1. Soc 3306a Lecture 11: Multivariate 4
ANOVA and Regression Models
Using GLM and Linear Regression

2. One-Way ANOVA (Figure 1)
Used when model has a quantitative response variable (DV) and a categorical explanatory variable (IV)
Actually special type of multiple regression.
Need a post hoc test for more information (to tell you which groups different)
Most common are the Tukey b test (displays group means) or the Bonferroni or the Tukey multiple comparison methods (confidence intervals)

3. Regression with Dummy Variable (Figure 2)
Can get same result with regression model if create dummy variable
Provides more information
Advantage is that regression calculates slopes to use for prediction as well as standardized coefficients, plots, etc.
With binary categorical variable can create dummy coded 1 and 0
But if categorical variable has 2+ categories, need to create K-1 dummies

4. Creating Dummy Variables for Race (1 White, 2 Black, 3 Other)
Use Recode into Different Variable
Code Dummy1 as White = 1, Else = 0
Code Dummy2 as Black = 1, Else = 0
Don’t need a dummy variable for last group
Dummy Coding:
Race Dummy1 Dummy2
White 1 0
Black 0 1
Other 0 0

5. Interpretation of Dummy Variable
E(Y) = a + b1(Dummy1) + b2(Dummy2)
For White: Dummy1 = 1, Dummy2 = 0
For Black: Dummy1 = 0, Dummy2 = 1
For Other: Dummy1 = 0, Dummy2 = 0
(See Agresti Table 12.5)

6. Regression Using 2 Dummies (Race and Sex) Figure 3
Dummysex coded Male=1 and Female=0
E(Y) = a + b1(Dummy1) + b2(Dummy2)+ b3(Dummysex)
White Male: Dummy1 = 1, Dummy2 = 0, Dummysex = 1
Black Male: Dummy1 = 0, Dummy2 = 1, Dummysex = 1
Other Male: Dummy1 = 0, Dummy2 = 0, Dummysex = 1
White Female: Dummy1 = 1, Dummy2 = 0, Dummysex = 0
Black Female: Dummy1 = 0, Dummy2 = 1, Dummysex = 0
Other Female: Dummy1 = 0, Dummy2 = 0, Dummysex = 0

7. GLM and Two Way ANOVA Figure 4
Two way ANOVA, using GLM, handles 2 or more categorical predictors at the same time
Recoding as dummies not needed
Compares means of response variable (DV) for all combinations of 2+ categorical IV’s
Can test main effects as well as interaction effects simultaneously

8. GLM vs Linear Regression Figure 5
GLM can be used for linear regression using both categorical and quantitative predictors.
Categorical IV’s entered as fixed factors and quantitative IV’s are entered as covariates
GLM
Dummy coding not needed
Interactions between categorical IV’s handled easily
Need to ask for parameter estimates
Linear regression
Gives parameter estimates and standardized coefficients (i.e. to estimate causal models using path analysis)