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I am trying to run a model to describe the rate of water table drawdown in the soil. The predicted variable is rate, and I am interested in the effect of two categorical variables: (1) if the water table is above a certain threshold (yes, no) and (2) if the rate is different between seasons (summer / fall). I have measurements from 3 watersheds, treated as random effects. The wrinkle is that the water table is above the threshold more in the fall.

The two questions I'm trying to answer are (1) is there a difference in rate above and below the threshold and (2) after accounting for this difference, is there a difference in rate between the summer and fall? I can handle significance testing, etc.. but am having a fard time constructing the model properly. I've been using the lmer function from the lme4 package in R.

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  • $\begingroup$ Is the question just on how to specify the model? The simplest one would be a random-intercepts model: lmer(rate ~ thresh * season + (1 | watershed), data = ...) $\endgroup$
    – Russ Lenth
    Commented Jul 27, 2014 at 21:16
  • $\begingroup$ I (sort of) know the syntax, I'm just not clear on what the appropriate model is. For example, the one you proposed: will that adequately separate the effect of the two different factors (thresh and season)? My concern is that because they are related (water table is above the threshold much more in the fall) that what seems to be the effect of season will instead be the effect of threshold. $\endgroup$
    – Iceberg Slim
    Commented Jul 27, 2014 at 22:45
  • $\begingroup$ I understand the concern, but the coefficients estimates in a regression model (including a mixed model) are the differential effects of each variable, subject to the others being held constant. So you do have the appropriate adjustment here. To interpret the results further, I (of course, since I wrote it) suggest the lsmeans package, which computes and compares predictions and equally-weighted averages thereof. $\endgroup$
    – Russ Lenth
    Commented Jul 28, 2014 at 0:02
  • $\begingroup$ Right on, will take a look at lsmeans. Thanks. Incidentally, happy to mark this as answered but something got bulloxed up with my accounts and I don't seem to be recognized as the user who posted the question. $\endgroup$
    – Iceberg Slim
    Commented Jul 28, 2014 at 0:13

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3 levels for the grouping variable is not sufficient to fit random intercepts. A linear model (without random effects) would be more appropriate with fixed effects for watershed.

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