seeking some advice on fixed vs random specification

Could this be accomplished by using an explicitly nested REGION:TIME
variable as a random effect and still keeping REGION and TIME
variables as fixed effects?


On Tue, Nov 1, 2011 at 3:35 PM, Douglas Bates <bates at stat.wisc.edu> wrote:

On Tue, Nov 1, 2011 at 1:03 PM, david depew <david.depew at queensu.ca> wrote:

Thanks for your response Peter,

I see what you mean about the nesting vs crossed.

My understanding (perhaps incorrect) is that by treating TIME 

and REGION as

fixed effects (i.e. the first formulation)

lmer(log(CONT) ~ TIME*REGION + WB_TYPE + PORT*len + (1|wb_id))

the specific contrasts of interest (i.e. REGION1 in TIME A vs REGION1 in
TIME B) could be accomplished, but that this would not be possible if TIME
and REGION were treated as random effects.

Are you suggesting that they should be treated as both "fixed" and
"random"? i.e.

lmer(log(CONT) ~ TIME*REGION + WB_TYPE + PORT*len + (1|TIME) +
(1|REGION/wb_id))

Not a good idea.  As one might expect the fixed and random effects for
the same factor end up confounded with one another.

On Tue, Nov 1, 2011 at 11:56 AM, Peter Claussen 

<dakotajudo at mac.com> wrote:

David,

Have you considered that is TIME*REGION is crossed as fixed effects, you
should also treat them as crossed if they are random effects (and not
nested), thus

lmer(log(CONT) ~ WB_TYPE + PORT*len + (1|TIME) + (1|REGION/wb_id))

Are TIME and REGION considered to be two independent sources of random
variation, which would be implied by this model?

If you want model variation across time differently for each region, then
perhaps (TIME | REGION/wb_id) may be more appropriate.

I would interpret (1|TIME/REGION), based on analogy to (1 | BLOCK/PLOT),
to mean the REGION identified as "1" in TIME "A" would not be in any way
related to REGION "1" in TIME "B"; that is, the region 

identifier only has

meaning within the context of the time identifier.

Peter Claussen
Gylling Data Management

On Oct 31, 2011, at 9:27 AM, david depew wrote:

Dear list,
I am seeking some thoughts/advice on whether my approach to 

this problem

(below) makes sense.

We have compiled a rather large dataset (n> 25,000 for most species of
interest) on the levels of a contaminant in fish covering 40 

years and a

continental scale. We would like to investigate broad temporal changes
across a large geographic region. Because the data comes from a variety

of

sources, with different resources and mandates for sampling fish, we do

not

consider this dataset to be a "true random sample", but in 

the absence of

such, this is the best possible approximation to one.

Sites that are sampled over time are generally not sampled frequently
enough and with sufficient constraints (sample sizes, sizes of fish) to

do

more focused analysis of temporal trends.

Having spent some time perusing the resources available on 

mixed models,

I

think this offers the best choice for making some sense of this messy
dataset. I'm less inclined to try and estimate site specific slopes
(regressed over year) for sites that have low sampling effort.

Rather, I split the dataset into time periods (A,B and C) of ~ 15 year
blocks. (Note: the levels of this particular contaminant are known to
change very slowly over time), and assigned each site  to an ecoregion
based on geographic location. Thus, I am aiming to assess (if possible)
whether levels of contaminant in each ecoregion change over the time

blocks

(A,B and C), where sites are assumed to represent a random selection of
possible locations within an ecoregion.

The variables of interest are as follows;
CONT=contaminant Conc.
WB_TYPE = waterbody type (lake, river)
PORT = portion (fillet, whole fish)
len=mean centered length of fish
REGION=Ecoregion (37 unique types)
TIME= time block (A, B or C)
wb_id=unique id of site

My initial thought was to specify the model with time and 

region as fixed

effects.

lmer(log(CONT) ~ TIME*REGION + WB_TYPE + PORT*len + (1|wb_id))

comparison of this model with one with only additive time and region

terms

suggests that this improves the model fit and the interaction 

is probably

important.

I can test TIME and REGION interaction contrasts specifically using the
multcomp package and the results indeed suggest some regions have
significant changes between time blocks.

Or,

would it make more sense to specify the time and region effects as part

of

the random terms with site nested within region, nested within time

period?

lmer(log(CONT) ~ WB_TYPE + PORT*len + (1|TIME/REGION/wb_id))

I'm assuming (perhaps wrongly) that the conditional means and 95% CI

could

be extracted and compared to assess changes within a region?

I'm aware that there are arguments that can be made to treat TIME and
REGION as either fixed or random, depending on the objective of the
analysis. I'm mainly seeking some clarification if a) my interpretation

of

the specified model is correct, and b) if this makes sense with respect

to

the initial problem.

Any thoughts or advice would be much appreciated.

thanks



--
David Depew
Postdoctoral Fellow
School of Environmental Studies
Queen's University
Kingston, Ontario
K7L 3N6

david.depew at queensu.ca

      [[alternative HTML version deleted]]

--
David Depew
Postdoctoral Fellow
School of Environmental Studies
Queen's University
Kingston, Ontario
K7L 3N6

david.depew at queensu.ca

       [[alternative HTML version deleted]]