Dear all,
Suppose I have a linear mixed-effects model (from the package nlme) with
nested random effects (see below); how would I present the results from
the random effects part in a publication?
Specifically, I?d like to know:
(1) What is the total variance of the random effects at each level?
(2) How can I test the significance of the variance components?
(3) Is there something like an "r squared" for the whole model which I
can state?
The data come from an experiment on plant performance with and without
insecticide, with and without grasses present, and across different
levels of plant diversity ("div").
Thanks for your help!
Christoph.
lme(asin(sqrt(response)) ~ treatment + logb(div + 1, 2) + grass,
random = ~ 1 | plotcode/treatment, na.action = na.exclude, method =
"ML")
Linear mixed-effects model fit by maximum likelihood
Data: NULL
AIC BIC logLik
-290.4181 -268.719 152.209
Random effects:
Formula: ~ 1 | plotcode
(Intercept)
StdDev: 0.04176364
Formula: ~ 1 | treatment %in% plotcode
(Intercept) Residual
StdDev: 0.08660458 0.00833387
Fixed effects: asin(sqrt(response)) ~ treatment + logb(div + 1, 2) + grass
Value Std.Error DF t-value p-value
(Intercept) 0.1858065 0.01858581 81 9.997225 <.0001
treatment 0.0201384 0.00687832 81 2.927803 0.0044
logb(div + 1, 2) -0.0203301 0.00690074 79 -2.946073 0.0042
grass 0.0428934 0.01802506 79 2.379656 0.0197
Standardized Within-Group Residuals:
Min Q1 Med Q3 Max
-0.2033155 -0.05739679 -0.00943737 0.04045958 0.3637217
Number of Observations: 164
Number of Groups:
plotcode ansatz %in% plotcode
82 164
It is unlikely that your request will be answered faster if you post it a second time in exactly the same way ...> Suppose I have a linear mixed-effects model (from the package > nlme) with nested random effects (see below); how would I present > the results from the random effects part in a publication? > > Specifically, I?d like to know: > (1) What is the total variance of the random effects at each level?> Random effects: > Formula: ~ 1 | plotcode > (Intercept) > StdDev: 0.04176364 > > Formula: ~ 1 | treatment %in% plotcode > (Intercept) Residual > StdDev: 0.08660458 0.00833387What is wrong with an estimted StdDev on the level of plotcode of 0.0418 and on the level of treatment (which is actually the same as to say that this is a block of plants within plotcode that received the same treatment?) of 0.087?> (2) How can I test the significance of the variance components?Calculate a model with an without the component of interest and compare the models using anova(). Perhaps you should read Pinheiro & Bates (2000)?> (3) Is there something like an "r squared" for the whole > model which I can state?None is provided and I do not know how easily it could be calculated. But the use of the measure can be questioned. It is an absolute measure on how much of the variability in the data is explained. Imagine you had true replicates (i.e. several measurements under absolutely identical situations). Imagine further that these measurements do nevertheless show some variability. If this variability was substantial, your r-squared would be low even though your model might pick up all the structure that you can find in the data. Thus you can only get as good as 'natural' variability in your data which is not considered by the r-squared measure. Thus, (corrected) r-squared values might tell you something if you compare different models based on the same data (in a similar way as the AIC and BIC criteria) but not if you compare completely different data sets. Regards, Lorenz - Lorenz Gygax, Dr. sc. nat. Centre for proper housing of ruminants and pigs Swiss Federal Veterinary Office agroscope FAT T?nikon, CH-8356 Ettenhausen / Switzerland