the handbook of food engineering practice crc press chapter 10 ...

statistical benefits of employing a one step method were demonstrated for computer
simulated food degradation data, following first order kinetics by Haralampu et al. (1985)
and for actual data for nonenzymatic browning of whey powder (zero order model) and for
thiamin loss in an intermediate moisture model system (first order model), by Cohen and
Saguy (1985). In this method , the Arrhenius parameters estimates were judged on the size
of the joint confidence region at 90%. The joint confidence region is an ellipsoid in which
the true parameters propably exist together at a specified confidence level. The extremes of
the 90% confidence ellipsoid region do not correspond to the 95% confidence intervals
(derived from a t-test) for the individual parameters. Since experience shows that E A and
lnk ref are highly correlated, the ellipsoid is thus a more accurate representation of the
confidence region (Draper an Smith, 1981; Hunter,1981).
The confidence region may be constrtucted by considering both the variance
and covariance of the parameters estimates, and by assuming that the estimates are from a
bivariate normal distribution. The confidence contours for a nonlinear regression creates a
deformed ellipsoid. The complexity of the computation hampers its application as a
routine statistical test. However, the appropriate extreme points of the confidence region
could be derived using a computer program (Draper and Smith, 1981) which incorporates
approximation for a nonlinear regression:
S = SS {1+ N p
n-Np F[N p, n-N p , (1-q)]} (27)
where f is the fitted nonlinear model, SS is the nonlinear least square estimate of the fitted
model, i.e. SS= Σ(A i -f) 2 for i=1 to n , n is the number of data points, N p the number of
parameters derived from the nonlinear least squares, 100(1-q)% the confidence level and F
the F -statistics. This method allows a reliable derivation of the confidence limits of the
determined parameters that can affect the application of the kinetic data for shelf life
prediction and product design and demonstrates the caution that should be exercised when
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