Cautionary tale toward a multisite dose response test
If we wanted to understand how something performed across a wide swath of environments, we should replicate the test in those environments. I would then recommend a mixed model, treating the environments (sites) as fixed and/or random effects.
We return to a data set for which we previously tested a response of our fictional MBoost product. Our analysis terms included one site, San Felipe, which showed a significant response of product dose rate. We reproduce the analysis with a random factor, location, and location interactions for rate and MBoost.
PROC Mixed DATA=WORK.RATETEST plots=all;
CLASS Block 'Location'n MBoost;
MODEL Yield_tonnes_ha = 'Location'n*Rate_kg_ha Rate_kg_ha 'Location'n*MBoost;
RANDOM int Block / subject=Block('Location'n);
LSMEANS 'Location'n*MBoost / slice=location;
RUN;While you may interpret the departure from normality as slight or egregious, most would agree that the residual scatterplot shows serious structural aspects to the error, i.e. the residuals are not independently distributed. We should try to diagnose why this is and avoid placing too much stock in the output until we understand the sources of variance.
Looking at the output, we see all factors and interactions are significant. The rate response is significant which indicates that overall there is at least one of the MBoost rates different from the others.
Interestingly, another significant factor is location by rate term, which means that at least one site is showing a different rate response than others. A valid approach would be to interpret the rate responses within sites.
Hence, we included the “slice=location” option on the LSMeans statement, which shows the test of the factor of interest within sites. Note, the LSMEANS statement only performs for categorical variables, i.e. those in the class statement. That’s why we include a test for MBoost, rather than rate.
The outcome of the slice statement shows two sites do not show a significant result for MBoost, whereas two others do. Note especially San Felipe shows no statistical significance whatsoever; we previously saw an effectof MBoost rate on this site. The reason for this may be that the mean difference in San Felipe was small in magnitude compared to the rest of the sites, which also could explain the significant rate*location interaction.
Finally, given the heterogenous variability among sites, sites with a small (but otherwise statistically significant) effect when standing alone, no longer show statistical significance when combined with the higher variability sites. Note when we include the block nested within location as part of the random “subject=” option, activates provision of a by-site by-block variance plots, which can help interpreting sources of heteroscedasticity.
Combining field trial data from multiple sites can be a fruitful means to reaching broader conclusions than other sites but take care to first check model assumptions and interpret the data accordingly.
