Researchers who conduct field trials find time point data (repeated measures) one of the most difficult types of data to wrangle. One common pitfall among enthusiastic amateurs is treating repeated measures as if they were independent. For independence to be true, treatments must be randomly assigned to experimental units, and it’s impossible to randomly assign time points to a single field plot or treatment.
One way around this is to apply an integral to each experimental unit, such as AUDPC. A more elaborate way would be to account for the variance caused by time while modeling the impact of the treatments. Block diagonal covariance matrices defray the time-based covariance errors across treatments.
PROC MIXED offers a ‘Repeated’ statement to specify the repeated variable. Fisher, 1921 data (the progenitor to the F-Statistic) provides an interesting example, where 70 years of wheat yield data were measured among strips. Source and data citations provided at the end of this post.
proc mixed data=work.fisher plots=all; class Alternating Kg_Mg Kg_N Kg_Na Kg_P yr; model Yield=Kg_N Kg_Na Kg_P Kg_N*Kg_P Alternating(Kg_N*Kg_P*Kg_Na) Kg_Mg / ddfm=kr2; repeated yr; run;
Although individual treatments were nonreplicated, there is enough factorial replication among nutrient composites to isolate and test the elements. Although there was no random component (such as block) in this example, PROC MIXED can certainly facilitate random and repeated statements too.
In terms of the p-values, most nutrients were highly significant. It goes to show how 70 years of fertilization with the same thing produced a strong effect on the land and the crop.
Learn more about PROC MIXED
And consider taking this excellent Mixed Model eLearning Course
Fisher, R. A. (1921). "Studies in Crop Variation. I. An examination of the yield of dressed grain from Broadbalk". Journal of Agricultural Science. 11 (2): 107–135. doi:10.1017/S0021859600003750. hdl:2440/15170.
Data from: Rothamsted Research (2018). “Fisher 1921 Broadbalk wheat grain yields 1852-1918”. Electronic Rothamsted Archive https://doi.org/10.23637/rbk1-data-fisher-1921-01.
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