals (SDRESID);
influence; DFFITSi; DFBETASi; clumps; index plots; best practice
for outliers. (R) Collinearity; tolerance; variance inflation factor
(VIF); condition number; respecification; ridge regression; principal
components regression.
Week 13 / Apr.
8-10:
For the next three
classes, we will study regression techniques where the dependent
variable has special properties. In Class 24 (T), we will look at
logistic regression, where the dependent variable is a dichotomy.
In Class 25 (R), we'll look at Poisson regression, a tool for modeling
count data.
Required Reading:
(T) 13.1-13.2; (R) 13.3-13.6.
Key concepts: (T) Linear probability model; probability Vs odds
Vs log(odds) or probit; odds ratio; deviance; maximum likelihood;
log likelihood. (R) Pseudo R square; Cox-Snell; Nagelkerke; score
test; Wald test; base rate.
Week 14 / Apr.
15-17:
In Class 26 (T),
we will continue our discussion of polytomous logistic regression
and Poisson regression. After this class, we have some options,
but my default is to devote Class 27 (R) to introducing path analysis,
a tool for modeling systems of multiple equations.
Required Reading:
(T) no new reading; (R) Chapter 11; (W) 12.1-12.3.
Key concepts: (T)
R square adjcount / Goodman-Kruskal lambda; polytomous logistic
regression; nested dichotomies regression; ordinal logistic regression
/ proportional odds model; Poisson regression. (R) TBA.
Week 15 / Apr.
22-24 (April 24 will actually be our last class meeting):
The remaining classes
will devoted to final exam review (class 28) and project presentations
(classes 29-30).
Required Reading:
none.
Last class (schedule
will be adjusted once we make up the Jan. 17 session):
Class 30--presentations,
continued, plus last-minute exam questions
Required Reading:
none.
Final exam is
Tuesday, April 29, noon.
|