no df of freedom to test the effect of an interaction in (lmer) mixed-model

x <- factor(c(1,1,2,2))
y <- 1:4     
lm(y ~ x)

lm(y ~ x - 1)

Dear sig-mixed-models list-members,

I placed this question before on R-help main list, but I think this forum is
more appropriate. I will reformulate the question though:

I have a model such as:
full <- lmer(y ~ S*C*t + (S*t | id), method="ML")   # both S and C are
factors with two levels each

First I want to test the effect of the interaction S:t. I fit the following
reduced models:
red1 <- lmer(y ~ S*C*t - S:t + (S*t | id), method="ML")   # excluding S:t
from the fixed effects, and
red2 <- lmer(y ~ S*C*t + (S + t | id), method="ML")   # excluding S:t:id
from the random effects

then:
anova(full, red1, red2)

            Df     AIC     BIC  logLik  Chisq Chi Df Pr(>Chisq)
red2     14 10525.0 10614.5 -5248.5
full       18 10493.7 10608.8 -5228.8 39.346  4  5.908e-08 ***
red1     18 10493.7 10608.8 -5228.8  0.000   0

The problem is that there is no degree of freedom to see differences between
full and red1

When looking at the fixed effects of both models:

1. full model
Fixed effects:
                                  Estimate Std. Error t value
(Intercept)                6.7822267  0.1475245   45.97
S                           -0.4902659  0.0814779   -6.02
C                           -0.2428243  0.2142228   -1.13
t                             0.0122836  0.0015711    7.82
S:C                         0.3716986   0.1232596    3.02
S:t                         -0.0001985  0.0028627   -0.07
C:t                         -0.0056198  0.0023020   -2.44
S:C:t                      0.0022598  0.0040779    0.55

2. red1 model
Fixed effects:
                              Estimate Std. Error t value
(Intercept)              6.7822722  0.1483886   45.71
S                         -0.4902454  0.0816564   -6.00
C                         - 0.2428498  0.2154232   -1.13
t                           0.0122829  0.0015684    7.83
S:C                      0.3716582  0.1235135    3.01
C:t                       -0.0056161  0.0022982   -2.44
S:C1:t                  - 0.0001986  0.0028619   -0.07
S:C2:t                   0.0020583  0.0029032    0.71

red1 model is analyzing the interaction S:C:t using both levels of C so that
the result is one more factor, and therefore no degree of freedom left to
compare with the full model.

Can anybody suggest how should I test the effect of S:t??


Thank you very much for any feedback!!

Ahimsa


For a more comprehensible explanation of the data you can check my previous
post ( http://tolstoy.newcastle.edu.au/R/e2/help/07/03/11468.html). Below
there is toi data and script.

**********************************************************************************************************

library(lme4)

# dataset
A <- as.factor(rep(1:2, each=600))
id <- as.factor(rep(1:6, each=200))
S <- as.factor(rep(1:2, each=100, times=6))
R <- as.factor(rep(1:10, each = 10, times = 12))
t <- rep(c(2,4,6,8,10,12,14,16,18,20), times=120)
y <- rnorm(1200, mean=100, sd=25)
dummy.df <- data.frame(A,id,S,R,t,y)
summary(dummy.df)
str(dummy.df)

full.model <- lmer(y ~ A*S*t + (S*t|id), dummy.df, method="ML")
summary(full.model)

red.model1 <- lmer(y ~ A*S*t - S:t + (S*t|id), dummy.df, method="ML")
summary(red.model1)

red.model2 <- lmer(y ~ A*S*t + (S+t|id), dummy.df , method="ML")
summary(red.model2)
anova (full.model, red.model1, red.model2)

-- 
ahimsa campos-arceiz
www.camposarceiz.com

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