[R-lang] mixed logit models, coding the effects and understanding the parameters

[Maria Carminati]

Please, can someone help me make sense of the parameters (intercepts and
coefficients) of my mixed logit model


The DV of my expt  is a target response (poresp)  which can be either
PO (coded as 1) or DO (coded as 0). So PO is a success and DO is a
failure. The predictors are prime and nounrep (nounrepetition), each
with 2 levels. I have effect coded the predictors (-.5 and +.5
respectively for each of the two levels of the predictors, following
Barr, 2008): with this coding, which I believe is a way of centering,
the intercept should correspond to the grand mean and the coefficients
to the differences between the means etc., like in an ANOVA. Please
correct me if I am wrong. I tried this coding in the past where the
outcome was a continuous variable and indeed when I checked the means
and differences in my data , I found a correspondence between the ANOVA
measures and the regression intercept and coefficients; however, now I
am dealing  with binomially distributed data, where the model parameters
are in log odds space, so it is a bit more complicated, because I have
to do transformations). 

The problem is that when I check the output of the mixed  logit
regression (using lmer and family = binomial ) and try to make sense of
the coefficients by checking, for example, whether the intercept
corresponds to the grand mean, in log odds, of course, things do not
match. I checked and re-checked, and I do not know where I am going
wrong. 

==========

> head(verbdiff)
     X subject cond item myscore poresp nounrep prime primec nounrepc
1 1069       1    2   19       p      1       0     1    0.5     -0.5
2 1070       1    3    6       p      1       1     0   -0.5      0.5
3 1071       1    3    5       p      1       1     0   -0.5      0.5
4 1072       1    2   12       p      1       0     1    0.5     -0.5
5 1073       1    4   16       p      1       1     1    0.5      0.5
6 1074       1    3   14       p      1       1     0   -0.5      0.5

#primec and nounrepc are effect coded



COUNTS OF 0s and 1s:

> xtabs (~ poresp +prime +nounrep, data=verbdiff)

     nounrep = 0

      prime
poresp   0   1
     0  89  58
     1 207 235

, , nounrep = 1

      prime
poresp   0   1
     0  91  64
     1 202 228


MODEL:

> verbdiff.lmer = lmer(poresp ~ primec *nounrepc + (1|subject) +
(1|item), data= verbdiff, family="binomial")

> print (verbdiff.lmer)


Generalized linear mixed model fit using Laplace 
Formula: poresp ~ primec * nounrepc + (1 | subject) + (1 | item) 
   Data: verbdiff 
 Family: binomial(logit link)
  AIC  BIC logLik deviance
 1092 1122   -540     1080
Random effects:
 Groups  Name        Variance Std.Dev.
 item    (Intercept) 1.2143   1.1020  
 subject (Intercept) 1.8470   1.3590  
number of obs: 1174, groups: item, 40; subject, 32

Estimated scale (compare to  1 )  0.917418 

Fixed effects:
                Estimate Std. Error z value Pr(>|z|)    
(Intercept)       1.6605     0.3121   5.320 1.04e-07 ***
primec            0.7854     0.1645   4.773 1.81e-06 ***
nounrepc         -0.1054     0.1612  -0.653    0.513    
primec:nounrepc  -0.2138     0.3224  -0.663    0.507    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’
0.1 ‘ ’ 1 

Correlation of Fixed Effects:
            (Intr) primec nonrpc
primec       0.053              
nounrepc    -0.009 -0.023       
primc:nnrpc -0.012 -0.028  0.128

=============

QUESTIONS:

1. THE ESTIMATED INTERCEPT IN THE LOGIT MODEL IS 1.66 IN LOG ODDS,
WHICH should correspond to grand mean, i.e. likelihood of successes (=PO
responses coded as "1") independent of the predictors.

THERE WERE OVERALL 872 SUCCESSES AND 302 FAILURES IN THE EXPT, SO ODDS
SHOULD BE 872/302=2.88 or (in probability space) .74/.26 = 2.85;
THIS SHOULD GIVE A LOG OF ODDS OF APPROX 1.05, BUT THE INTERCEPT
PREDICTED BY THE MODEL  IS MUCH HIGHER (1.66)

SAME THING WHEN I USE THE CORRESPONDING DUMMY CODED (0-1) V
ARIABLES
-INTERCEPT IS MUCH HIGHER THAN WHAT MY DATA SUGGEST 



2. I ALSO TRIED TO APPLY THE Somers Dxy test, BUT I GET AN ERROR
MESSAGE THAT I DO NOT UNDERSTAND; ISN'T  Y  BINARY (1/0) IN THE DATA
FILE?


> probs = binomial()$linkinv(fitted(verbdiff.lmer))
> somers2(probs,as.numeric(verbdiff$poresp)-1)
Error in somers2(probs, as.numeric(verbdiff$poresp) - 1) : 
  y must be binary


DATA FRAME  verbdiff ATTACHED

MANY THANKS

Dr. Maria Nella Carminati
Department of Psychology
University of Dundee
Dundee DD1 4HN

Tel: +44 1382 388258
Fax: +44 1382 229993

Email: m.n.carminati at dundee.ac.uk 
          mnc at interfree.it

The University of Dundee is a registered Scottish charity, No: SC015096
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