Change intercept using lmer function in R

Question

I am trying to use the lmer function to investigate if there is an interaction effect on the reaction time (RT) between 3 different conditions (cond=0, 1, 2) and the presence of the target (target=False or True) in patients (Patient).

I wrote the following equation:

lmer(RT~cond*target+(1|Patient))

My problem is that the default intercept for this function is cond = 0 and target = False, whereas I would like the intercept to be cond= 0 and target=True (in order to see if there is a significant difference between cond0*target=True and cond1*target=True).

I would really appreciate your help.

Here is the output I have

stu3<-lmer(RT~cond*target+(1|Patient), 
   data=subset(ss, Groupe=="ugs" & primeable ==TRUE     & 
          Correct==TRUE & NoPrac==TRUE))

pvals.fnc(stu3)


$fixed
                  Estimate MCMCmean HPD95lower HPD95upper  pMCMC Pr(>|t|)
(Intercept)         0.5511   0.5513     0.5258     0.5807 0.0001   0.0000
cond1               0.0618   0.0619     0.0498     0.0741 0.0001   0.0000
cond2               0.0285   0.0285     0.0142     0.0438 0.0002   0.0001
targetFALSE         0.1389   0.1389     0.1239     0.1549 0.0001   0.0000
cond1:targetFALSE  -0.0752  -0.0751    -0.0943    -0.0545 0.0001   0.0000
cond2:targetFALSE  -0.0788  -0.0786    -0.0998    -0.0564 0.0001   0.0000

$random
    Groups        Name Std.Dev. MCMCmedian MCMCmean HPD95lower HPD95upper
1  Patient (Intercept)   0.0610     0.0583   0.0599     0.0425     0.0797
2 Residual               0.1674     0.1674   0.1674     0.1650     0.1699

Based on my data, the intercept being chosen is cond0:targetTRUE and the other levels in the output are cond1:targetFALSE and cond2:targetFALSE.

Answer 1

See if standard "factor management" is effective:

target=factor(target, levels=c("TRUE", "FALSE")
lmer(RT~cond*target+(1|Patient))

(I would have used the phrase "changing the reference levels" rather than "changing the intercept", but I suppose it's really the same process. I suspect the phrase "[r] change reference level" would have gotten you quite few hits on a Google or SO search.)

Answer 2

If I understood correctly, your model is already doing the interpretation you would wish to have inside target==TRUE. If I am correct, you could translate the model terms in your example as follows:

"(Intercept)"       -> target==TRUE, cond==0 (even if model matrix contains all conds)
"cond1"             -> target==TRUE, cond==1 on top of cond==0
"cond2"             -> target==TRUE, cond==2 on top of cond==0
"targetFALSE"       -> target==FALSE, cond==0 (even if model matrix contains all conds)
"cond1:targetFALSE" -> target==FALSE, cond==1 on top of cond==0
"cond2:targetFALSE" -> target==FALSE, cond==2 on top of cond==0

So isn't the interesting difference detected in terms "(Intercept)", "cond1" and "cond2"? Taking a look at the fixed effects' model matrix structure in getME(stu3,'X') may be helpful.

Below is an example data I constructed to test your case. Notice that I built three different responses: one without any effect, one with just target==TRUE effect, and one with an effect for target==TRUE and an interaction effect with target==TRUE and the different levels of cond. The artificially introduced effect is detected in fit1 and fit2:

set.seed(0)
struct <- expand.grid(target = c(FALSE,TRUE), cond = as.factor(0:2), patient = LETTERS[1:20])
attach(struct)
ranpatient <- rep(rnorm(20), each=6)
rerror <- rnorm(120)
# Just random noise
response0 <- ranpatient + rerror
# When target==TRUE we increment the response by 1 and add errors
response1 <- 1*target + ranpatient + rerror
# When target==TRUE we increment the response by  1,
# to which we also add an interaction effect condition {0,1,2} * target {0,1}
# notice that numeric transformation of cond {0,1,2} transforms to ranks {1,2,3}
response2 <- 1*target + target*(as.numeric(cond)-1) + ranpatient + rerror

dat <- data.frame(cond, target, patient, response0, response1, response2)   
detach(struct)

require(lme4)
fit0 <- lmer(response0 ~ cond*target + (1|patient), data=dat)
fit1 <- lmer(response1 ~ cond*target + (1|patient), data=dat)
fit2 <- lmer(response2 ~ cond*target + (1|patient), data=dat)

head(dat)
round(coef(summary(fit0)),2) # Notice low t values
round(coef(summary(fit1)),2) # High t value for targetTRUE
round(coef(summary(fit2)),2) # High t value for interaction cond0/1/2 with targetTRUE
# Notice how cond==1 adds 1, and cond==2 adds 2 in comparison to cond==0 when targetTRUE
# Notice also that coefficient "cond2:targetTRUE" is incremental to term "targetTRUE", not "cond1:targetTRUE"
head(getME(fit2,'X')) # Columns correspond to the fixed effect terms

With the output

> head(dat)
  cond target patient response0 response1 response2
1    0  FALSE       A  1.038686  1.038686  1.038686
2    0   TRUE       A  1.640350  2.640350  2.640350
3    1  FALSE       A  1.396291  1.396291  1.396291
4    1   TRUE       A  2.067144  3.067144  4.067144
5    2  FALSE       A  1.205848  1.205848  1.205848
6    2   TRUE       A  1.766562  2.766562  4.766562
> round(coef(summary(fit0)),2) # Notice low t values
                 Estimate Std. Error t value
(Intercept)         -0.13       0.31   -0.40
cond1                0.18       0.29    0.62
cond2                0.00       0.29    0.00
targetTRUE           0.00       0.29   -0.01
cond1:targetTRUE     0.13       0.41    0.32
cond2:targetTRUE     0.08       0.41    0.19
> round(coef(summary(fit1)),2) # High t value for targetTRUE
                 Estimate Std. Error t value
(Intercept)         -0.13       0.31   -0.40
cond1                0.18       0.29    0.62
cond2                0.00       0.29    0.00
targetTRUE           1.00       0.29    3.42
cond1:targetTRUE     0.13       0.41    0.32
cond2:targetTRUE     0.08       0.41    0.19
> round(coef(summary(fit2)),2) # High t value for interaction cond0/1/2 with targetTRUE
                 Estimate Std. Error t value
(Intercept)         -0.13       0.31   -0.40
cond1                0.18       0.29    0.62
cond2                0.00       0.29    0.00
targetTRUE           1.00       0.29    3.42
cond1:targetTRUE     1.13       0.41    2.75
cond2:targetTRUE     2.08       0.41    5.04
> # Notice how cond==1 adds 1, and cond==2 adds 2 in comparison to cond==0 when targetTRUE
> # Notice also that coefficient "cond2:targetTRUE" is incremental to term "targetTRUE", not "cond1:targetTRUE"
> head(getME(fit2,'X')) # Columns correspond to the fixed effect terms
     [,1] [,2] [,3] [,4] [,5] [,6]
[1,]    1    0    0    0    0    0
[2,]    1    0    0    1    0    0
[3,]    1    1    0    0    0    0
[4,]    1    1    0    1    1    0
[5,]    1    0    1    0    0    0
[6,]    1    0    1    1    0    1