[R] nlme question

[Wassell, James T., Ph.D.]

-----Original Message-----
From: Wassell, James T., Ph.D. 
Sent: Thursday, November 17, 2005 9:40 AM
To: 'Deepayan Sarkar'
Subject: RE: nlme question

Deepayan, 

Thanks for your interest.   It's difficult in email but I need the
variance of Kappa = mu + 1.645*tau + 1.645* sigma

Just using the standard variance calculation Var(K) = Var(mu) +
(1.645)^2 * Var(tau) + 1.645^2 * var(sigma) + [three covariance terms
with constant multipliers]. 

So, I can get var(mu) [or actually the standard error] from the summary
function -- and var(tau) and var(sigma) using the VarCorr function, but
I still need the covariance terms.

I am trying to duplicate methods in a paper by Nicas & Neuhaus,
"Variability in Respiratory Protection and the Assigned Protection
Factor"  J. Occ & Environ Health, Feb. 2004.   p 99-109.  (see eqn. 12).


The authors used Proc Mixed, but I can't figure out how to get
covariance terms with SAS either.  

Thanks again. 

Terry Wassell

-----Original Message-----
From: Deepayan Sarkar [mailto:deepayan.sarkar at gmail.com] 
Sent: Thursday, November 17, 2005 2:52 AM
To: Wassell, James T., Ph.D.
Cc: r-help at stat.math.ethz.ch
Subject: Re: nlme question

On 11/16/05, Wassell, James T., Ph.D. <jtw2 at cdc.gov> wrote:
> I am using the package nlme to fit a simple random effects (variance
> components model)
>
> with 3 parameters:  overall mean (fixed effect), between subject
> variance (random) and  within subject variance (random).

So to paraphrase, your model can be written as (with the index i
representing subject)

y_ij = \mu + b_i + e_ij

where

b_i ~ N(0, \tao^2)
e_ij ~ N(0, \sigma_2)
and all b_i's and e_ij's are mutually independent. The model has, as
you say, 3 parameters, \mu, \tao and \sigma.

> I have 16 subjects with 1-4 obs per subject.
>
> I need a 3x3 variance-covariance matrix that includes all 3 parameters
> in order to compute the variance of a specific linear combination.

Can you specify the 'linear combination' that you want to estimate in
terms of the model above?

Deepayan