[R-sig-ME] likelihood-ratio tests in conflict with coefficiants in maximal random effect model

Emilia Ellsiepen emilia.ellsiepen at gmail.com
Wed Mar 5 11:15:35 CET 2014


2014-03-04 18:39 GMT+01:00 Levy, Roger <rlevy at ucsd.edu>:
>
>
>
> On Mar 4, 2014, at 3:10 AM, Emilia Ellsiepen <emilia.ellsiepen at gmail.com> wrote:
>
>> Thank you for your support, Roger - actually the problem vanished when
>> I used sum-coding (after installing the packages and reloading the
>> data, I accidentally skipped this step yesterday). So, in fact with
>> the old lme4.0 version, the model did converge. I pasted in all model
>> summaries and LRTs for dummy and sum coding below.
>> Would you recommend to always use the old version then?
>
> Thanks so much, Emilia, for following up.  This is very interesting.  Something doesn't quite add up, though, in the model summaries and LRTs that you pasted below, because the log-likelihoods in the model summaries are not the same as the log-likelihoods reported in the results of anova().  I notice that you're not using REML=F as an argument in your call to lmer().  Could you perhaps rerun all four model-fitting functions and the two anova() calls with REML=F, and show us the complete results?
>
> Best & thanks again,
>
> Roger
>
Rerunning with REML=F led to a singular convergence in the
null-hypothesis model with dummy coding. The sum coded variant still
converges without warnings. While the two LRTs give in general the
same result for both coding schemes, as I would have expected, there
are minimal differences in the logLik, AIC and BIC values.

Here are the results in detail:
**** dummy coding:

> m1 = lmer(score ~ Order*Voice + (Order*Voice|subject)+(Order*Voice|sentence), REML=F ,rawdata)
> summary(m1)
Linear mixed model fit by maximum likelihood
Formula: score ~ Order * Voice + (Order * Voice | subject) + (Order *
Voice | sentence)
   Data: rawdata
  AIC  BIC logLik deviance REMLdev
 1612 1726 -780.8     1562    1576
Random effects:
 Groups   Name                         Variance Std.Dev. Corr
 subject  (Intercept)                  0.092788 0.30461
          OrderDat second              0.051950 0.22793  -0.689
          VoicePassive                 0.152335 0.39030  -0.954  0.875
          OrderDat second:VoicePassive 0.171303 0.41389   0.736 -0.991 -0.903
 sentence (Intercept)                  0.013700 0.11705
          OrderDat second              0.060511 0.24599  -0.652
          VoicePassive                 0.021227 0.14570  -0.215 -0.067
          OrderDat second:VoicePassive 0.045796 0.21400   0.016 -0.587 -0.404
 Residual                              0.466165 0.68276
Number of obs: 720, groups: subject, 36; sentence, 20

Fixed effects:
                             Estimate Std. Error t value
(Intercept)                   0.16341    0.07650   2.136
OrderDat second              -0.01835    0.09823  -0.187
VoicePassive                 -0.05604    0.10234  -0.548
OrderDat second:VoicePassive  0.54250    0.13194   4.112

Correlation of Fixed Effects:
            (Intr) OrdrDs VcPssv
OrderDtscnd -0.646
VoicePassiv -0.757  0.461
OrdrDscn:VP  0.514 -0.719 -0.730

> mi = lmer(score ~ Order+Voice + (Order*Voice|subject)+(Order*Voice|sentence) ,REML=F,rawdata)
Warning message:
In mer_finalize(ans) : singular convergence (7)
> summary(mi)
Linear mixed model fit by maximum likelihood
Formula: score ~ Order + Voice + (Order * Voice | subject) + (Order *
    Voice | sentence)
   Data: rawdata
  AIC  BIC logLik deviance REMLdev
 1622 1732 -787.2     1574    1586
Random effects:
 Groups   Name                         Variance Std.Dev. Corr
 subject  (Intercept)                  0.112099 0.33481
          OrderDat second              0.095834 0.30957  -0.743
          VoicePassive                 0.206993 0.45497  -0.953  0.895
          OrderDat second:VoicePassive 0.333823 0.57777   0.765 -0.999 -0.906
 sentence (Intercept)                  0.017953 0.13399
          OrderDat second              0.105527 0.32485  -0.832
          VoicePassive                 0.046129 0.21478  -0.473  0.454
          OrderDat second:VoicePassive 0.183020 0.42781   0.526 -0.786 -0.819
 Residual                              0.463528 0.68083
Number of obs: 720, groups: subject, 36; sentence, 20

Fixed effects:
                Estimate Std. Error t value
(Intercept)     0.008662   0.065187   0.133
OrderDat second 0.275830   0.068133   4.048
VoicePassive    0.237267   0.069355   3.421

Correlation of Fixed Effects:
            (Intr) OrdrDs
OrderDtscnd -0.468
VoicePassiv -0.632 -0.161
> anova(m1,mi)
Data: rawdata
Models:
mi: score ~ Order + Voice + (Order * Voice | subject) + (Order *
mi:     Voice | sentence)
m1: score ~ Order * Voice + (Order * Voice | subject) + (Order *
m1:     Voice | sentence)
   Df    AIC    BIC  logLik  Chisq Chi Df Pr(>Chisq)
mi 24 1622.4 1732.3 -787.21
m1 25 1611.6 1726.1 -780.82 12.788      1  0.0003489 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1


**** sum coding:

> contrasts(rawdata$Order) = contr.sum(2)
> contrasts(rawdata$Voice) = contr.sum(2)
> m1 = lmer(score ~ Order*Voice + (Order*Voice|subject)+(Order*Voice|sentence), REML=F ,rawdata)
> summary(m1)
Linear mixed model fit by maximum likelihood
Formula: score ~ Order * Voice + (Order * Voice | subject) + (Order *
    Voice | sentence)
   Data: rawdata
  AIC  BIC logLik deviance REMLdev
 1612 1726 -780.9     1562    1581
Random effects:
 Groups   Name          Variance   Std.Dev.  Corr
 subject  (Intercept)   1.8907e-02 0.1375028
          Order1        1.2567e-05 0.0035449 -1.000
          Voice1        1.2530e-02 0.1119373  0.866 -0.866
          Order1:Voice1 1.0808e-02 0.1039636  0.292 -0.292  0.630
 sentence (Intercept)   2.7251e-03 0.0522022
          Order1        1.0143e-02 0.1007109  0.250
          Voice1        5.1207e-03 0.0715590  0.333 -0.465
          Order1:Voice1 2.9324e-03 0.0541514 -0.877  0.186 -0.353
 Residual               4.6608e-01 0.6826980
Number of obs: 720, groups: subject, 36; sentence, 20

Fixed effects:
              Estimate Std. Error t value
(Intercept)    0.26184    0.03618   7.238
Order1        -0.12645    0.03398  -3.721
Voice1        -0.10761    0.03538  -3.042
Order1:Voice1  0.13562    0.03308   4.100

Correlation of Fixed Effects:
            (Intr) Order1 Voice1
Order1       0.042
Voice1       0.338 -0.147
Order1:Voc1 -0.007  0.043  0.116
> mi = lmer(score ~ Order+Voice + (Order*Voice|subject)+(Order*Voice|sentence) ,REML=F,rawdata)
> summary(mi)
Linear mixed model fit by maximum likelihood
Formula: score ~ Order + Voice + (Order * Voice | subject) + (Order *
    Voice | sentence)
   Data: rawdata
  AIC  BIC logLik deviance REMLdev
 1623 1732 -787.3     1575    1589
Random effects:
 Groups   Name          Variance   Std.Dev.  Corr
 subject  (Intercept)   1.9424e-02 0.1393698
          Order1        2.6892e-06 0.0016399 -1.000
          Voice1        1.3041e-02 0.1141955  0.838 -0.838
          Order1:Voice1 2.0839e-02 0.1443579  0.290 -0.290  0.541
 sentence (Intercept)   2.4074e-03 0.0490650
          Order1        1.0471e-02 0.1023269  0.323
          Voice1        4.3300e-03 0.0658028  0.280 -0.571
          Order1:Voice1 1.1412e-02 0.1068262 -0.784  0.204 -0.300
 Residual               4.6362e-01 0.6808933
Number of obs: 720, groups: subject, 36; sentence, 20

Fixed effects:
            Estimate Std. Error t value
(Intercept)  0.26513    0.03609   7.346
Order1      -0.13474    0.03407  -3.955
Voice1      -0.11837    0.03480  -3.401

Correlation of Fixed Effects:
       (Intr) Order1
Order1  0.063
Voice1  0.334 -0.173

> anova(m1,mi)
Data: rawdata
Models:
mi: score ~ Order + Voice + (Order * Voice | subject) + (Order *
mi:     Voice | sentence)
m1: score ~ Order * Voice + (Order * Voice | subject) + (Order *
m1:     Voice | sentence)
   Df    AIC    BIC  logLik  Chisq Chi Df Pr(>Chisq)
mi 24 1622.5 1732.4 -787.26
m1 25 1611.7 1726.2 -780.86 12.796      1  0.0003473 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1



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