I am running glmer logit models using the lme4 package. I am interested in various two and three way interaction effects and their interpretations. To simplify, I am only concerned with the fixed effects coefficients.
I managed to come up with a code to calculate and plot these effects on the logit scale, but I am having trouble transforming them to the predicted probabilities scale. Eventually I would like to replicate the output of the effects package.
The example relies on the UCLA's data on cancer patients.
library(lme4)
library(ggplot2)
library(plyr)
getmode <- function(v) {
uniqv <- unique(v)
uniqv[which.max(tabulate(match(v, uniqv)))]
}
facmin <- function(n) {
min(as.numeric(levels(n)))
}
facmax <- function(x) {
max(as.numeric(levels(x)))
}
hdp <- read.csv("http://www.ats.ucla.edu/stat/data/hdp.csv")
head(hdp)
hdp <- hdp[complete.cases(hdp),]
hdp <- within(hdp, {
Married <- factor(Married, levels = 0:1, labels = c("no", "yes"))
DID <- factor(DID)
HID <- factor(HID)
CancerStage <- revalue(hdp$CancerStage, c("I"="1", "II"="2", "III"="3", "IV"="4"))
})
Until here it is all data management, functions and the packages I need.
m <- glmer(remission ~ CancerStage*LengthofStay + Experience +
(1 | DID), data = hdp, family = binomial(link="logit"))
summary(m)
This is the model. It takes a minute and it converges with the following warning:
Warning message:
In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
Model failed to converge with max|grad| = 0.0417259 (tol = 0.001, component 1)
Even though I am not quite sure if I should worry about the warning, I use the estimates to plot the average marginal effects for the interaction of interest. First I prepare the dataset to be feed into the predict function, and then I calculate the marginal effects as well as the confidence intervals using the fixed effects parameters.
newdat <- expand.grid(
remission = getmode(hdp$remission),
CancerStage = as.factor(seq(facmin(hdp$CancerStage), facmax(hdp$CancerStage),1)),
LengthofStay = seq(min(hdp$LengthofStay, na.rm=T),max(hdp$LengthofStay, na.rm=T),1),
Experience = mean(hdp$Experience, na.rm=T))
mm <- model.matrix(terms(m), newdat)
newdat$remission <- predict(m, newdat, re.form = NA)
pvar1 <- diag(mm %*% tcrossprod(vcov(m), mm))
cmult <- 1.96
## lower and upper CI
newdat <- data.frame(
newdat, plo = newdat$remission - cmult*sqrt(pvar1),
phi = newdat$remission + cmult*sqrt(pvar1))
I am fairly confident these are correct estimates on the logit scale, but maybe I am wrong. Anyhow, this is the plot:
plot_remission <- ggplot(newdat, aes(LengthofStay,
fill=factor(CancerStage), color=factor(CancerStage))) +
geom_ribbon(aes(ymin = plo, ymax = phi), colour=NA, alpha=0.2) +
geom_line(aes(y = remission), size=1.2) +
xlab("Length of Stay") + xlim(c(2, 10)) +
ylab("Probability of Remission") + ylim(c(0.0, 0.5)) +
labs(colour="Cancer Stage", fill="Cancer Stage") +
theme_minimal()
plot_remission
I think now the OY scale is measured on the logit scale but to make sense of it I would like to transform it to predicted probabilities. Based on wikipedia, something like exp(value)/(exp(value)+1) should do the trick to get to predicted probabilities. While I could do newdat$remission <- exp(newdat$remission)/(exp(newdat$remission)+1) I am not sure how should I do this for the confidence intervals?.
Eventually I would like to get to the same plot what the effects package generates. That is:
eff.m <- effect("CancerStage*LengthofStay", m, KR=T)
eff.m <- as.data.frame(eff.m)
plot_remission2 <- ggplot(eff.m, aes(LengthofStay,
fill=factor(CancerStage), color=factor(CancerStage))) +
geom_ribbon(aes(ymin = lower, ymax = upper), colour=NA, alpha=0.2) +
geom_line(aes(y = fit), size=1.2) +
xlab("Length of Stay") + xlim(c(2, 10)) +
ylab("Probability of Remission") + ylim(c(0.0, 0.5)) +
labs(colour="Cancer Stage", fill="Cancer Stage") +
theme_minimal()
plot_remission2
Even though I could just use the effects package, it unfortunately does not compile with a lot of the models I had to run for my own work:
Error in model.matrix(mod2) %*% mod2$coefficients :
non-conformable arguments
In addition: Warning message:
In vcov.merMod(mod) :
variance-covariance matrix computed from finite-difference Hessian is
not positive definite or contains NA values: falling back to var-cov estimated from RX
Fixing that would require adjusting the estimation procedure, which at the moment I would like to avoid. plus, I am also curious what effects actually does here.
I would be grateful for any advice on how to tweak my initial syntax to get to predicted probabilities!
