Question

Let's say I have measured the abscisic acid content (could be any metabolite really) of 10 individual plants which we can consider biologically independent. Then I repeat that measurement for all 10 plants on 15 different days over the course of a year. I then want to correlate, with a linear regression model, the values of abscisic acid with the amount of rainfall (from publicly available regional data, say) on each of those days.What is statistically appropriate? Firstly, I believe that a mixed model should be used, with individual plant as a random effect, to account for the fact that I am repeatedly measuring the same plant over time. On top of that, am I not also in danger of pseudo-replication from the fact that my rainfall has only been measured once for all 10 abscisic acid measurements (i.e. the abscisic acid vs rainfall measurements are not really independent on each day either)?

Answer 1

Using a mixed model with individual plants as random effects is suitable for repeated measures over time, and addressing pseudo-replication due to shared rainfall data might necessitate clustered standard errors or a generalized estimating equation.

Step-by-step explanation:

When correlating the abscisic acid content of plants with rainfall measurements, using a mixed model with individual plants as a random effect is indeed statistically appropriate. This approach accounts for the fact that each plant is measured multiple times, introducing a random variation among the individual plants. However, you also identified a potential issue of pseudo-replication because the rainfall data is a single measurement applied to all 10 plants on each day. This could violate the assumption of independence in a standard linear regression model.

To address this, you may consider using clustered standard errors or a generalized estimating equation that accounts for the fact that observations within a cluster (in this case, measurements from the same day) may be correlated. This can give a better estimate of the uncertainty around your regression coefficients when dealing with repeated measures on the same subjects (plants). To analyze the relationship between abscisic acid content and rainfall, a mixed model should be used with the individual plant as a random effect to account for the repeated measurements over time. Additionally, there is a concern about pseudo-replication due to the fact that rainfall has only been measured once for all 10 abscisic acid measurements. Therefore, the abscisic acid vs. rainfall measurements are not truly independent on each day.