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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

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    $\begingroup$ 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. $\endgroup$ – Jeremy Miles Oct 15 '13 at 18:57
  • $\begingroup$ You get the same result with glm, not just glmer. $\endgroup$ – Jeremy Miles Oct 15 '13 at 19:00
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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  
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    $\begingroup$ 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 ... $\endgroup$ – Ben Bolker Oct 16 '13 at 0:54
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    $\begingroup$ 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 ... $\endgroup$ – Ben Bolker Oct 16 '13 at 13:43
  • $\begingroup$ @BenBolker: ha, yes, an error message like that would have been helpful! $\endgroup$ – Sol Oct 19 '13 at 5:31

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