Plotting random effects for a binomial GLMER in ggplot

Question

I've been using ggplot2 to plot binomial fits for survival data (1,0) with a continuous predictor using geom_smooth(method="glm"), but I don't know if it's possible to incorporate a random effect using geom_smooth(method="glmer"). When I try I get the following a warning message:

Warning message: Computation failed in stat_smooth(): No random effects terms specified in formula

Is it possible to specific random effects in stat_smooth(), and if so, how is this done?

ggplot GLM

Example code and dummy data below:

library(ggplot2)
library(lme4)

# simulate dummy dataframe

x <- data.frame(time = c(1, 1, 1, 1, 1, 1,1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2,
                         3, 3, 3, 3, 3, 3, 3, 3, 3,4, 4, 4, 4, 4, 4, 4, 4, 4),
                type = c('a', 'a', 'a', 'b', 'b', 'b','c','c','c','a', 'a', 'a', 
                         'b', 'b', 'b','c','c','c','a', 'a', 'a', 'b', 'b', 'b',
                         'c','c','c','a', 'a', 'a', 'b', 'b', 'b','c','c','c'), 
                randef = c('aa', 'ab', 'ac', 'ba', 'bb', 'bc', 'ca', 'cb', 'cc',
                           'aa', 'ab', 'ac', 'ba', 'bb', 'bc', 'ca', 'cb', 'cc', 
                           'aa', 'ab', 'ac', 'ba', 'bb', 'bc', 'ca', 'cb', 'cc', 
                           'aa', 'ab', 'ac', 'ba', 'bb', 'bc', 'ca', 'cb', 'cc'), 
                surv = sample(x = 1:200, size = 36, replace = TRUE), 
                nonsurv= sample(x = 1:200, size = 36, replace = TRUE))


# convert to survival and non survival into individuals following 
https://stackguides.com/questions/51519690/convert-cbind-format-for- binomial-glm-in-r-to-a-dataframe-with-individual-rows

x_long <- x %>%
  gather(code, count, surv, nonsurv)

# function to repeat a data.frame
x_df <- function(x, n){
  do.call('rbind', replicate(n, x, simplify = FALSE))
        }

# loop through each row and then rbind together
x_full <- do.call('rbind', 
                  lapply(1:nrow(x_long), 
                         FUN = function(i) x_df(x_long[i,], x_long[i, ]$count)))

# create binary_code
x_full$binary <- as.numeric(x_full$code == 'surv')

### binomial glm with interaction between time and type:
summary(fm2<-glm(binary ~ time*type, data = x_full, family = "binomial"))

### plot glm in ggplot2
ggplot(x_full, 
       aes(x = time, y = as.numeric(x_full$binary), fill= x_full$type)) +
   geom_smooth(method="glm", aes(color = factor(x_full$type)), 
               method.args = list(family = "binomial"))

### add randef to glmer
summary(fm3 <- glmer(binary ~ time * type + (1|randef), data = x_full, family = "binomial"))

### incorporate glmer in ggplot?
ggplot(x_full, aes(x = time, y = as.numeric(x_full$binary), fill= x_full$type)) +
  geom_smooth(method = "glmer", aes(color = factor(x_full$type)), 
              method.args = list(family = "binomial"))

Alternatively, how can I approach this using predict and incorporate the fit/error into ggplot?

Any help greatly appreciated!

UPDATE

Daniel provided an incredibly useful solution here using sjPlot and ggeffects here. I've attached a more lengthy solution using predict below that i've been meaning to update this weekend. Hopefully this comes in useful for someone else in the same predicament!

newdata <- with(fm3, 
                expand.grid(type=levels(x$type),
                            time = seq(min(x$time), max(x$time), len = 100)))

Xmat <- model.matrix(~ time * type, newdata)
fixest <- fixef(fm3)
fit <- as.vector(fixest %*% t(Xmat))
SE <- sqrt(diag(Xmat %*% vcov(fm3) %*% t(Xmat)))
q <- qt(0.975, df = df.residual(fm3))

linkinv <- binomial()$linkinv
newdata <- cbind(newdata, fit = linkinv(fit), 
                 lower = linkinv(fit - q * SE),
                 upper = linkinv(fit + q * SE))

ggplot(newdata, aes(y=fit, x=time , col=type)) +
  geom_line() +       
  geom_ribbon(aes(ymin=lower, ymax=upper, fill=type), color=NA, alpha=0.4)

I don't think you can do it in stat_smooth(), because the smoothing function in stat_smooth() only has access to the x and y variables, not to any aux variables (such as grouping variables). Try sjPlot::plot_model() ? — Ben Bolker
Hi Ben, starstruck that you'd answer my post (let alone such a rapid response!). sjPlot gives me the oddsratios but not the binomial fit along the continuous predictor. — Thomas Moore
OK. You can do it with predict + the stuff in the GLMM FAQ that shows how to get (approximate) confint on predictions (it ignores uncertainty in the random effects parameters). May post something tomorrow AM if no-one else gets to it first. — Ben Bolker
Legend Ben, thank you! I'll give it a crack meanwhile and update if I get an answer — Thomas Moore
Hey Ben, I've updated the above with code that I think is correct. Any chance you could take a look and let me know if i've done this correctly? — Thomas Moore

Daniel Daniel · Accepted Answer · 2018-11-23T13:06:10

I'm not sure if your update produces the correct plot, because the "regression line" is almost a straight line, while the related CI's are not symmetrical to the line.

However, I think you can produce the plot you want with either sjPlot or ggeffects.

plot_model(fm3, type = "pred", terms = c("time", "type"), pred.type = "re")

pr <- ggpredict(fm3, c("time", "type"), type = "re")
plot(pr)

If you don't want to condition your predictions on random effects, simply leave out the pred.type resp. type argument:

plot_model(fm3, type = "pred", terms = c("time", "type"))

pr <- ggpredict(fm3, c("time", "type"))
plot(pr)

You can also plot your predictions conditioned on the different levels of the random effects, simply by adding the random effect term to the terms-argument:

pr <- ggpredict(fm3, c("time", "type", "randef"))
plot(pr)

... or the other way round:

# NOTE! predictions are almost identical for each random
# effect group, so lines are overlapping!
pr <- ggpredict(fm3, c("time", "randef", "type"))
plot(pr)

You can find more details in this package-vignette.

Plotting random effects for a binomial GLMER in ggplot

2 Answers