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I'm trying to understand the regression analysis done in a published study.

They use GAM models to predict plant growth, and to test for the most important predictors. They have measured growth of individual plants at 20 different sites, and also have several environmental measures (e.g. temperature, precipitation, soil characteristics) which seem to be measured at the site level.

They say that the environmental variables are included as fixed effects predictors, and site is included as a random effect. I'm confused as surely within a site, all the plant growth measurements have identical environmental measurements associated with them (as these seem to be measured at the site level) - what does this leave to test?

Am I misunderstanding fixed/random effects, or is the methodology poorly explained? Is it still possible to test which of the fixed effects is the strongest predictor if site is included as a random effect?

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  • $\begingroup$ What do you mean by "test for strongest predictor" ? $\endgroup$ Jul 31, 2020 at 4:21
  • $\begingroup$ I mean test which predictor has the biggest effect on the response. People often use multiple regression to test this in ecology. $\endgroup$
    – rw2
    Jul 31, 2020 at 13:55
  • $\begingroup$ Sure. The variable with the largest estimate will have the biggest "effect" on the response. No need for a test. Just look at the effect sizes $\endgroup$ Jul 31, 2020 at 14:02

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I don't know what you mean by "strongest predictor" but there is no problem in having a mixed model where all the predictors vary at the group-level only. It just means that the predictions will be the same for each unit in the same group, and all the estimates for the regression coefficients will be "between subject" and not "within subject" and not a combination of between and within.

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