My experiments was mainly a split-plot design with water treatment as the main factor. Measurements were taken in 6 harvests from Dec 2012 to May 2013. In Dec, all plots under irrigation; from Jan to March, half plots under irrigation and the other half withholding water; from Apr to May, all plots under irrigation. In each harvest, plants were defoliated after other measurements were taken. I do not know whether I should do an ANCOVA with measurements in the first harvest as covariates, or do a repeated measures ANOVA?
I would actually recommend a mixed linear regression for longitudinal data. The trouble with AN(C)OVA is that the sequence (or time or repetition) is not explicit in the repeated measure. The mixed longitudinal designs allow fitting repeated harvest as a linear effect rather than just another qualitative variable as it would be for RM ANOVA, not to mention random effects not just for the different plots but also for the linear changes for different plots over the different measurements.
I would actually recommend a mixed linear regression for longitudinal data. The trouble with AN(C)OVA is that the sequence (or time or repetition) is not explicit in the repeated measure. The mixed longitudinal designs allow fitting repeated harvest as a linear effect rather than just another qualitative variable as it would be for RM ANOVA, not to mention random effects not just for the different plots but also for the linear changes for different plots over the different measurements.
Repeated measure will provide the solution for intended experimentation.
Thanks.
Hello. The problem with ANCOVA is that each measure is not independent of previous measures from the same subject. On the other hand, ANOVA for repeated measures requires a complete number of observations per subject. If you have such database, you could use the ANOVA, as suggested by Rajiv. If something is incomplete, I agree with Damian, use the mixed models. Best regards.
As Damian pointed, mixed models are definitely much more flexible than repeated measures anova and allow for missing data.
I always would go through RM-ANOVA because there's no independece between measuraments taken at the same plots from time to time. Importantly, I see the design is temporally asymetrical, in the sense that assigning plots to irrigation vs. non-irrigation varied temporally. I see this adds an extra difficulty to analyze this dataset. Keep this is mind.
Hi, David, can you please explain to me what is the REML procedure stand for?
Fernando mentioned that my design is temporally asymetrical, in the sense that assigning plots to irrigation vs. non-irrigation varied temporally. That is also what I am worried about. The mixed linear regression sounds good, but is that valid in this case that my treatment was temporally asymetrical?
Thank you very much for all your contribution. Great minds.
Interesting problem. REML means restricted maximum likelihood, it refers to a way of partitioning variation when you are including random effects. You absolutely need to include random effects in your model. The way I understand it, you are asking if there is an effect of changing the irrigation treatment. I would use a model that includes month (since measurements taken the same month are not fully independent due to cliamte) and plot (since plots might have different "personalities" that show up as you repeat the measurements) as random effects.
The fixed effects should be treatment (continuous vs interrupted irrigation) and treatment time (before vs after irrigation change), as well as an interaction between the two. The interaction term tests the hypothesis that either of the treatments changes its response more than the other after the date when irrigation was interrupted. Your prediction, I think, is that the plots in the "interrupted irrigation" treatment will change more than the control.
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