Hello,
I am performing analyses on water quality data. I want to test whether there are difference in average TP concentrations between 5 sites, and whether these differences depend on the year of sampling.
I have three years of data: 12 samples were taken between March and October in 2014, 11 samples were taken between March and October in 2015, and 9 samples were taken between March and October in 2016.
For every sampling date measurements were taken at all 5 sites. I have attached some “fake” data so you can see how it is structured.
I want to “pair” samples by date to account for variability caused by weather etc. on a given date. I also want to “correct for” temporal autocorrelation- samples taken close together in time are more similar than those taken further apart. I am assuming samples taken in a given year are independent from samples taken in other years. The intervals between measurements are not equal so I am theoretically unable to use variance-covariance structures such as AR(1), toep, arma(1,1), and ante(1).
I have attempted the above in proc mixed with the code at the bottom of the post. To block by day I have included a repeated statement with Date(Year) as the subject. Analyses without accounting for temporal autocorrelation showed an unstructured variance-covariance structure to be the best fit. I am allowing different var-cov matrices for each year with the group=year option. To account for temporal (residual) autocorrelation I added another repeated statement, with Site as the subject, that models the structure of temporal autocorrelation using the sp(exp) option and the variable “Day_nmbr”, which is a continuous variable representing the day as a number between 1 and 365. Note that I also have “Date” as a class variable for purpose of blocking, above. Again, I used the group=year option to allow a different autocorrelation structure in each year. Note-I haven’t explored the best residual autocorrelation model yet, but sp(exp) is a likely fit.
When I run this code with either one of the repeated statements it works, but when I run it with both statements SAS only uses the second statement (I get this message: WARNING: Only the last REPEATED statement is used). I am presuming (or perhaps hoping!) that I have just coded something incorrectly. Perhaps there is a way to combine the repeated statements? Can anyone help me think of a way to code that will allow me to do what I have described?
Thanks for any help!!
Code:
Proc mixed data=sites;
class Date Year Site;
model TP = Site Year Site*Year / solution ddfm=kenwardroger outp= pred_data;
Repeated / subject= Date(Year) type=un group=year r rcorr;
Repeated / subject= Site type=sp(exp)(Day_nmbr)group=year r rcorr;
run;
I am using SAS 9.3
