[R-sig-ME] models with fixed effets nested in random effects

[Andrew Robinson]

Hi Wayne,

On Mon, Mar 05, 2007 at 12:10:16PM -0700, Hallstrom, Wayne (Calgary) wrote:
> Hi Andrew,
> 
> The reason I did not include year in the random effects part of the
> model was since in terms of the actual data those are the individual
> observations. Putting year into the model made the groups messed up. The
> model statement "FenceEnd/FEsection/MIT_UNMIT" thus had the proper
> number of groups to match the physical chatacteristics of the design
> setup, 
> [number of obs: 1230, groups: MIT_UNMIT:(FEsection:FenceEnd), 93;
> FEsection:FenceEnd, 58; FenceEnd, 7] 
> and then there are the count data from each year within each of these
> groups.  It made sense to me when I was writing the formula but maybe
> this is not right?

The decision about year looks good to me, based on your description
above.

There may well be a temporal correlation structure to watch out for
within the lowest- level random effects.  If that be the case then you
might want to move to using lme(), which has well-configured helper
functions for fitting the more complicated models.

> As well, I have the treatment effects in the random part of the formula
> since without doing this there would not be the proper structure to fit
> the data, and would I not then have pseudoreplication? It is not
> entirely clear to me what should be done with fixed/random effects in
> this case where the treatmetn effects need to be used to define the
> grouping of the data. Maybe as you say I could define a new variable
> with the same characterisitces as 'FEsection' and 'MIT_UNMIT' in order
> to have one for the random section to account for data structure, and
> another in the fixed section to account for the fixed effects. Wouldn't
> that just produce the same results by a different name?

Yes, it would.  I hope that my addition of that text wasn't confusing.
I merely meant to include it as a possiblity to deal with concerns
about the same effects being fixed and random.  I do think that it
would be clearler in some cases.

> In terms of the study layout:
> -Parts of the highway were fenced at different intervals
> (treatment=MIT_UNMIT), creating fence ends (location=FenceEnd).

Ok, this implies to me that MIT_UNMIT represents the intervals
somehow, and that each interval has one or more FenceEnd associated
with it.  What exactly does MIT_UNMIT mean?  I assume that it's
mitigation vs no mitigation.  

> Subsequent fencing extended the fence, removing some fence ends but
> creating new ends. Generally, fence ends are far apart from the previous
> fence end since most phases of fencing are ~20km long.
> -roadkill count data were collected, and summed on a yearly basis
> (year).
> -roadkill location data were then processed and categorized by UTM
> coordinates into five 1km segments inside each fence end and five 1km
> segments outdside, centered on the fence end (subsite=FEsection). This
> sort of like having 10 different levels of the 2 treatments at each
> fence end. The treatment effects being accounted for by the MIT_UNMIT
> variable that defines whether the sample had fencing or not, and the
> FEsection variable defining how far from the fence end the mortalities
> occurred. Of course there could be many ways to look at this, I tried to
> keep things as simple as possible. Feel free to make suggestions if you
> can think of alternatives...

I'm a bit confused by the nesting of MIT_UNMIT inside FEsection.  Your
earlier text implies to me that the MIT_UNMIT treatment differed at
the FenceEnd level.  Nesting it inside FEsection implies that every
level of FEsection has all the MIT_UNMIT levels nested within them.
That seems like a contradiction to me.

Also, based on your description I wonder if FEsection should be
recoded to have a continuous basis as well as a categorical one - for
the purposes of representing an underlying distance?  I note from your
earlier email that FEsection appears as a 10-level factor, and that
seems (prima facie) more difficult to interpret.

Cheers,

Andrew

> A variety of models were fit to the data with the intention of
> determining how fencing affected the distribution of mortality at a
> fence end. Questions asked were - Does mitigation cause a shift in
> mortality locations to the unfenced area beyond the fence end (segments
> 1-5->outside versus 6-10->inside)? This would imply the fence end should
> perhaps be relocated elsewhere. Is there a notable difference in
> mortality among the segments inside and the segments outside the fence
> end? Higher mortality inside the fence could show whether animals are
> getting inside at the fence end and then being killed, in which case
> deterrents to keep them out and mitigations to allow trapped animals to
> escape should be considered. If there is a concentration of mortality in
> the 1km FEsections nearest the fence end this would support the idea
> that substantial numbers of animals are rounding the fence end and being
> killed at that location, implying the fence is not located properly
> relative to animal migrations in the area and needs to be extended,
> and/or perhaps more crossing structures are needed. Mainly elk are the
> animal killed in this area.
> 
> The model I pasted into the last email was best of the the 3 best-fit
> models. The others were similar in structure but with different form,
> such as:
>   u0 <- lmer(ung ~ 1 + (1|FenceEnd/FEsection/MIT_UNMIT),
> family=quasipoisson(link ="log")
>   u01<- lmer(ung ~ year + (1|FenceEnd/FEsection/MIT_UNMIT),
> family=quasipoisson(link ="log")
>   u1 <- lmer(ung ~ FEsection + (1|FenceEnd/FEsection/MIT_UNMIT),
> family=quasipoisson(link ="log"))
>   u2 <- lmer(ung ~ MIT_UNMIT + (1|FenceEnd/FEsection/MIT_UNMIT),
> family=quasipoisson(link ="log"))
> 	.
> 	.
> 	.
>   u5 <- lmer(ung ~ FEsection + MIT_UNMIT +
> (1|FenceEnd/FEsection/MIT_UNMIT), family=quasipoisson(link ="log"))
> 
> 
> Anyway I really appreciate the help since it is a new and confusing
> issue to me. This is for some work I do on my own time, with data from a
> pproject I worked on in the past. The data are for one of the larger
> highway wildlife fencing studies out there, and since roadkill is an
> issue growing with the growing traffic volumes, these results will
> probably be used as reference for how to design other fencing projects.
> 
> Wayne
> 

-- 
Andrew Robinson  
Department of Mathematics and Statistics            Tel: +61-3-8344-9763
University of Melbourne, VIC 3010 Australia         Fax: +61-3-8344-4599
http://www.ms.unimelb.edu.au/~andrewpr
http://blogs.mbs.edu/fishing-in-the-bay/