Kirsty-

In cases where all ponds start at 0 (or a constant) at time 0, it can make
sense to omit a random intercept for ponds.  You don't show your code, but
in lmer you can specify the random effect the same as any other formula:
(0+Time | Pond)

However, how is your date or time variable coded?  Is it a date or
datetime?  Is Time=0 at the time of first application of your treatments?
 This matters because an intercept in (1+Time|Pond) with Time as numeric
will be values at Time=0, which could be Jan 1, 1960, 1970, 1900, 1899, or
perhaps some other epoch, depending on how you handled your data.
 [Rereading your post, I'm not sure whether your slope is with respect to
Time, or with Temperature.  If with Temperature, think about 0K, 0c, etc.,
and whether that temperature makes sense for intercepts or is well outside
of your range of observed temperatures (I'm down south where we complain
when the ocean is 10c).]

Based on my experience, changing the values of your Time or Temperature
variable will have a huge impact on whether you have among pond variances
in intercepts and slopes.    If Time=0 at the onset of your treatments is
meaningful, go with that.  Otherwise consider if you want a "main effect"
rather than intercept by centering your times or temperatures so that
Time=0 or Temperature=0 is the mean of your times or temperatures.

Tom


On Thu, Dec 6, 2012 at 1:43 PM, Kirsty E. B. Gurney <kegurney@alaska.edu>wrote:

> Good afternoon;
>
> I have recently come across a *general question* about linear mixed models
> that I can't seem to find an answer for on my own.  I am hoping that one of
> the braintrust on this list might be willing / able to help.
>
> Specifically, I am analyzing a dataset that describes pond temperatures
> for a series (n = 25 ponds, 436 measurements).  Ponds were assigned to 1 of
> 4 treatments, and I want to find find out if temperature was affected by
> treatment.
>
> Pond-level inference, in general, is not of interest, so it seemed clear
> that POND should be included as a random effect.  However, I have good
> reason to believe that the change in temperature across the study was also
> variable by POND, and a model that includes a random slope term has good
> support, as determined by AIC.
>
> However, as it turns out, the covariance parameter estimate for the
> intercept term in the random slope model is pretty small (i.e., I think
> most ponds start out at a pretty similar temperature).
>
> I am just wondering if it makes good statistical sense to run a random
> slope model without the random intercept term?
>
> If so, does anyone know how one would one specify this in the model
> structure?
>
> Many thanks in advance,
> kbg
>
> -~-~-~-
> Kirsty E. B. Gurney, Ph.D.
> Alaska Cooperative Fish and Wildlife Research Unit
> Institute of Arctic Biology
> 209 Irving 1 Building
> University of Alaska Fairbanks
> Fairbanks, AK 99775
> T: (907) 474 - 7738
> -~-~-~-
>
>
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>
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-- 
-------------------------------------------
Tom Philippi, Ph.D.
Quantitative Ecologist & Data Therapist
Inventory and Monitoring Program
National Park Service
(619) 523-4576
Tom_Philippi@nps.gov
http://science.nature.nps.gov/im/monitor
library(fortunes)
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