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I have a set of data measuring response variable (length) on the same individual over several time points in nine different treatments (pH). Due to the confounding effect of temperature and it's biological relevance for interpretation, this data are split into three observation periods. I am analyzing each period separately. For each observation period, I want to know if there is an effect of pH on the mean growth rate (population response); is there a relationship between mean length growth rate and pH? I'm not interested in the effect of pH on growth rate over time at this particular moment. I have performed GEE to obtain population-response while accounting for the multiple measurements on the same individual, ignoring time (not of interest now). I get the regression coefficients for each pH and when I plot these coefficients or EMMs against pH, I can see a strong relationship (positive or negative, depending on the observation period).

My question is: how can I quantify this relationship? For example (in terms I understand) - when we are performing linear regression on data we get the R2 value to see if there is a trend and how strong it is. Can I do that on this EMMs data obtained from GEE? If not, what are my options here, how to quantify this relationship?

Please note that for this particular case I need to work with mean population response - effect of pH on the mean shell growth rate (while accounting for repeated measurements).

Sanja_
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  • R^2 doesn't usually make sense for a GEE because we don't claim independence or identical distribution of the error terms. "strength of relationship" usually has to do with regression coefficients and their 95% (or other) CIs. – AdamO Apr 15 '23 at 17:03
  • I guessed that, but how can I quantify this relationship then? Any ideas? – Sanja_ Apr 15 '23 at 17:07
  • Let me ask this: how does a regression slope NOT quantify a relationship? – AdamO Apr 15 '23 at 20:54
  • What I am asking here is what can I do to confirm this trend I see when I plot the EMMs against predictor? Am I allowed to use regression or not, is there some other way? Maybe I don't use right terminology, but I think it's clear what I want to know from data – Sanja_ Apr 16 '23 at 06:22
  • I was wondering if is it OK to model the relationship between pH as the predictor variable and the EMMs as the outcome variable with linear regression or not? Not sure about this. From my layman's point of view - I can see the relationship when I plot the data, but not sure what is an appropriate way to assess this. I am new at this, as I haven't dealt with repeated measures before, so maybe my questions are arbitrary, but I can't find answer to this through the literature I have read so far. – Sanja_ Apr 16 '23 at 14:23
  • Yes 100% you can do this. What you are proposing is basically a forest plot, though a forest plot typically models the coefficient on the X axis and labels groups on the $Y$. Earlier you say you are trying to "confirm" and the trend and I'm not sure what you mean - these are epistemiological problems. Inference doesn't prove anything. If you mean, "show" the trend then yes the plot's the way to go – AdamO Apr 17 '23 at 15:53

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