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Statistical Problem


James Kirkley <[log in to unmask]>


Academic forum on fisheries ecology and related topics <[log in to unmask]>


Wed, 18 Sep 1996 07:56:38 -0400





text/plain (1 lines)

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.

> 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.
> 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

e-mail:[log in to unmask]

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