[R-lang] Simple effects in mixed logit models
Roger van-Gompel
r.p.g.vangompel at dundee.ac.uk
Fri Dec 18 06:39:26 PST 2009
Stefan, thanks for your comments. You are right, I don’t have a
*significant* interaction, all I have is an effect of langcent.
Exploring simple effects is therefore not so useful, but it’s just
something that reviewers suggested.
Thanks a lot, Florian, that’s exactly what I wanted to know. I have
now analysed both the simple effect of prime for Swedish and the effect
of prime on English (the complete analyses are below).
You said:
Now, the problem, of course, is that treatment coding leads to
collinearity between the "main" effects and the interaction (even in a
balanced sample). In a perfectly balanced sample, the correlation (not
the fixed effect correlation) will be .33, which is still ok. As long as
unbalance due to data exclusion is pretty much random, this correlation
should not go up much beyond .38 (I did some simulation).
I have a quite lot of missing responses, and as you can see in the
summary of the results, there are correlations between the “main”
effects and the interaction. But you say “not the fixed effect
correlation”, so are you referring to a different correlation?
I haven’t done the model comparisons yet. You said:
In any case, since ANOVA are omnibus test, you can get at least that by
simple comparing the above model to a model without the interaction or
without any of the simple (main) effects (using anova(model1, model2)).
Model comparison is robust against collinearity.
I find it hard to conceptualize what the model comparisons tell me.
What can I conclude if the model with which I got the simple effect
differs from a model without the interaction or without any of the
simple effects?
My previous analyses were done with R 2.2.0. I have now updated to
2.10.1 and suddenly, all the coefficients are different, which I find a
bit worrying. The p-values are now quite a bit larger, although the new
R version doesn’t change any of the conclusions that I can draw from the
data.
Roger
> library(lme4)
Loading required package: Matrix
Loading required package: lattice
> L2prim = read.table("forLME.txt", header=TRUE) # open data file
> head(L2prim) # show first 6 lines
LIST PID ITEM language prime score
1 1 2 4 swe do 1
2 1 2 7 swe do 0
3 1 2 8 swe pp 0
4 1 2 20 swe pp 0
5 1 2 22 eng pp 0
6 1 2 23 swe pp 0
>
> # effect code vars so that they can be interpreted as main effects in
ANOVAs
> L2prim$langcent <- scale(as.numeric(L2prim$language)) # effect code
language
> L2prim$primecent <- scale(as.numeric(L2prim$prime)) # effect code
prime
>
> L2prim$PID=as.factor(L2prim$PID) # convert subject no to factor
> L2prim$ITEM=as.factor(L2prim$ITEM) # convert item no to factor
> head(L2prim)
LIST PID ITEM language prime score langcent primecent
1 1 2 4 swe do 1 1.008740 -0.9742244
2 1 2 7 swe do 0 1.008740 -0.9742244
3 1 2 8 swe pp 0 1.008740 1.0248334
4 1 2 20 swe pp 0 1.008740 1.0248334
5 1 2 22 eng pp 0 -0.989767 1.0248334
6 1 2 23 swe pp 0 1.008740 1.0248334
>
> # mixed logit model with variables effect coded (main effects as in
ANOVA)
> primanal=lmer(score ~langcent*primecent + (1|PID) + (1|ITEM),
data=L2prim, family = "binomial")
> summary(primanal)
Generalized linear mixed model fit by the Laplace approximation
Formula: score ~ langcent * primecent + (1 | PID) + (1 | ITEM)
Data: L2prim
AIC BIC logLik deviance
650.5 677.2 -319.2 638.5
Random effects:
Groups Name Variance Std.Dev.
ITEM (Intercept) 1.9705 1.4037
PID (Intercept) 2.2791 1.5097
Number of obs: 632, groups: ITEM, 40; PID, 32
Fixed effects:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -1.06339 0.37331 -2.849 0.004392 **
langcent 0.01506 0.108
22 0.139 0.889334
primecent 0.36986 0.11024 3.355 0.000793 ***
langcent:primecent -0.10630 0.10898 -0.975 0.329365
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Correlation of Fixed Effects:
(Intr) lngcnt prmcnt
langcent -0.001
primecent -0.028 -0.030
lngcnt:prmc 0.008 -0.055 -0.008
>
>
> # Analysis of simple effect of prime for Swedish (coded as 0)
>
> L2prim[,2:3] # Outputs col 2 and 3 (to check no of rows)
PID ITEM
1 2 4
2 2 7
3 2 8
4 2 20
5 2 22
6 2 23
629 34 35
630 34 36
631 34 37
632 34 38
>
> # create column for language that is treatment coded
> x =c(1:632) # creates 632 rows of numbers
> x[1:632] = 0 # sets the numbers to 0
> cbind(L2prim,x) # adds the 0s to L2prim
LIST PID ITEM language prime score langcent primecent x
1 1 2 4 swe do 1 1.008740 -0.9742244 0
2 1 2 7 swe do 0 1.008740 -0.9742244 0
3 1 2 8 swe pp 0 1.008740 1.0248334 0
4 1 2 20 swe pp 0 1.008740 1.0248334 0
5 1 2 22 eng pp 0 -0.989767 1.0248334 0
6 1 2 23 swe pp 0 1.008740 1.0248334 0
629 4 34 35 eng pp 1 -0.989767 1.0248334 0
630 4 34 36 swe do 1 1.008740 -0.9742244 0
631 4 34 37 eng pp 1 -0.989767 1.0248334 0
632 4 34 38 eng do 0 -0.989767 -0.9742244 0
> L2prim[L2prim[,4] =="swe",9] = 0 # recodes swe (col 4) into 1 (col
9)
> L2prim[L2prim[,4] =="eng",9] = 1 # recodes eng (col 4) into 0 (col
9)
>
> # create column for prime that is treatment coded
> y =c(1:632) # creates 632 rows of numbers
> y[1:632] = 0 # sets the numbers to 0
> cbind(L2prim,y) # adds the 0s to L2prim
LIST PID ITEM language prime score langcent primecent V9 y
1 1 2 4 swe do 1 1.008740 -0.9742244 0 0
2 1 2 7 swe do 0 1.008740 -0.9742244 0 0
3 1 2 8 swe pp 0 1.008740 1.0248334 0 0
4 1 2 20 swe pp 0 1.008740 1.0248334 0 0
5 1 2 22 eng pp 0 -0.989767 1.0248334 1 0
6 1 2 23 swe pp 0 1.008740 1.0248334 0 0
629 4 34 35 eng pp 1 -0.989767 1.0248334 1 0
630 4 34 36 swe do 1 1.008740 -0.9742244 0 0
631 4 34 37 eng pp 1 -0.989767 1.0248334 1 0
632 4 34 38 eng do 0 -0.989767 -0.9742244 1 0
> L2prim[L2prim[,5] =="do",10] = 1 # recodes do (col 5) into 1 (col
10)
> L2prim[L2prim[,5] =="pp",10] = 0 # recodes pp (col 5) into 0 (col
10)
>
> L2prim$langtreat=as.factor(L2prim$V9) # convert language (v9) into
factor
> L2prim$primetreat=as.factor(L2prim$V10) # convert prime (v10) into
factor
> L2prim[1:20,] # Outputs rows 1-20
LIST PID ITEM language prime score langcent primecent V9 V10
langtreat
1 1 2 4 swe do 1 1.008740 -0.9742244 0 1
0
2 1 2 7 swe do 0 1.008740 -0.9742244 0 1
0
3 1 2 8 swe pp 0 1.008740 1.0248334 0 0
0
4 1 2 20 swe pp 0 1.008740 1.0248334 0 0
0
5 1 2 22 eng pp 0 -0.989767 1.0248334 1 0
1
6 1 2 23 swe pp 0 1.008740 1.0248334 0 0
0
20 1 3 10 eng pp 0 -0.989767 1.0248334 1 0
1
primetreat
1 1
2 1
3 0
4 0
5 0
6 0
20 0
>
> # mixed logit model with variables treatment coded
> primanal=lmer(score ~langtreat*primetreat + (1|PID) + (1|ITEM),
data=L2prim, family = "binomial")
> summary(primanal)
Generalized linear mixed model fit by the Laplace approximation
Formula: score ~ langtreat * primetreat + (1 | PID) + (1 | ITEM)
Data: L2prim
AIC BIC logLik deviance
650.5 677.2 -319.2 638.5
Random effects:
Groups Name Variance Std.Dev.
ITEM (Intercept) 1.9705 1.4038
PID (Intercept) 2.2791 1.5097
Number of obs: 632, groups: ITEM, 40; PID, 32
Fixed effects:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -0.7790 0.4155 -1.875 0.0608 .
langtreat1 0.1875 0.3022 0.621 0.5348
primetreat1 -0.5251 0.3100 -1.694 0.0903 .
langtreat1:primetreat1 -0.4246 0.4354 -0.975 0.3294
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Correlation of Fixed Effects:
(Intr) lngtr1 prmtr1
langtreat1 -0.364
primetreat1 -0.354 0.477
lngtrt1:pr1 0.262 -0.699 -0.703
> # primetreat is the simple effect of prime on Swedish
> # the sum of the estimates for primetreat and the interaction
(0.9497) is the simple effect
> # of prime on English (no z and p values can be calculated)
>
>
> # Analysis of simple effect of prime for English (coded as 0)
>
> L2prim[,2:3] # Outputs col 2 and 3 (to check no of rows)
PID ITEM
1 2 4
2 2 7
3 2 8
4 2 20
5 2 22
6 2 23
629 34 35
630 34 36
631 34 37
632 34 38
>
> x =c(1:632) # creates 632 rows of numbers
> x[1:632] = 0 # sets the numbers to 0
> cbind(L2prim,x) # adds the 0s to L2prim
LIST PID ITEM language prime score langcent primecent V9 V10
langtreat
1 1 2 4 swe do 1 1.008740 -0.9742244 0 1
0
2 1 2 7 swe do 0 1.008740 -0.9742244 0 1
0
3 1 2 8 swe pp 0 1.008740 1.0248334 0 0
0
4 1 2 20 swe pp 0 1.008740 1.0248334 0 0
0
5 1 2 22 eng pp 0 -0.989767 1.0248334 1 0
1
6 1 2 23 swe pp 0 1.008740 1.0248334 0 0
0
629 4 34 35 eng pp 1 -0.989767 1.0248334 1 0
1
630 4 34 36 swe do 1 1.008740 -0.9742244 0 1
0
631 4 34 37 eng pp 1 -0.989767 1.0248334 1 0
1
632 4 34 38 eng do 0 -0.989767 -0.9742244 1 1
1
primetreat x
1 1 0
2 1 0
3 0 0
4 0 0
5 0 0
6 0 0
629 0 0
630 1 0
631 0 0
632 1 0
> L2prim[L2prim[,4] =="swe",9] = 1 # recodes swe (col 4) into 1 (col
9)
> L2prim[L2prim[,4] =="eng",9] = 0 # recodes eng (col 4) into 0 (col
9)
>
> y =c(1:632) # creates 632 rows of numbers
> y[1:632] = 0 # sets the numbers to 0
> cbind(L2prim,y) # adds the 0s to L2prim
LIST PID ITEM language prime score langcent primecent V9 V10
langtreat
1 1 2 4 swe do 1 1.008740 -0.9742244 1 1
0
2 1 2 7 swe do 0 1.008740 -0.9742244 1 1
0
3 1 2 8 swe pp 0 1.008740 1.0248334 1 0
0
4 1 2 20 swe pp 0 1.008740 1.0248334 1 0
0
5 1 2 22 eng pp 0 -0.989767 1.0248334 0 0
1
6 1 2 23 swe pp 0 1.008740 1.0248334 1 0
0
629 4 34 35 eng pp 1 -0.989767 1.0248334 0 0
1
630 4 34 36 swe do 1 1.008740 -0.9742244 1 1
0
631 4 34 37 eng pp 1 -0.989767 1.0248334 0 0
1
632 4 34 38 eng do 0 -0.989767 -0.9742244 0 1
1
primetreat y
1 1 0
2 1 0
3 0 0
4 0 0
5 0 0
6 0 0
628 0 0
629 0 0
630 1 0
631 0 0
632 1 0
> L2prim[L2prim[,5] =="do",10] = 1 # recodes do (col 5) into 1 (col
10)
> L2prim[L2prim[,5] =="pp",10] = 0 # recodes pp (col 5) into 0 (col
10)
>
> L2prim$langtreat=as.factor(L2prim$V9)
> L2prim$primetreat=as.factor(L2prim$V10)
> L2prim[1:20,] # Outputs rows 1-20
LIST PID ITEM language prime score langcent primecent V9 V10
langtreat
1 1 2 4 swe do 1 1.008740 -0.9742244 1 1
1
2 1 2 7 swe do 0 1.008740 -0.9742244 1 1
1
3 1 2 8 swe pp 0 1.008740 1.0248334 1 0
1
4 1 2 20 swe pp 0 1.008740 1.0248334 1 0
1
5 1 2 22 eng pp 0 -0.989767 1.0248334 0 0
0
6 1 2 23 swe pp 0 1.008740 1.0248334 1 0
1
20 1 3 10 eng pp 0 -0.989767 1.0248334 0 0
0
primetreat
1 1
2 1
3 0
4 0
5 0
6 0
20 0
>
> primanal=lmer(score ~langtreat*primetreat + (1|PID) + (1|ITEM),
data=L2prim, family = "binomial")
> summary(primanal)
Generalized linear mixed model fit by the Laplace approximation
Formula: score ~ langtreat * primetreat + (1 | PID) + (1 | ITEM)
Data: L2prim
AIC BIC logLik deviance
650.5 677.2 -319.2 638.5
Random effects:
Groups Name Variance Std.Dev.
ITEM (Intercept) 1.9705 1.4038
PID (Intercept) 2.2791 1.5097
Number of obs: 632, groups: ITEM, 40; PID, 32
Fixed effects:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -0.5915 0.4153 -1.424 0.15435
langtreat1 -0.1875 0.3022 -0.621 0.53489
primetreat1 -0.9496 0.3095 -3.068 0.00215 **
langtreat1:primetreat1 0.4244 0.4354 0.975 0.32973
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Correlation of Fixed Effects:
(Intr) lngtr1 prmtr1
langtreat1 -0.363
primetreat1 -0.354 0.507
lngtrt1:pr1 0.247 -0.699 -0.702
> # primetreat is the simple effect of prime on English
> # the sum of the estimates for primetreat and the interaction
(0.5252) is the simple effect
> # of prime on Swedish (no z and p values can be calculated)
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