1 The greatest achievement in life is to be able to get up again from failure.

2 Categorical Data Analysis Chapter 5 II: Logistic Regression for Qualitative/Mixed Factors

3 Anova Type Representation of Factors Binary response variable: Y ~ Bernoulli( ) Qualitative factors: A, B, … SAS textbook Sec 8.4

4 Example: Berkeley Admissions Data (Table 2.10) MenWomen Major# of applicants % admitted # of applicants % admitted A B C D E F

Anova-Type Logistic Regression 5 Only one factor (eg. Department) Only main effects of two factors Full model

Anova-Type Logistic Regression Parameterization (in SAS): The effect at the last level of each factor is set as 0 (Regular) logistic regression expression by dummy variables (one factor example) 6

7 Mixed-type Logistic Regression Binary response variable: Y ~ Bernoulli( ) Qualitative factors: A, B, … Quantitative factors: X SAS textbook Sec 8.5

8 Example: Horseshoe Crab Dataset is given in Table 4.3, textbook Each female crab had a male crab attached to her in her nest; other males residing nearby her are called satellites Y= # of satellites X= female crab’s color (C), spine condition (S), weight (Wt), and carapace width (W) –C = 1 to 4 (light to dark); –S = 1 to 3 (good to worst)

Mixed-Type Logistic Regression 9 Numerical factors Wt, W and: Only one factor (eg. color) Only main effects of two factors With interaction effects (Not the saturated model)

Mixed-Type Logistic Regression Parameterization (PROC GENMOD in SAS): The effect at the last level of each factor is set as 0 (Regular) logistic regression expression by dummy variables (C + W example) 10

11 Quantitative Treatment of Ordinal factors Assign scores to its categories for each ordinal factor Treat the ordinal factors as quantitative factors to fit GLM e.g. color

Goodness of Fit Deviance or comparison to the full model Residuals Model comparisons (L-R tests) 12