#####R Script for Week 7--Dummy Variable Regression

# dichtomous factor

library(car)

fix(Davis)

attach(Davis)

sex
class(sex)
contrasts(sex)  # dummy regressors for sex

scatterplot(weight ~ repwt | sex, smooth=FALSE)

mod.davis.1 <- lm(weight ~ repwt + sex)  # additive model
summary(mod.davis.1)

mod.davis.2 <- lm(weight ~ repwt*sex)  # model with interaction
summary(mod.davis.2)

linear.hypothesis(mod.davis.2, c("sexM", "repwt:sexM")) # slopes AND intercepts
                                                        # the same for M and F
detach(Davis)

# polytomous factor

Prestige <- na.omit(Prestige)
attach(Prestige)

    # treatment of factors in R

type
class(type)
contrasts(type)  # dummy regressors

type <- factor(type, levels=c("bc", "wc", "prof"))  # change order of levels
contrasts(type)

    # additive dummy-regression model

mod.prestige.1 <- lm(prestige ~ income + education + type)
summary(mod.prestige.1)

mod.prestige.0 <- lm(prestige ~ income + education)
anova(mod.prestige.0, mod.prestige.1)  # incremental F-test for type

Anova(mod.prestige.1)  # "type II" tests

linear.hypothesis(mod.prestige.1, c("typewc", "typeprof"))

    # dummy regression with interactions

mod.prestige.2 <- lm(prestige ~ income + education +
                   type + income:type + education:type)

mod.prestige.2 <- lm(prestige ~ income*type + education*type) # equivalent

mod.prestige.2 <- lm(prestige ~ type*(income + education)) # equivalent
summary(mod.prestige.2)

Anova(mod.prestige.2)  # type-II tests

    # "effect" plots

library(effects)  # effects package must be installed
plot(all.effects(mod.prestige.2), ask=FALSE)
plot(all.effects(mod.prestige.2), multiline=TRUE, ask=FALSE)