1 Stat 8053, Fall 2011: GLMMs

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Linette Bates
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1 Stat 805, Fall 0: GLMMs The data come from a 988 fertility survey in Bangladesh. Data were collected on 94 women grouped into 60 districts. The response of interest is whether or not the woman is using contraceptives at the time of the survey. Predictors include age, number of existing children, and whether the district is urban or rural. > url <- " > data <- read.csv(url) > data$nchild <- factor(data$nchild) > data$area <- factor(data$area) > data$cage <- data$age - mean(data$age) > require(car) > library(effects) > require(lme4) > print(xyplot( ~ Age Nchild *, data, type = c("g", + "r", "smooth", "p"))) 0 Yes No 0 Yes No Age The package effects must be loaded before lme4 because of a problem in lme4. The function xyplot is from the lattice package. When used with Sweave, as I have done here, you need to enclose xyplot by a print statement. This is also required on the plot method for effects, used below, because this function also uses the lattice package. GLM fit(s) > m <- glm( ~ (Nchild + poly(cage,, raw = TRUE) + )^, + data = data, family = binomial) > Anova(m) Analysis of Deviance Table (Type II tests)

2 Response: LR Chisq Df Pr(>Chisq) Nchild.0.78e-07 poly(cage,, raw = TRUE) e e- Nchild:poly(Cage,, raw = TRUE) Nchild: poly(cage,, raw = TRUE): > Anova(m <- update(m, ~Nchild * poly(cage,, raw = TRUE) + + )) Analysis of Deviance Table (Type II tests) Response: LR Chisq Df Pr(>Chisq) Nchild e-07 poly(cage,, raw = TRUE) e e- Nchild:poly(Cage,, raw = TRUE) > print(plot(effect("nchild*poly(cage,, raw=true)", m), multiline = TRUE, + type = "link")) Nchild*Cage effect plot 0 Nchild Cage > data$kids <- factor(ifelse(data$nchild == 0, "n", "y")) > m <- update(m, ~kids * poly(cage,, raw = TRUE) + ) > print(plot(effect("kids*poly(cage,, raw=true)", m), multiline = TRUE, + type = "link")) > Anova(m)

3 Analysis of Deviance Table (Type II tests) Response: LR Chisq Df Pr(>Chisq) kids e-09 poly(cage,, raw = TRUE) e e- kids:poly(cage,, raw = TRUE) kids*cage effect plot n y kids Cage GLMM fit > g <- lmer( ~ kids * poly(cage,, raw = TRUE) ( Area), data = data, family = binomial) > Anova(g) Analysis of Deviance Table (Type II tests) Response: Chisq Df Pr(>Chisq) kids e-08 poly(cage,, raw = TRUE) e e-09 kids:poly(cage,, raw = TRUE) > print(plot(effect("kids:poly(cage,, raw=true)", g), multiline = TRUE, + type = "link"))

4 kids*cage effect plot n y kids Cage Coefficients > comparecoefs(m, g) Call: :glm(formula = ~ kids + poly(cage,, raw = TRUE) + + kids:poly(cage,, raw = TRUE), family = binomial, data = data) :glmer(formula = ~ kids * poly(cage,, raw = TRUE) + + ( Area), data = data, family = binomial) Est. SE Est. SE (Intercept) kidsy poly(cage,, raw = TRUE) poly(cage,, raw = TRUE) kidsy:poly(cage,, raw = TRUE) kidsy:poly(cage,, raw = TRUE) > exp(fixef(g)) (Intercept) kidsy poly(cage,, raw = TRUE) poly(cage,, raw = TRUE) kidsy:poly(cage,, raw = TRUE) kidsy:poly(cage,, raw = TRUE)

5 Random effects > str(ranef(g)) List of $ Area:'data.frame': 60 obs. of variable:..$ (Intercept): num [:60] attr(*, "class")= chr "ranef.mer" > par(mfrow = c(, )) > plot(density(ff <- ranef(g)$area[, ]), main = "Density of Area effects", + ylim = c(0,.), lwd = ) > xx <- seq(-.5,.5, length = 00) > lines(mean(ff) + sd(ff) * xx, dnorm(xx)/sd(ff)) > qqnorm(ff, main = "QQ-plot of random effects") > qqline(ff) Density of Area effects QQ plot of random effects Density Sample Quantiles N = 60 Bandwidth = 0.49 Theoretical Quantiles > print(g <- update(g, ~. - ( Area) + ( - Area)), + corr = FALSE) Generalized linear mixed model fit by the Laplace approximation Formula: ~ kids + poly(cage,, raw = TRUE) + + ( - Data: data AIC BIC loglik deviance Random effects: Groups Name Variance Std.Dev. Corr Area Number of obs: 94, groups: Area, 60 Area) + k 5

6 Fixed effects: Estimate Std. Error z value Pr(> z ) (Intercept) e-09 kidsy e-08 poly(cage,, raw = TRUE) poly(cage,, raw = TRUE) e-07 kidsy:poly(cage,, raw = TRUE) kidsy:poly(cage,, raw = TRUE) > anova(g, g, text = "Chisq") Data: data Models: g: ~ kids * poly(cage,, raw = TRUE) + + ( Area) g: ~ kids + poly(cage,, raw = TRUE) + + ( - g: Area) + kids:poly(cage,, raw = TRUE) Df AIC BIC loglik Chisq Chi Df Pr(>Chisq) g g

Step 1: Load the appropriate R package. Step 2: Fit a separate mixed model for each independence claim in the basis set.

Step 1: Load the appropriate R package. You will need two libraries: nlme and lme4. Step 2: Fit a separate mixed model for each independence claim in the basis set. For instance, in Table 2 the first basis