I have a data analysis job for which lme may be used. Prof. Spencer Graves had helped me much on that. I'm really appreciated for that. Could anybody else in the list give me some hints from other perspectives? I hope I can learn as much as possible for this complicated real data.
Thanks in advance.
Hanhan
 
To briefly describe my data: My data is health effect measurements (y) and personal exposure to ozone and some other pollutants (x1,x2,x3,...). For each of the totally 5 subjects, 3 weeks' daily data were available with some missing values. To pool the 5 subjects together, I use lme in R as try1 <- lme(y~x1+x2+x3,random=~1|sub,na.action=
na.exclude). Is it proper to do so? (only intercept will be treated as random)
 
If the initial model contain 8 variables with 3 of  them insignificant. My first step would be to try various corARMA possibilities. There are several possible results:
> 1. Maybe there is one corARMA model (with the lowest AIC of 
 course) that makes all the eight variables significant. I'll happily 
 stop at that! (but this is not the case for my data)
> 2. There is one corARMA model with a much lower AIC and anova test 
shows significant difference of it from the original model. But in the new 
model, there is still one or two insignificant variables. What can I 
do next? (that's the problem in my data)
> 3. No correlation structure in the residuals. In this case, I'll use 
 drop1 on the original model, and test various corARMA again for the new 
model.  And the cycle from step 1 to 3 goes on.

try1$resid (or resid(try1)? I forget) would give me two columns of residuals, the first colomn being residuals and the second being subject-specific residuals.  I want to analyze the residuals using arima, so which colomn should I use?
 
In my imagination (maybe a silly idea), considering all possible time lags between variables, to cope with the regression above, I would make pilot pairwise cross-correlation analysis first between y~x1, y~x2, y~x3, etc. After that, if a linear model is assumed, I would like the equation to be as follows: y[t]+b1*[t-1]+b2*[t-2]+...=c1*x1[t]+c2*x1[t-1]+c3*x1[t-2]+d1*x2[t]+d2*x2[t-1]+d3*x2[t-2]+e1*x3[t]+e2*x3[t-1]+e3*x3[t-2]+... So I'll produce new time lag variables from y, x1,x2, x3,.... This will make the equation much more complicated. Is this reasonable?
 
If x <- rnorm(100,5)  and y <- 1.5*x+rnorm(100,0). Delete the first value in x and the last value in y, there would be no correlation between y~x, and the residual would show no patern. But obviously y[t]~x[t-1] would give a wonderful regression. So, in practice, if we encounter such situation (with no correlation between two variables and no correlation structure in residuals), we should not stop at that. But how can this be diagnosed but by time lag? Am I right in this point?




Xianglu Han

206 Environmental Health Science

University of Georgia 30602

Phone: 706 255 2308

 



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