Date:         Wed, 9 Jan 2008 15:01:40 -0500
Reply-To:     Ryan Utz <rutz@AL.UMCES.EDU>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         Ryan Utz <rutz@AL.UMCES.EDU>
Subject:      Re: AIC mystery in MIXED

My responses to the past 2 posts:

Peter-I completely agree, and have more or less already done so with the
data already and derived an answer I'm happy with.  I am simply attempting
the model selection exercise to back my assertions/findings (as others do in
the literature), but may end up just going with what seems like an obviously
more appropriate model.  In the literature, both linear and power
relationships have been identified for this subject (more below).

Warren-Thanks for the suggestion with NLMIXED (I didn't even know it
existed).  But at first glance I'm not sure it runs repeated measures
analyses, which is what I need here.

The specific situation is this: I am concerned with the effects of fish
density on growth rates.  I measured fish size monthly for four months and
recorded mean fish size and fish density (# per meter squared).  Since size
and density data are temporally autocorrelated (the same sites were analyzed
each time), I need a repeated measures ANCOVA model.  In the literature, for
similar situations, both power relationships and linear relationships
between density and fish size/growth are found, with power relationships
more commonly found.  In my case, the growth-density relationship changes
with time (the interaction term is usually significant), but in nearly every
case the best fit is a linear, rather than power, relationship (as seen when
plotting all data or month-specific data).  The data and my current running
model is below.  I'm using an auto-regressive covariance structure because
it seems most appropriate for the situation.

Any thoughts/comments would be welcome, particularly a robust means of
deciding whether to go with a power or linear relationship.

-Ryan

data test; input month $ stream $ length density;
cards;
1 A 69.96774194 0.133496332
1 B 65.52941176 0.033526012
1 C 68.10526316 0.100531915
1 D 54 0.326097973
1 E 64.33333333 0.052635229
1 F 63.24137931 0.196749226
1 G 66.875 0.034366577
1 H 66.15384615 0.062547529
1 I 68.54237288 0.177382646
2 A 71 0.092420538
2 B 73.52380952 0.041907514
2 C 75.16666667 0.10668693
2 D 62.72222222 0.28277027
2 E 72.94117647 0.055825243
2 F 70.12328767 0.26873065
2 G 75 0.033221024
2 H 74.83333333 0.039923954
2 I 74.16981132 0.158819346
3 A 82.8125 0.099266504
3 B 85.05405405 0.048193642
3 C 84.34210526 0.114893617
3 D 70.515625 0.257685811
3 E 86.92857143 0.044660194
3 F 76.37647059 0.244736842
3 G 89.5 0.020619946
3 H 93.6 0.058555133
3 I 84.08888889 0.125817923
4 A 92.5 0.071882641
4 B 100.1666667 0.020953757
4 C 97.88888889 0.043085106
4 D 80.02 0.16875
4 E 101.4545455 0.031900139
4 F 84.21428571 0.158359133
4 G 101.2941176 0.032075472
4 H 100.2857143 0.03460076
4 I 89.65957447 0.142318634
;

proc mixed data=test method=ml covtest;
class stream month;
model length= month Density month*density;
repeated / subject=stream type=ar(1);
run;