Dear all,

I apologize if this issue has already been covered in the list.

I am analyzing accuracy data on a picture naming task. Correct responses
are coded as 1, errors as 0. I have 2 fixed-effects predictors:

1. Condition, 3 levels, within participants and items
2. Freq_group: 2 levels, within participants but between items

Here are the contrasts:

contrasts(joint$Condition)<-cbind(c(-2/3,1/3,1/3), c(0,-1/2,1/2))
contrasts(joint$Freq_group)<-cbind(c(-0.5,0.5))

In addition, I have a between-participants continuous predictor
(E_proficiency_SP: English Spoken Language Proficiency) that has been
centered, but not scaled.

I analyzed these data some time ago using a version of lme4 <1. When I ran
the analyses in R 3.0.3 using lme4.0, I obtained the same output as in my
old analyses. See below.

----------------------------------------------------------------------
Generalized linear mixed model fit by the Laplace approximation
Formula: Resp.bin ~ 1 + Freq_group * Condition * E_proficiency_SP + (1
+      Freq_group * Condition | Subject) + (1 + Condition | Item_numb)
   Data: joint.NS
  AIC  BIC logLik deviance
 2094 2330  -1008     2016
Random effects:
 Groups    Name                   Variance  Std.Dev.
Corr
 Item_numb (Intercept)            0.9656165
0.982658
           Condition1             1.6699788 1.292277
-0.035
           Condition2             0.0077218 0.087874 -0.052
1.000
 Subject   (Intercept)            0.1608360
0.401044
           Freq_group1            0.1649723 0.406168
-0.417
           Condition1             0.4448590 0.666978 -0.678
0.269
           Condition2             0.1776654 0.421504  0.274 -0.739
0.319
           Freq_group1:Condition1 0.7216097 0.849476 -0.940  0.701  0.647
-0.478
           Freq_group1:Condition2 0.7144539 0.845254 -0.345 -0.683  0.079
0.375  0.010
Number of obs: 3107, groups: Item_numb, 131; Subject, 24

Fixed effects:
                                        Estimate Std. Error z value
Pr(>|z|)
(Intercept)                              2.70027    0.14160  19.070  <
2e-16 ***
Freq_group1                             -1.04832    0.24404  -4.296
1.74e-05 ***
Condition1                               0.68127    0.22876   2.978
0.00290 **
Condition2                              -0.56823    0.20482  -2.774
0.00553 **
E_proficiency_SP                         0.04677    0.08473   0.552
0.58096
Freq_group1:Condition1                  -0.32467    0.40460  -0.802
0.42229
Freq_group1:Condition2                  -0.10520    0.40897  -0.257
0.79700
Freq_group1:E_proficiency_SP            -0.20632    0.12643  -1.632
0.10268
Condition1:E_proficiency_SP             -0.13266    0.15364  -0.863
0.38791
Condition2:E_proficiency_SP             -0.39620    0.16135  -2.456
0.01407 *
Freq_group1:Condition1:E_proficiency_SP -0.26202    0.25468  -1.029
0.30357
Freq_group1:Condition2:E_proficiency_SP  0.14582    0.31966   0.456
0.64827
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
            (Intr) Frq_g1 Cndtn1 Cndtn2 E_p_SP Fr_1:C1 Fr_1:C2 F_1:E_
C1:E__ C2:E__ F_1:C1:
Freq_group1
-0.202

Condition1  -0.155
-0.008
Condition2  -0.032 -0.048
0.010
E_prfcnc_SP  0.033 -0.052  0.007
-0.094
Frq_grp1:C1 -0.299  0.214  0.032 -0.038
-0.037
Frq_grp1:C2 -0.036 -0.214  0.064 -0.252  0.077
-0.075
Frq_1:E__SP -0.061  0.052 -0.043  0.101 -0.323  0.012
-0.126
Cndt1:E__SP  0.006 -0.032  0.044 -0.077 -0.281 -0.045   0.063
0.035
Cndt2:E__SP -0.079  0.071 -0.073  0.068 -0.037  0.065  -0.119  -0.119
-0.017
F_1:C1:E__S -0.034  0.008 -0.050  0.074 -0.443  0.060  -0.093   0.343
0.103 -0.078
F_1:C2:E__S  0.063 -0.094  0.059 -0.117 -0.079 -0.087   0.066  -0.317
0.039 -0.186 -0.130
----------------------------------------------------------------------------------------------------------------

However, having read recently that lmer version 1.1-7 obtains better fits
than lme4.0, I fitted the same model using glmer with the bobyqa optimizer
and maxfun=16000. Here is the output. There were no convergence issues or
any other warnings (when I increased the number of iterations as suggested).

-------------------------------------------------------------------------------------------------------------------
Generalized linear mixed model fit by maximum likelihood (Laplace
Approximation) ['glmerMod']
 Family: binomial  ( logit )
Formula: Resp.bin ~ 1 + Freq_group * Condition * E_proficiency_SP + (1
+      Freq_group * Condition | Subject) + (1 + Condition | Item_numb)
   Data: joint.NS
Control: glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 16000))

     AIC      BIC   logLik deviance df.resid
  2094.4   2330.0  -1008.2   2016.4     3068

Scaled residuals:
    Min      1Q  Median      3Q     Max
-6.7090  0.1461  0.2251  0.3482  1.6999

Random effects:
 Groups    Name                   Variance Std.Dev.
Corr
 Item_numb (Intercept)            0.965582
0.98264
           Condition1             1.669926 1.29226
-0.04
           Condition2             0.007722 0.08788  -0.05
1.00
 Subject   (Intercept)            0.160826
0.40103
           Freq_group1            0.164960 0.40615
-0.42
           Condition1             0.444855 0.66697  -0.68
0.27
           Condition2             0.177659 0.42150   0.27 -0.74
0.32
           Freq_group1:Condition1 0.721550 0.84944  -0.94  0.70  0.65
-0.48
           Freq_group1:Condition2 0.714430 0.84524  -0.35 -0.68  0.08
0.37  0.01
Number of obs: 3107, groups:  Item_numb, 131; Subject, 24

Fixed effects:
                                        Estimate Std. Error z value
Pr(>|z|)
(Intercept)                              2.70023    0.16124  16.747  <
2e-16 ***
Freq_group1                             -1.04829    0.25693  -4.080
4.5e-05 ***
Condition1                               0.68123    0.27441   2.483
0.0130 *
Condition2                              -0.56822    0.29971  -1.896
0.0580 .
E_proficiency_SP                         0.04675    0.08527   0.548
0.5835
Freq_group1:Condition1                  -0.32464    0.43299  -0.750
0.4534
Freq_group1:Condition2                  -0.10517    0.44365  -0.237
0.8126
Freq_group1:E_proficiency_SP            -0.20633    0.12692  -1.626
0.1040
Condition1:E_proficiency_SP             -0.13266    0.15570  -0.852
0.3942
Condition2:E_proficiency_SP             -0.39620    0.16214  -2.443
0.0145 *
Freq_group1:Condition1:E_proficiency_SP -0.26201    0.25735  -1.018
0.3086
Freq_group1:Condition2:E_proficiency_SP  0.14583    0.31962   0.456
0.6482
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
            (Intr) Frq_g1 Cndtn1 Cndtn2 E_p_SP Fr_1:C1 Fr_1:C2 F_1:E_
C1:E__ C2:E__ F_1:C1:
Freq_group1
-0.249

Condition1  -0.032
-0.056
Condition2  -0.085 -0.059
-0.056
E_prfcnc_SP  0.046 -0.055  0.001
-0.094
Frq_grp1:C1 -0.289  0.211 -0.065 -0.045
-0.028
Frq_grp1:C2 -0.042 -0.174  0.036 -0.328  0.079
-0.053
Frq_1:E__SP -0.060  0.047 -0.044  0.080 -0.313  0.019
-0.117
Cndt1:E__SP  0.001 -0.024  0.061 -0.070 -0.291 -0.048   0.056
0.031
Cndt2:E__SP -0.092  0.071 -0.074  0.069 -0.032  0.060  -0.122  -0.122
-0.012
F_1:C1:E__S -0.038  0.015 -0.047  0.059 -0.443  0.044  -0.083   0.321
0.116 -0.077
F_1:C2:E__S  0.061 -0.081  0.050 -0.115 -0.077 -0.071   0.076  -0.305
0.035 -0.177 -0.124
---------------------------------------------------------------------------------------------------------------

The two models are very similar, with almost identical estimates and the
same AIC, BIC, and logLik. However, the model fitted with the newer glmer
has generally higher standard errors.

Any idea as to what might be behind this? And is there any reason to prefer
one method to the other a priori?

Many thanks,

Chiara Gambi


Psycholinguistics Group
Saarland University

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