Date:         Tue, 15 Oct 2002 11:57:11 -0700
Reply-To:     Kimberly Austin <austinkimberly@YAHOO.COM>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         Kimberly Austin <austinkimberly@YAHOO.COM>
Subject:      Re: repeated cov structure question...
In-Reply-To:  <20021014233320.3233.qmail@web21109.mail.yahoo.com>
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Dale and other interested SAS-Lers,
Thanks (again) for your input on my cov structure question. Of course, I have a few follow-up questions that I am currently mulling over:
1. How should I approach selection of a spatial cov structure? Initially I thought a linear structure was most intuitive given that the spatial (time) effect I am using is Julian date. However, after doing some snooping, I found that SP(LIN) would not run because the convergence criteria for REML wasn't met. I have tried a few other structures and found the exponential SP(EXP) structure does run. Before I do any further snooping I need to get a better grasp of how to "properly" approach selection of a cov structure.  Should this be a concern, and if so, how should I approach it?
2. I am still wrestling with the idea that I need to include my experimental unit as a random effect to account for between-subject variation with in my treatments (repeated observations were taken on experimental units within treatments only, i.e., units belonged to only one treatment group through the course of the study). However, when including a random statement [random unit(treatment)] in addition to a repeated statement, the number of subjects listed under "model information" in the output is given as 1 (where as without the random statement  the correct number of subjects is given).  Also, the maximum number of observations on a subject is given as my total sample size as opposed to the actual maximum number of observations made of a subject.  So I guess my question is, when inluding subjects (within treatment) as a random effect to account for between-subject variation, in addition to using a repeated statement to account for correlation among repeated observations on a subject, does the repeated statement still "work" proplerly given these differences? I hope that made sense.
Any input, or relevant references to dig into that you know of, are welcomed.
Thanks, again, for your time,
Kimberly
 Dale McLerran <stringplayer_2@YAHOO.COM> wrote:Kimberly,

It sounds like you are questioning whether time is needed on the
MODEL statement as well as on the REPEATED statement. The answer
to that is "No, it is not necessary to have time in both parts of
the model." However, you do need time as an effect in the
REPEATED statement. When you use a spatial covariance structure,
you specify the covariance structure as

SP(structure)(variables employed in computing distances)

where structure is one of EXP, EXPA, GAU, LIN, LINL, POW, POWA,
or SPH. One or more variables must be specified for computing the
distance between a pair of observations. In your case, there is
just one variable defining distance and that variable is time.
Suppose that for the i-th observation, you had values of time

1, 4, 10, 13

Now, suppose that you specified the structure SP(POW)(TIME). Then
the covariance matrix for the i-th observation is given as

cov = | V*p^(1-1) V*p^(4-1) V*p^(10-1) V*p^(13-1) |
| V*p^(4-1) V*p^(4-4) V*p^(10-4) V*p^(13-4) |
| V*p^(10-1) V*p^(10-4) V*p^(10-10) V*p^(13-10) |
| v*p^(13-1) V*p^(13-4) V*p^(13-10) V*p^(13-13) |

= | V V*p^3 V*p^9 V*p^12 |
| V*p^3 V V*p^6 V*p^9 |
| V*p^9 V*p^6 V V*p^3 |
| V*p^12 V*p^9 V*p^3 V |


The distance between pairs of observations for the various spatial
covariance structures is based on the variables specified in what
the reference manual refers to as the c-list. This can be a single
variable (as with time), or it can be a pair of variables
describing geographical coordinates in two-dimensional space, or
it could be a triplet of variables defining distance in 3-D space,
or a pair of variables defining distance in 2-D space and a time
variable, or ... Hopefully, you get the idea. Just about any of
the spatial covariance structures could be reasonable, though you
would not want to employ either of the anisotropic structures. You
also do not want to use the ANTE(1) covariance structure. A
template for your code might be:

proc mixed data=mydata;
class exp_unit trt ...;
model response = trt ...;
repeated / subject=exp_unit type=sp(pow)(time);
run;

HTH,

Dale


--- Kimberly Austin wrote:
> Greetings All:
>
> I have a data set with repeated observations on the same experimental
> units over time and am working in PROC MIXED. I am interested in
> examining a treatment effect when accounting for other
> climate/weather related variables. The distance between repeated
> observations in this data set is unequal and irregular with the
> number of observations on the subjects ranging from 8 to 31. I would
> like to try to specify a cov structure in my REPEATED statement that
> describes correlation between pairs of observations on the same unit
> as decreasing with increasing time between them. I am using SAS
> System for Mixed Models as a reference. The example given in that
> text (p127) recommends using a spatial covariance structure.
> However, I am not interested in the effect of time of each
> observation on my response and therefore have no time effect in the
> model. The example in the text does include the time each
> observation was taken as an explanatory variable. This makes me
> question how SAS keeps track of the distance between paris of
> observations if there is no time/space variable specified? Is a time
> variable required for these types of cov structures?
>
> Does anyone have experience with fitting a mixed effects model to a
> similar data set? Any recommendations regarding which cov structures
> are appropriate [SP(POW), ANTE(1) ?]? If any of my above ramblings
> are unclear (probably the case, I've had far too much coffee today),
> please let me know and I will try to clarify.
>
> Thanks much for your help,
>
> Kimberly
>



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