[R] How to estimate variance components with lmer for models with random effects and compare them with lme results

[KL]

Hi,

I performed an experiment where I raised different families coming from two
different source populations, where each family was split up into a
different treatments. After the experiment I measured several traits on each
individual. 
To test for an effect of either treatment or source as well as their
interaction, I used a linear mixed effect model with family as random
factor, i.e.
lme(fixed=Trait~Treatment*Source,random=~1|Family,method="ML")

so far so good,
Now I have to calculate the relative variance components, i.e. the
percentage of variation that is explained by either treatment or source as
well as the interaction.

Without a random effect, I could easily use the sums of squares (SS) to
calculate the variance explained by each factor. But for a mixed model (with
ML estimation), there are no SS, hence I thought I could use Treatment and
Source as random effects too to estimate the variance, i.e.

lme(fixed=Trait~1,random=~(Treatment*Source)|Family, method="REML")

However, in some cases, lme does not converge, hence I used lmer from the
lme4 package:

lmer(Trait~1+(Treatment*Source|Family),data=DATA)

Where I extract the variances from the model using the summary function:

model<-lmer(Trait~1+(Treatment*Source|Family),data=regrexpdat)
results<-model at REmat
variances<-results[,3]

I get the same values as with the VarCorr function. I use then these values
to calculate the actual percentage of variation taking the sum as the total
variation.

Where I am struggling is with the interpretation of the results from the
initial lme model (with treatment and source as fixed effects) and the
random model to estimate the variance components (with treatment and source
as random effect). I find in most cases that the percentage of variance
explained by each factor does not correspond to the significance of the
fixed effect.

For example for the trait HD,
The initial lme suggests a tendency for the interaction as well as a
significance for Treatment. Using a backward procedure, I find that
Treatment has a close to significant tendency. However, estimating variance
components, I find that Source has the highest variance, making up to 26.7%
of the total variance.

   
anova(lme(fixed=HD~as.factor(Treatment)*as.factor(Source),random=~1|as.factor(Family),method="ML",data=test),type="m")
                                          numDF denDF  F-value p-value
    (Intercept)                                1   426 0.044523  0.8330
    as.factor(Treatment)                       1   426 5.935189  0.0153
    as.factor(Source)                          1    11 0.042662  0.8401
    as.factor(Treatment):as.factor(Source)     1   426 3.754112  0.0533





   
summary(lmer(HD~1+(as.factor(Treatment)*as.factor(Source)|Family),data=regrexpdat))
    Linear mixed model fit by REML 
    Formula: HD ~ 1 + (as.factor(Treatment) * as.factor(Source) | Family) 
       Data: regrexpdat 
        AIC    BIC logLik deviance REMLdev
     -103.5 -54.43  63.75   -132.5  -127.5
    Random effects:
     Groups   Name                                      Variance  Std.Dev.
Corr                 
     Family   (Intercept)                               0.0113276 0.106431                      
              as.factor(Treatment)                      0.0063710 0.079819 
0.405               
              as.factor(Source)                         0.0235294 0.153393
-0.134 -0.157        
              as.factor(Treatment)L:as.factor(Source)   0.0076353 0.087380
-0.578 -0.589 -0.585 
     Residual                                           0.0394610 0.198648                      
    Number of obs: 441, groups: Family, 13
    
    Fixed effects:
                Estimate Std. Error t value
    (Intercept) -0.02740    0.03237  -0.846



Hence my question is, is it correct what I am doing? Or should I use another
way to estimate the amount of variance explained by each factor (i.e.
Treatment, Source and their interaction). For example, would the effect
sizes be a more appropriate way to go?


Thanks!

Kay Lucek


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