Far East Journal of Theoretical Statistics
Volume 19, Issue 2, Pages 219 - 230
(July 2006)
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DUAL-REGRESSION ANALYSIS OF HEAD AND BODY LENGTH RELATIONSHIPS
FOR NARROW-BARRED SPANISH MACKEREL, SCOMBEROMORUS COMMERSON, IN WESTERN
AUSTRALIA
Yuk W. Cheng (Australia) and Michael Mackie (Australia)
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Abstract: Body length (in this case fork
length) is a fundamental statistic in fisheries science because it is cheap to
gather and is linked to various biological processes. This study examines the
relationship between fork length (FL) and three head parameters for the
narrow-barred Spanish mackerel (Scomberomorus commerson) in order to
provide a more cost affective means of gaining body measurements for this
species. Conversion equations derived from single regression models overestimate
FL in small fish and underestimate it when fish are large. This bias was reduced
using a mixture of two regressions with parameters and variance-covariance
matrices estimated by the EM algorithm and Newton-Raphson methods. The
relationship between FL and head length (HL) has the smallest coefficients of
variation and is recommended for future estimation of body length. Intersection
points for the dual regressions between fork and head weight occurred at 841 mm
and 1022 mm for male and female fish, respectively, which approximates the size
at 95% sexual maturity for each sex. Conversion equations presented here will
enable collection of length data for monitoring the Western Australian mackerel
fishery. |
Keywords and phrases: complete data log likelihood, observed data log likelihood, the size of maturity, narrow-barred Spanish mackerel. |
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