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Subject: Statistical Problem
From: James Kirkley <[log in to unmask]>
Reply-To:Academic forum on fisheries ecology and related topics <[log in to unmask]>
Date:Wed, 18 Sep 1996 07:56:38 -0400
Content-Type:text/plain
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Sorry for posting appearing to all but attempts to directly e-mail to Thomas 
on statistical problems he posed on network continued to be returned because 
of address problem.

>
>
>Thomas,
>
>        It may not help much but I had a paper published in 1991 on 
different problems of the allometric model (weight/length relationship).  I 
think I addressed some of the problems about which you are concerned.  My 
major concerns were pooling data over time and area and choice of functional 
form.  Reference: J.E. Kirkley, W.D. DuPaul, and A. Schmitzer (1991) 
"Factors affecting the relationship between meat weight and shell height of 
Placopecten magellanicus (Gemlin, 1791) in the Mid-Atlantic Region," World 
Aquaculture Society, An International Compendium of Scallop Biology and 
Culture, A Tribute of James Mason, Sandra Shumway and Paul Sandifer 
(Editors) Selected Papers from the 7th International Pectinid Workshop, pp. 
134-139.  
>
>        Your ANOVA/ANCOVA is a valid approach to the problem of comparing 
coefficients.  It appears that your problem is whether or not you can pool 
the data which is simply a test of whether or not the regressions for each 
group of data are the same.
>
>        Swamy, P.A.V.B., R.K. Conway, and Michael LeBlanc (1988) The 
Stochastic Coefficients Approach to Econometric Modeling, Part III: 
Estimation, Stability Testing, and Prediction (The Journal of Agricultural 
Economics Research, Winter, Vol. 41, No. 1: 4-20) and other researchers have 
argued that the standard F-test may result in erroneous conclusions about 
the stability of coefficients (i.e., the ANCOVA may not be the best 
approach).  The above article provides 61 references on the subject of 
stability testing.  
>        The standard approach is to conduct an F-test.  Consider the simple 
regression Y = X  + u where X is a matrix of independent variables and  is 
a vector of parameters.  Assume that the variables are over different 
periods of time, geographical areas, or populations.  You want to know 
whether  (t) =  (t+i).  The test of whether or not the regression 
equations for the two time periods are equal is the standard F-test with K, 
n+m-2K degrees of freedom where K is the number of parameters, n is the 
number of observations in one equation and m is the number of observations 
in the other equation.  
>
>        Alternatively, use F = ((SSE(c) - SSE(1)-SSE(2))/K) / 
((SSE(1)+SSE(2)/(n+m-2K)).  This is the familiar Chow or Rao test.  An 
alternative which is quite simple is the cusum and cusum (squared) test 
statistics of Brown, Durbin, and Evans.  This latter test really applies 
best to time series models.  There are numerous other tests which also can 
be used.  You might benefit from reviewing a good econometric test.
>
>Jim Kirkley
>
James (Jim) E. Kirkley
College of William and Mary
Virginia Institute of Marine Science
School of Marine Science
Gloucester Point, VA 23062

FAX:804-642-7161
WORK:804-642-7160
e-mail:[log in to unmask]

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