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I wanted to check here to see if a repeated measures ANOVA would be a good option to analyze my data, or if you have any other suggestions? I have read that GLMM is another option for time series data, but my data is not linear. I use R for analysis.

  • Experiment:

I counted the number of flowers (Total) on 168 plants every other day (Day), so repeated measurements on the same plant subjects (PlantID) evenly spaced through time. I had 4 Treatments: Early, Peak, Late and Control, which differed in the timing that a heatwave was applied. I used 4 growth chambers to grow my plants, with 42 plants in each chamber. There was one chamber for each heat treatment. I used 6 genetic lines of this plant (RIL).

  • Research Question:

I am interested in determining if the shapes of the 'flowering schedules' are different across RIL and Treatment combinations. Do control and treatment plants differ in their response to heatwaves? How do the genetic lines differ in their response? For example, do Control/RIL10 plants differ in their flowering response compared to Early/RIL10 plants, and so on for all other combinations.

I included a figure of my data to better illustrate this. Each gam curve represents the average flower counts for one RIL over time. The green curves are Control plants, the red curves are the Early plants. I would basically like to do a post hoc test to see which curves are significantly different from each other, and where they differ, if possible. Smoothed mean flower production over time

  • My Data:

Here is an example of my data. Day starts at day 19 because this data is a subset for flower production after the early heatwave ended. This is the flower counts (Total) over time (Day) for plant #85 in the Early heatwave treatment and belonging to RIL 206.

 PlantID    Date     Day    Total  Treatment  RIL
    85     June 26    19      2     Early     206
    85     June 28    21      5     Early     206
    85     June 30    23     15     Early     206
    85     July 2     25     15     Early     206
    85     July 4     27     29     Early     206
    85     July 6     29     67     Early     206

If you would like a larger sample of my data to look at please let me know.

What do you guys think?

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You seem to have repeated count data, i.e., the number of flowers per plant. Hence, you could use a Poisson-type of regression model. To account for the correlations in the repeated measurements, you could use a GEE for count data or a mixed effects Poisson regression. The choice between them depends on several factors, i.e., if you have missing data or if you're interested in coefficients with a marginal/population interpretation or a subject-specific one. Both types of analysis are available in R.

You could find more information about these models in Chapters 4 & 5 of my Repeated Measurements Course notes.

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  • $\begingroup$ Thanks for the suggestion! When reading about the Poisson distribution, I noticed that counts must occur independently through time if I am understanding correctly. An example given was counting the # of letters mailed to you each day - the mail you receive today doesn't effect the # of letters you get the next day. However in my experiment, the # of flowers produced by a plant today does effect the # that can be produced the next day, due to the use of resources within a plant. My plants increase flowering to a peak and then decline. Does GEE include a term to account for this? $\endgroup$ – Abbey Oct 22 '18 at 16:17
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    $\begingroup$ Yes, the GEE will account for the fact that you have correlated counts. $\endgroup$ – Dimitris Rizopoulos Oct 22 '18 at 16:55

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