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 <ka...@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
>
>
> [[alternative HTML version deleted]]
>
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--
Stas Kolenikov, also found at http://stas.kolenikov.name
Small print: I use this email account for mailing lists only.
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