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

Emilia Ellsiepen emilia.ellsiepen at gmail.com
Tue Mar 4 11:10:27 CET 2014


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?



*** with dummy coding:

> m1 = lmer(score ~ Order*Voice + (Order*Voice|subject)+(Order*Voice|sentence) ,rawdata)
Warning message:
In mer_finalize(ans) : singular convergence (7)
> summary(m1)
Linear mixed model fit by REML
Formula: score ~ Order * Voice + (Order * Voice | subject) + (Order *
    Voice | sentence)
   Data: rawdata
  AIC  BIC logLik deviance REMLdev
 1626 1740 -787.9     1562    1576
Random effects:
 Groups   Name                         Variance Std.Dev. Corr
 subject  (Intercept)                  0.097201 0.31177
          OrderDat second              0.055057 0.23464  -0.690
          VoicePassive                 0.161333 0.40166  -0.952  0.878
          OrderDat second:VoicePassive 0.182879 0.42764   0.732 -0.986 -0.900
 sentence (Intercept)                  0.015671 0.12518
          OrderDat second              0.068464 0.26166  -0.663
          VoicePassive                 0.025271 0.15897  -0.237 -0.031
          OrderDat second:VoicePassive 0.053708 0.23175   0.031 -0.589 -0.425
 Residual                              0.465541 0.68231
Number of obs: 720, groups: subject, 36; sentence, 20

Fixed effects:
                             Estimate Std. Error t value
(Intercept)                   0.16341    0.07791   2.097
OrderDat second              -0.01835    0.10062  -0.182
VoicePassive                 -0.05604    0.10449  -0.536
OrderDat second:VoicePassive  0.54250    0.13458   4.031

Correlation of Fixed Effects:
            (Intr) OrdrDs VcPssv
OrderDtscnd -0.647
VoicePassiv -0.754  0.459
OrdrDscn:VP  0.509 -0.717 -0.729

> mi = lmer(score ~ Order+Voice + (Order*Voice|subject)+(Order*Voice|sentence) ,rawdata)
> summary(mi)
Linear mixed model fit by REML
Formula: score ~ Order + Voice + (Order * Voice | subject) + (Order *
    Voice | sentence)
   Data: rawdata
  AIC  BIC logLik deviance REMLdev
 1634 1744 -793.2     1574    1586
Random effects:
 Groups   Name                         Variance Std.Dev. Corr
 subject  (Intercept)                  0.115077 0.33923
          OrderDat second              0.094406 0.30726  -0.738
          VoicePassive                 0.211833 0.46025  -0.951  0.893
          OrderDat second:VoicePassive 0.330228 0.57465   0.761 -0.999 -0.902
 sentence (Intercept)                  0.019567 0.13988
          OrderDat second              0.111327 0.33366  -0.814
          VoicePassive                 0.048545 0.22033  -0.451  0.420
          OrderDat second:VoicePassive 0.184456 0.42948   0.478 -0.771 -0.793
 Residual                              0.463180 0.68057
Number of obs: 720, groups: subject, 36; sentence, 20

Fixed effects:
                Estimate Std. Error t value
(Intercept)     0.009676   0.066665   0.145
OrderDat second 0.276029   0.069910   3.948
VoicePassive    0.237470   0.071133   3.338

Correlation of Fixed Effects:
            (Intr) OrdrDs
OrderDtscnd -0.472
VoicePassiv -0.631 -0.160

> 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 -787.24
m1 25 1611.7 1726.2 -780.86 12.772      1  0.0003518 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

*** with 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) ,rawdata)
> summary(m1)
Linear mixed model fit by REML
Formula: score ~ Order * Voice + (Order * Voice | subject) + (Order *
    Voice | sentence)
   Data: rawdata
  AIC  BIC logLik deviance REMLdev
 1631 1746 -790.7     1562    1581
Random effects:
 Groups   Name          Variance   Std.Dev.  Corr
 subject  (Intercept)   1.9949e-02 0.1412424
          Order1        1.4195e-05 0.0037676 -1.000
          Voice1        1.3413e-02 0.1158136  0.833 -0.833
          Order1:Voice1 1.1566e-02 0.1075434  0.286 -0.286  0.615
 sentence (Intercept)   2.9850e-03 0.0546352
          Order1        1.1405e-02 0.1067934  0.257
          Voice1        5.8322e-03 0.0763687  0.297 -0.438
          Order1:Voice1 3.4893e-03 0.0590699 -0.884  0.182 -0.328
 Residual               4.6543e-01 0.6822234
Number of obs: 720, groups: subject, 36; sentence, 20

Fixed effects:
              Estimate Std. Error t value
(Intercept)    0.26184    0.03674   7.127
Order1        -0.12645    0.03489  -3.625
Voice1        -0.10761    0.03620  -2.972
Order1:Voice1  0.13562    0.03380   4.013

Correlation of Fixed Effects:
            (Intr) Order1 Voice1
Order1       0.047
Voice1       0.331 -0.150
Order1:Voc1 -0.018  0.046  0.113
> mi = lmer(score ~ Order+Voice + (Order*Voice|subject)+(Order*Voice|sentence) ,rawdata)
> summary(mi)
Linear mixed model fit by REML
Formula: score ~ Order + Voice + (Order * Voice | subject) + (Order *
    Voice | sentence)
   Data: rawdata
  AIC  BIC logLik deviance REMLdev
 1637 1747 -794.6     1575    1589
Random effects:
 Groups   Name          Variance   Std.Dev.  Corr
 subject  (Intercept)   2.0497e-02 0.1431662
          Order1        4.1101e-06 0.0020273 -1.000
          Voice1        1.3959e-02 0.1181500  0.808 -0.808
          Order1:Voice1 2.0579e-02 0.1434552  0.290 -0.290  0.540
 sentence (Intercept)   2.6765e-03 0.0517352
          Order1        1.1696e-02 0.1081500  0.320
          Voice1        5.0552e-03 0.0710997  0.275 -0.531
          Order1:Voice1 1.1587e-02 0.1076410 -0.805  0.200 -0.293
 Residual               4.6331e-01 0.6806653
Number of obs: 720, groups: subject, 36; sentence, 20

Fixed effects:
            Estimate Std. Error t value
(Intercept)  0.26626    0.03667   7.261
Order1      -0.13508    0.03495  -3.865
Voice1      -0.11835    0.03568  -3.317

Correlation of Fixed Effects:
       (Intr) Order1
Order1  0.066
Voice1  0.332 -0.175
> 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 1622.6 1732.5 -787.29
m1 25 1611.8 1726.3 -780.90 12.78      1  0.0003504 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1


2014-03-03 18:22 GMT+01:00 Levy, Roger <rlevy at ucsd.edu>:
> (cc-ing the list, which I forgot to do on the last response...)
>
>
> On Mar 3, 2014, at 8:41 AM, Emilia Ellsiepen <emilia.ellsiepen at gmail.com> wrote:
>
>>
>>
>> 2014-03-03 16:23 GMT+01:00 Levy, Roger <rlevy at ucsd.edu>:
>>>
>>>> On Mar 3, 2014, at 3:09, "Emilia Ellsiepen" <emilia.ellsiepen at gmail.com> wrote:
>>>>
>>>> Thank you for your feedback and this interesting discussion.
>>>>
>>>>
>>>>>> First off, it is not clear that Emilia's specific problem is being caused
>>>>>> by over-parameterization.  Emilia, could you perhaps give more information
>>>>>> about the nature of the dataset that you're analyzing?  Is it a 2x2
>>>>>> within-subjects, within-sentence balanced design without a great deal of
>>>>>> missing data?  In my experience with the last few pre-1.0 versions, lme4 is
>>>>>> generally very good at converging to an optimum for these kinds of datasets
>>>>>> with the number of observations and groups your fitted model reports.  Have
>>>>>> you tried fitting the model with the nlminb optimizer, either by including
>>>>>>
>>>>>> optimizer="optimx",optCtrl=list(method="nlminb")
>>>>>>
>>>>>> in the list of arguments to lmerControl, or by using the last pre-1.0
>>>>>> version of lme4 (available as lme4.0 on R-Forge)?  Do you still get similar
>>>>>> problems with the nlminb optimizer?  (You should definitely not get the
>>>>>> result that the simpler model has a higher log-likelihood.)
>>>>
>>>> The design was a balanced 2x2 with-in subjects and with-in sentences
>>>> design without any missing data from a magnitude estimation
>>>> experiment.
>>>> When I use the nlminb optimizer (by installing the lme4.0 version), I
>>>> do get the interaction using the likelihood-ratio test, but I also get
>>>> the following warning message:
>>>>
>>>> Warning message:
>>>> In mer_finalize(ans) : singular convergence (7)
>>>
>>> Thanks for this follow-up, Emilia! Question: do you get this warning when you fit the more complex model (with the fixed-effects interaction), or the null-hypothesis model (without the fixed-effects interaction)?
>
>> That was for the more complex model with interaction. The one without
>> interaction converged without problems.
>
> Thanks Emilia.  Could you please give us a bit more information -- show us the fitted models (both the null and alternative-hypothesis models), and also the results of the call to anova()?
>
> Best
>
> Roger



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