Dear List:

I'm trying to use the boot function to estimate some standard errors. I

actually programmed a bootstrap using some homebrew code and it worked

fine. But, I am trying to use the more efficient boot function. I have

placed some sample data for replication of my problem at the bottom of

this email. For the sample problem, I have 10 subjects each with 5

observations Y_t = (t_1, ..., t_5). Consider these 'longitudinal' data.

So, I use reshape to put into the long format in order to regress the

observations onto time, a time-varying covariate. I do the regression

for each individual separately:

Y_{t} = \mu + \beta(time) + \epsilon_{t}

To get the statistic of interest (sigma_theta), I do the following with

the original data:

theta <- numeric(10)

sigma <- numeric(10)

for(i in 1:10){

tmp <- subset(long, ID==i)

tmp.lm <- lm(obs ~ time, tmp)

theta[i] <- coef(tmp.lm)[2]

sigma[i] <- sum((tmp.lm$residuals)^2)/ (dim(tmp)[1] -2)

}

sigma_theta <- var(theta) - ( mean(sigma) / 10) # This is my point

estimate

All that I do is perform an OLS regression for each subject individually

and use these estimates to derive a measure of between-unit variability

for the parameter \beta. Now, I want to put a bootstrap confidence

interval around sigma_theta using the values from the empirical

distribution. I realize I could be using lmer() here, but I am

experiementing with a method for getting some variance components.

Simply programming this was not too difficult, albeit maybe a little

hokey. I simply resampled from the original data (DD), reshaped into the

long format, and then repeated the loop above 4000 times. It was

basically the following in a loop:

p <- sample(10, replace=TRUE)

pD <- DD[p,]

pD$ID <- seq(1:10) # This was needed so reshape doesn't give error

regarding duplicate IDs

plong <- reshape(pD, idvar='ID',

varying=list(c('t1','t2','t3','t4','t5')), v.names='obs',

direction='long')

Now, I have read through Bootstrapping regression models by J. Fox and

of course the boot help as well as a few others online. I see how the

boot function works for the most part and have been successful with

basic things like means and medians. But, what is confusing me, and

maybe I am overthinking this, is how to work with resampling when the

data are in the long format.

>From what I understand, I need to write the following function to

compute my statistic of interest:

my.fun <- function(DD,p){

E <- DD[p,]

var(theta) - ( mean(sigma) / 10)

}

Then I do something like

boot(DD, my.fun, 4000)

Well, those of you experienced with this see this is not working. This

is my effort to illustrate what I have done and see if anyone can offer

a little didactic advice.

Thanks,

Harold

R 2.2.0

Windows XP

DD <- data.frame(ID= c(1,2,3,4,5,6,7,8,9,10),

t1=c(61,65,57,46,47,43,53,72,53,72),

t2 =

c(72,85,68,74,85,58,62,96,54,98),t3=c(118,129,130,116,103,109,82,117,87,

114),

t4=c(130,148,143,124,117,133,112,129,120,144)

,t5=c(176,174,201,157,148,152,156,154,138,177),

z=c(170,194,187,156,155,150,138,154,149,167))

long <- reshape(DD, idvar='ID',

varying=list(c('t1','t2','t3','t4','t5')), v.names='obs',

direction='long')

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