[R-sig-ME] Nonsensical results in glmer (bglmer)

[Francesco Romano]

Dear all,


I wonder if anyone can account for a counterintuitive result in my analyses
of a logistic regression run with glmer. The data, where I only use the
columns RESP as a binomial outcome coded as character (correct vs.
incorrect), Type as a factor with 2 levels where 'islands' constitutes the
reference level, Group as a factor with two levels where 'L1' constitutes
the reference level, and SUBJ and ITEM as random effects, is attached. In
this particular analysis I use bglmer but the same result ensues from glmer
or even a bernoulli brm analysis in the Bayesian framework (i.e. brms
package).

The following output shows that the group L1, the reference group, has a
lower probability of a correct score compared to L2. If the output is
garbled in your email, feel free to run the code yourself to get a clearer
picture. Under the fixed-effects of the output, we interpret the
coefficient -1.38 of r*elevel(masterPT$Group, ref = "L2")L1        -1.3802
    0.6907  -1.998  0.04567 * *to mean that the probability of scoring a
correct answer is approximately 34% lower in the L1 than the L2 group
(following Gelman and Hill, 2007, p.93) we divide the coeffecient -1.38
expressed in log odds by 4 to obtain an approximate corresponding
probability). This is counterintuitive because the L1 group is basically a
group of native speakers of Spanish, the language being tested, while the
L2 is a bilingual group being tested in Spanish as a foreign language which
they learned later in life. Even playing devil's advocate, a quick look at
a prop table or even the figures also attached shows the L1 group exhibit
lower counts of incorrect responses. In the figures, this can be easily
seen by comparing the amount of light blue splash for either of the Type
levels between the L1 and L2 groups. There is far less of a splash in the
L1 data which suggests they should statisticall have a higher chance of
selecting a correct response.

> freqmodel2<-bglmer(as.factor(RESP)~Type*relevel(masterPT$Group, ref =
"L2")+(1+Type|SUBJ)+(1+Group|ITEM), family = binomial(link="logit"),
data=masterPT, control=glmerControl(optimizer = "bobyqa"), nAGQ=1)
> summary(freqmodel2)
Cov prior  : SUBJ ~ wishart(df = 4.5, scale = Inf, posterior.scale = cov,
common.scale = TRUE)
           : ITEM ~ wishart(df = 4.5, scale = Inf, posterior.scale = cov,
common.scale = TRUE)
Prior dev  : -5.3929

Generalized linear mixed model fit by maximum likelihood (Laplace
Approximation) ['bglmerMod']
 Family: binomial  ( logit )
Formula: as.factor(RESP) ~ Type * relevel(masterPT$Group, ref = "L2") +
 (1 + Type | SUBJ) + (1 + Group | ITEM)
   Data: masterPT
Control: glmerControl(optimizer = "bobyqa")

     AIC      BIC   logLik deviance df.resid
  1676.8   1734.1   -828.4   1656.8     2265

Scaled residuals:
    Min      1Q  Median      3Q     Max
-4.1192 -0.3447 -0.1315  0.1106  4.8595

Random effects:
 Groups Name        Variance Std.Dev. Corr
 SUBJ   (Intercept) 1.915    1.384
        Type2       1.642    1.281    -0.74
 ITEM   (Intercept) 8.970    2.995
        Group2      6.479    2.545    -0.74
Number of obs: 2275, groups:  SUBJ, 65; ITEM, 35

Fixed effects:
                                            Estimate Std. Error z value
Pr(>|z|)
(Intercept)                                  -1.3577     0.4947  -2.745
 0.00606 **
Type2                                         1.4683     0.8340   1.760
 0.07834 .
relevel(masterPT$Group, ref = "L2")L1        -1.3802     0.6907  -1.998
 0.04567 *
Type2:relevel(masterPT$Group, ref = "L2")L1  -4.0366     1.2383  -3.260
 0.00112 **
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
            (Intr) Type2  r(Pr="
Type2       -0.546
r(PT$G,r="L -0.325  0.157
T2:(PT$Gr="  0.151 -0.221 -0.442


What am I missing here?
Am I interpreting something wrong?

Many thanks in advance for any help,

Best,

Francesco Romano PhD

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