[R-sig-ME] random slopes model specification

[Karista Hudelson]

Hello Mixed Modelers,

I was hoping to get a bit of feedback on the random effects structure of
the model below.  I wanted to allow two of the fixed effects (my effects of
interest) to have random slopes and also random intercepts for each
watershed (there are 5 watersheds, 27 observations of Spring_MST &
Summer_Rain, and 790 fish (so there are 790 measurements of Hg and
FishLength).

 model6<-lmer(Hg~FishLength+Spring_MST+Summer_Rain+(1+Spring_MST+Summer_Rain|watershed),data=FSV,REML=FALSE)

this model converges, and the output looks "like I want it to look"; ie,
slopes are different for the two effects which logically should have
different slopes:

>   coef(model6)
$watershed
       (Intercept)    FishLength Spring_MST Summer_Rain
877911    -1.7734565 0.02147013 0.03245297 -0.04841394
3319324   -1.2429440 0.02147013 0.03037712 -0.04472220
11597701  -1.6688121 0.02147013 0.03204351 -0.04768574
31121323  -0.9214729 0.02147013 0.02911923 -0.04248513
97032352  -1.4819562 0.02147013 0.03131236 -0.04638544


Here is a bit of the summary() for model6:
Fixed effects:
              Estimate Std. Error         df t value Pr(>|t|)
(Intercept)  -1.417728   0.144246   6.000000  -9.829 6.18e-05 ***
Length        0.021470   0.001085 783.800000  19.794  < 2e-16 ***
Spring_MST    0.031061   0.007518 312.000000   4.132 4.63e-05 ***
Summer_Rain  -0.045938   0.007276 132.100000  -6.314 3.82e-09 ***

It seems to be doing what I intended, but the random effects structure
looks like a bit of a run-on sentence compared to most of the other models
I've seen.  Does this appear correct?

Also....if I'm allowing for the slopes of  the effects of interest to be
different for each watershed and allowing intercepts to be different, in
your opinion(s) would it be easier to understand if I just run separate
models for each lake?  Here how that looks for the Lake with watershed  877911
(corresponding to top line of coef() table above):

> clim<-Hg~FishLength+Spring_MST+Summer_Rain
> climS<-lm(clim,data=Smid)
> summary(climS)

              Estimate Std. Error t value Pr(>|t|)
(Intercept) -1.3531180  0.2152754  -6.286 2.19e-09 ***
Length       0.0276015  0.0027818   9.922  < 2e-16 ***
Spring_MST   0.0247300  0.0081347   3.040 0.002699 **
Summer_Rain -0.0025433  0.0007216  -3.525 0.000531 ***

Any thoughts are appreciated.  Thanks in advance for your time and brain
power.

Much Obliged,
Karista Hudelson

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