# Load lme4 library.
library(lme4)

# Fit Model 6.1 (see chapter6_R_final.R for code to load the data).
model6.1.fit.lmer <- lmer(vsae ~ age.2 + I(age.2^2) + sicdegp2.f +
                            age.2*sicdegp2.f + I(age.2^2)*sicdegp2.f + (age.2 + I(age.2^2) | childid),
                          REML = T, data = autism.updated)

summary(model6.1.fit.lmer)

# Fit Model 6.2.
model6.2.fit.lmer <- lmer(vsae ~ age.2 + I(age.2^2) + sicdegp2.f +
                            age.2*sicdegp2.f + I(age.2^2)*sicdegp2.f +
                            (age.2 + I(age.2^2) - 1 | childid),
                          REML = T, data = autism.updated)

summary(model6.2.fit.lmer)

# Fit Model 6.2a.
model6.2a.fit.lmer <- lmer(vsae ~ age.2 + I(age.2^2) + sicdegp2.f +
                             age.2*sicdegp2.f + I(age.2^2)*sicdegp2.f +
                             (age.2 - 1 | childid),
                           REML = T, data = autism.updated)

# Test Hypothesis 6.1.
h6.1.pvalue <- 0.5*(1-pchisq(83.9,1)) + 0.5*(1-pchisq(83.9,2))
h6.1.pvalue

# Test Hypothesis 6.2.
model6.2.ml.fit.lmer <- lmer(vsae ~ age.2 + I(age.2^2) + sicdegp2.f +
                               age.2*sicdegp2.f + I(age.2^2)*sicdegp2.f +
                               (age.2 + I(age.2^2) - 1 | childid),
                             REML = F, data = autism.updated)
model6.3.ml.fit.lmer <- lmer(vsae ~ age.2 + I(age.2^2) + sicdegp2.f +
                               age.2*sicdegp2.f +
                               (age.2 + I(age.2^2) - 1 | childid),
                             REML = F, data = autism.updated)
anova(model6.2.ml.fit.lmer, model6.3.ml.fit.lmer)

# Fit Model 6.3.
model6.3.fit.lmer <- lmer(vsae ~ age.2 + I(age.2^2) + sicdegp2.f +
                            age.2*sicdegp2.f + (age.2 + I(age.2^2) - 1 | childid),
                          REML = T, data = autism.updated)

# View results.
summary(model6.3.fit.lmer)

# Plot the predicted random effects along with measures of uncertainty.
library(merTools)
REsim(model6.3.fit.lmer)
plotREsim(REsim(model6.3.fit.lmer))