R help - Nov 2013 - lmer specification for random effects: contradictory reults

Hi All,

 

I was wondering if someone could help me to solve this issue with lmer.
In order to understand the best mixed effects model to fit my data, I
compared the following options according to the procedures specified in many
papers (i.e. Baayen
<http://www.google.it/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0CDsQFjAA
&url=http%3A%2F%2Fwww.ualberta.ca%2F~baayen%2Fpublications%2FbaayenDavidsonB
ates.pdf&ei=FhqTUoXuJKKV7Abds4GYBA&usg=AFQjCNFst7GT7mBX7w9lXItJTtELJSKWJg&si
g2=KGA5MHxOvEGwDxf-Gcqi6g&bvm>  R.H. et al 2008)
Here, dT_purs is the response variable, T and Z are the fixed effects, and
subject is the random effect. Random and fixed effects are crossed.:
 
mod0 <- lmer(dT_purs ~ T + Z + (1|subject), data = x) 
mod1 <- lmer(dT_purs ~ T + Z + (1 +tempo| subject), data = x)
mod2 <- lmer(dT_purs ~ T + Z + (1 +tempo| subject) + (1+ Z| subject), data x)
mod3 <- lmer(dT_purs ~ T * Z + (1 +tempo| subject) + (1+ Z| subject), data x)
mod4 <- lmer(dT_purs ~ T * Z + (1| subject), data = x) 
 

anova(mod0, mod1,mod2, mod3, mod4)

 

Data: x

Models:

mod0: dT_purs ~ T + Z + (1 | subject)

mod4: dT_purs ~ T * Z + (1 | subject )

mod1: dT_purs ~ T + Z + (1 + T| subject)

mod2: dT_purs ~ T + Z + (1 + T| subject ) + (1 + Z | subject)

mod3: dT_purs ~ T * Z + (1 + T| subject) + (1 + Z | subject)

     Df     AIC     BIC logLik deviance   Chisq Chi Df Pr(>Chisq)   

mod0  5 -689.81 -669.46 349.91  -699.81                             

mod4  6 -689.57 -665.14 350.78  -701.57  1.7532      1   0.185473   

mod1  7 -689.12 -660.62 351.56  -703.12  1.5504      1   0.213070   

mod2 10 -695.67 -654.97 357.84  -715.67 12.5563      3   0.005701 **

mod3 11 -695.83 -651.05 358.92  -717.83  2.1580      1   0.141825   

---

Signif. codes:  0 ''***'' 0.001 ''**'' 0.01
''*'' 0.05 ''.'' 0.1 '' '' 1

 

 

It turns out that mod2 has the right level of complexity for this dataset.

However when I looked at its summary, I got a correlation of -0.87 for the
random effects relative to the T effect and -1 for the random effects
relatively to the Z.

 

 

summary(mod2)

Linear mixed model fit by maximum likelihood [''lmerMod'']

Formula: dT_purs ~T + Z + (1 + T | subject) + (1 + Z | subject) 

   Data: x 

 

      AIC       BIC    logLik  deviance 

-695.6729 -654.9655  357.8364 -715.6729 

 

Random effects:

Groups     Name        Variance  Std.Dev. Corr 

 subject   (Intercept) 0.0032063 0.05662       

            T       0.0117204 0.10826  -0.87

subject.1 (Intercept) 0.0005673 0.02382       

            Z           0.0025859 0.05085  1.00 

 Residual               0.0104551 0.10225       

Number of obs: 433, groups: soggetto, 7

 

Fixed effects:

            Estimate Std. Error t value

(Intercept)  0.02489    0.03833   0.650

T        0.52010    0.05905   8.808

Z           -0.09019    0.02199  -4.101

 

Correlation of Fixed Effects:

      (Intr) tempo 

T -0.901       

Z      0.218 -0.026

 

 

If I understand correctly what the correlation parameters reported in the
table are, the correlation of 1 means that, for the Z effects the random
intercept is perfectly collinear with the random slope. Thus, we fit the
wrong model. A random intercept only model would have sufficed.

Am I correct?

 

If so, should I take mod1 (mod1 <- dT_purs ~ T + Z + (1 + T | subject )
instead of mod2 to fit my data?

Why are these results contradictory?

Finally is a correlation value of -0.87 a too high or an acceptable value ?

 

Thanks for help me in advance!

 

Best

 

Benedetta

 

 

---

Benedetta Cesqui, Ph.D.

Laboratory of Neuromotor Physiology

IRCCS Fondazione Santa Lucia

Via Ardeatina 306

00179 Rome, Italy

tel: (+39) 06-51501485

fax:(+39) 06-51501482

E_mail:  b.cesqui@hsantalucia.it

 


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