Multilevel Modeling using R
In most biometric applications, those variances are treated as nuisance parameters. They only need to be controlled for, while the main purpose is to get the right point estimates and standard errors for the fixed effects. In social science multilevel modeling (of which education is probably the heaviest user), the variances usually mean something, so there is interest in conducting inference on them (as you probably want to do). As noted by Harold Doran, whatever you do with these random effects is quite sensitive to their distributions. Getting the standard errors on those variances usually comes from assuming a particular model such as the normal one. What you do looks more like ANOVA to me. So you can use aov() to get some F-statistics on your within- and between-school variability.
On 3/17/09, WONG, Ka Yau <kayau at ied.edu.hk> wrote:
Dear experts,
I use R to conduct multilevel modeling. However, I have a problem about the interpretation of random effect. Unlike the variables in fixed effects, the variables in random effects have not shown the standard error (s.e.) and p-value, so I don't know whether they are significant or not? I want to obtain these figures to make the decision. Thank you for your great help!
Below is the syntax and output of my program:
library(nlme)
dataset <- read.csv("d:/dataset.csv")
lme11 <- lme(Overall~1, random=~1|School, method="ML", data=dataset)
summary(lme11)
Linear mixed-effects model fit by maximum likelihood
Data: dataset
AIC BIC logLik
12637.06 12656.27 -6315.53
Random effects:
Formula: ~1 | School
(Intercept) Residual
StdDev: 0.2912031 0.9894488 (<-- No s.e. & p-value)
Fixed effects: Overall ~ 1
Value Std.Error DF t-value p-value
(Intercept) 0.7755495 0.06758038 4444 11.47596 0 (<-- Have s.e. & p-value)
Standardized Within-Group Residuals:
Min Q1 Med Q3 Max
-3.797466473 -0.661750231 -0.007874993 0.652625939 3.549169733
Number of Observations: 4464
Number of Groups: 20
Best Regards,
Tommy
Research Assistant of HKIEd
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