The Visual World | Walkthrough: Eyetracking data w/empirical logit regression

Walkthrough: Eyetracking data w/empirical logit regression

Wed 12 Sep, 2007 at 1:35 PM

MLR paper

my previous post

> library(lme4)

> load("bySubj.bin")
> load("byItem.bin")

bySubj

byItem

> bySubj[bySubj$SubjID==30,c(1:4,8,13:14)]

   SubjID AggID SpeakerT CogLoadT Bin y  N
1      30   241     Same     None   3 0 12
2      30   241     Same     None   2 0 12
3      30   241     Same     None   1 0 12
4      30   241     Same     None   0 0 12
5      30   243     Diff     None   0 3 12
6      30   243     Diff     None   1 3 12
7      30   243     Diff     None   2 5 12
8      30   243     Diff     None   3 4 12
9      30   245     Same     Load   3 6 12
10     30   245     Same     Load   2 7 12
11     30   245     Same     Load   1 3 12
12     30   245     Same     Load   0 3 12
13     30   247     Diff     Load   0 3 12
14     30   247     Diff     Load   1 3 12
15     30   247     Diff     Load   2 3 12
16     30   247     Diff     Load   3 3 12

empirical logit

# compute the empirical logit
> elogS <- log((bySubj$y + .5) / (bySubj$N - bySubj$y + .5))
# note that in R the default base of log is e

# compute the weights
> wts <- 1/(bySubj$y + .5) + 1/(bySubj$N - bySubj$y + .5)

MLR paper

> bySubj.lmer = lmer2(
elogS ~
Spkr + CLoad + SbyL +
t1 + t1S + t1L + t1SL +
(1 + t1 | SubjID:AggID) + (1 + t1 | SubjID),
data=bySubj, weights=1/wts)

bySubj.lmer

lmer2

elogS ~ Spkr + CLoad + SbyL + t1 + t1S + t1L + t1SL + (1 + t1 | SubjID:AggID) + (1 + t1 | SubjID)

lmer2

Spkr

CLoad

SbyL

CLoad

sgn(Spkr)*sgn(CLoad)*.5

sgn

slope

t1S

t1*Spkr

t1L

t1*CLoad

t1SL

lmer

SubjID:AggID

(1 + t1 | SubjID:AggID)

(1 | SubjID:AggID)

(1 + t1 | SubjID)

data=bySubj

lmer

bySubj

weights=1/wts

options(verbose=TRUE)

> summary(bySubj.lmer)

Linear mixed-effects model fit by REML 
Formula: elogS ~ Spkr + CLoad + SbyL + t1 + t1S + t1L + t1SL + (1 + t1 |      SubjID:AggID) + (1 + t1 | SubjID) 
   Data: bySubj 
  AIC  BIC logLik MLdeviance REMLdeviance
 2469 2536  -1220       2437         2441
Random effects:
 Groups       Name        Variance  Std.Dev. Corr   
 SubjID:AggID (Intercept)  1.363521 1.16770         
              t1          39.474848 6.28290  -0.452 
 SubjID       (Intercept)  0.025466 0.15958         
              t1           0.191524 0.43763  1.000  
 Residual                  0.249136 0.49914         
Number of obs: 896, groups: SubjID:AggID, 224; SubjID, 56

Fixed effects:
            Estimate Std. Error t value
(Intercept) -1.25874    0.08417 -14.955
Spkr         0.32142    0.16284   1.974
CLoad       -0.02784    0.16284  -0.171
SbyL        -0.05813    0.16284  -0.357
t1           2.42557    0.48479   5.003
t1S         -2.27101    0.96249  -2.360
t1L         -0.33024    0.96249  -0.343
t1SL         0.43564    0.96252   0.453

Correlation of Fixed Effects:
      (Intr) Spkr   CLoad  SbyL   t1     t1S    t1L   
Spkr  -0.005                                          
CLoad -0.001  0.004                                   
SbyL   0.004 -0.001 -0.005                            
t1    -0.440  0.006  0.000 -0.006                     
t1S    0.006 -0.490 -0.006  0.000 -0.006              
t1L    0.000 -0.006 -0.490  0.006 -0.001  0.007       
t1SL  -0.005  0.000  0.006 -0.490  0.007 -0.001 -0.006

Baayen, Davidson, and Bates (in press)

Baayen

pvals.fnc()

[update Mar 14, 2007]. The MCMC function works with lmer but not with lmer2 objects. There is a way to get the MCMC values for lmer2, but the values seem a bit wacky; I wonder if it has to do with the weighting of the observations in the lmer2 regression. Anyway-- I would suggest testing for significance using the t values instead, by comparing them against a critical value of t=2.00; that is probably the best way of doing things for now. With this criterion, we have a significant effect of Speaker on the slope, p<.05, and a marginal effect of Speaker on the intercept (p < .10).

rate effects

anticipatory effects

Item Analysis

> elogI <- log((byItem$y + .5) / (byItem$N - byItem$y + .5))
>
> wtsI <- 1/(byItem$y + .5) + 1/(byItem$N - byItem$y + .5)
>
> byItem.lmer <- lmer2(
elogI ~
Spkr + CLoad + SbyL +
t1 + t1S + t1L + t1SL +
(1 + t1 | ItemID:AggID) + (1 + t1 | ItemID)
,data=byItem, weights=1/wtsI)

Estimated variance-covariance for factor 'ItemID' is singular

> byItem1.lmer <- lmer2(
elogI ~
Spkr + CLoad + SbyL +
t1 + t1S + t1L + t1SL +
(1 + t1 | ItemID:AggID) + (1 | ItemID)
,data=byItem, weights=1/wtsI)