Puzzling behavior of glmer()

I'd like your opinion on a very strange behavior that I recently encountered running glmer(). The problem is that when I make the dependent variable into a logical vector, glmer behaves weirdly. My dependent variable is Accuracy, and it is coded in terms of 1 (accurate response) and 0 (wrong response). What puzzles me is that transforming accuracy to a logical vector should work the same way for glmer, as a logical vector is coded in terms of TRUE or FALSE, having also 2 levels. However, glmer gives me different results depending on the transformation of the dependent variable I use. Have you guys encountered this before? Do you know why it happens? Below is sample code so you can replicate the problem yourselves.

#Create fake data
Subject   <- c(rep("S1",4), rep("S2",4), rep("S3",4), rep("S4",4))
Item      <- rep(c("I1","I2","I3","I4"),4)
Factor1   <- c(c(rep("e1",2),rep("e2",2)), c("e1","e2","e2","e1"),
c(rep("e2",2),rep("e1",2)), c("e2","e1","e1","e2"))
Accuracy  <- c(1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,1)

#Create data frame and make "Accuracy" into a factor with 2 levels
data          <- data.frame(Subject,Item,Factor1, Accuracy)
data$Accuracy <- factor(data$Accuracy)  #Accuracy is a factor w/ 2 levels
#Run glmer
m1 <- glmer(Accuracy ~ Factor1 + (1+Factor1|Subject) + (1+Factor1|Item), family = "binomial", data= data)
summary(m1)
Fixed effects:
Estimate Std. Error z value Pr(>|z|)
(Intercept)    1.946      1.069   1.820   0.0687 .
Factor1e2     -1.946      1.282  -1.518   0.1290
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


That is the output of the first model. Now, look at what happens if I transform data$Accuracy into a logical vector when I run the model: m2 <- glmer(as.logical(as.numeric(Accuracy)) ~ Factor1 + (1+Factor1|Subject) + (1+Factor1|Item), family = "binomial", data= data) summary(m2) Fixed effects: Estimate Std. Error z value Pr(>|z|) (Intercept) 2.557e+01 1.259e+05 0 1 Factor1e2 2.223e-06 1.781e+05 0 1  As you can see, now the coefficient estimates are very different. As I said, this seems very puzzling to me and I'd like yo know if you have some thoughts on why this should be. Thanks a lot! --Sol • I'm not sure why, but breaking it into two steps works for me: AccLog <- as.logical(as.numeric(Accuracy)) then run m2 with AccLog. Oct 15 '13 at 18:57 • You get the same result with glm, not just glmer. Oct 15 '13 at 19:00 1 Answer More of a programming question. Compare: > as.logical(as.numeric(data$Accuracy))
[1] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
[16] TRUE
> as.logical(as.numeric(Accuracy))
[1]  TRUE  TRUE FALSE FALSE  TRUE FALSE  TRUE FALSE  TRUE FALSE  TRUE  TRUE
[13]  TRUE  TRUE  TRUE  TRUE


You're performing the former with your call to glmer since you are using the data = ... argument

m2 <- glmer(as.logical(as.numeric(Accuracy)) ~ Factor1 + (1+Factor1|Subject) + (1+Factor1|Item), family = "binomial", data= data)


As to why this is happening:

> as.numeric(data$Accuracy) [1] 2 2 1 1 2 1 2 1 2 1 2 2 2 2 2 2 > as.numeric(Accuracy) [1] 1 1 0 0 1 0 1 0 1 0 1 1 1 1 1 1  Basically as.numeric returns the numeric representation of the levels of a factor variable, and then as.logical treats all non-zero values as TRUE (not entirely sure about negative values, actually). To get the original values back, you need to use > as.numeric(levels(data$Accuracy)[data\$Accuracy])
[1] 1 1 0 0 1 0 1 0 1 0 1 1 1 1 1 1


Thus...

> m2 <- glmer(as.logical(as.numeric(levels(Accuracy)[Accuracy])) ~ Factor1 + (1+Factor1|Subject) + (1+Factor1|Item), family = "binomial", data= data)
> summary(m2)
...
Fixed effects:
Estimate Std. Error z value Pr(>|z|)
(Intercept)    1.946      1.069   1.820   0.0687 .
Factor1e2     -1.946      1.282  -1.518   0.1290

• it might be worth submitting this as an issue at github.com/lme4/lme4/issues -- I think it should work correctly with a factor, as glm() does ... Oct 16 '13 at 0:54
• oops. Reading this more carefully I see that it isn't a glmer issue at all. I will say that at least the development version of lme4 gives an error Response is constant - cannot fit the model , which at least gives a clue ... Oct 16 '13 at 13:43
• @BenBolker: ha, yes, an error message like that would have been helpful!
– Sol
Oct 19 '13 at 5:31