Estimation of Arrhenius Model Parameters Using Three Least Squares Methods

Kinetics of Food Deterioration and Shelf-Life Prediction

“…confidence limit values of the reaction rates included will give narrower confidence limits for the Arrhenius parameters (Kamman and Labuza, 1985) Alternatively, a multiple linear regression fit to all concentration vs. time data for all tested temperatures, by eliminating the need to estimate a separate A o for each experiment and thus increasing the degrees of freedom, results in a more accurate estimation of k at each temperature (Haralampu et al, 1985). Since it is also followed by a linear regression of ln k vs. 1/T, it is a two step method as the previous ones.…”

“…These equations have as variables both time and temperature and the nonlinear regression gives simultanously estimates of A o , k A (or k ref ) and E A /R (Haralampu et al, 1985;Arabshahi and Lund, 1985). Experimental data of concentration vs. time for all tested temperatures are used, substantially increasing the degrees of freedom and hence giving much narrower confidence intervals for the estimated parameters.…”

“…Experimental data of concentration vs. time for all tested temperatures are used, substantially increasing the degrees of freedom and hence giving much narrower confidence intervals for the estimated parameters. The use and the 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%.…”

“…It is worth noting that in both examples, the reference temperature, T ref , was chosen as 300 K. As pointed out previously, this transformtaion is important for improving the stability during numerical integration and for nonlinear parameter estimation. The transformation is also recommended since the parameters are highly co-linear and are not easily regressed directly (Cohen and Saguy, 1985;Haralampu et al, 1985;Nelson, 1983).…”

Evaluation of Two Fitting Methods Applied for Thin-Layer Drying of Cape Gooseberry Fruits

“…There are plenty number of studies (mostly about microbial survival under the effect of thermal and non-thermal processes) looking for the best methodology to describe the experimental data sets and they have announced that the 1-step method is better than the 2-step one [15][16][17] . Arabshahi and Lund 18 and Haralampu et al 19 showed that the 1-step method gave smaller confidence intervals for the coefficients than the 2-step method. Bréand et al 20 and Fernández et al 21 also concluded that the 1-step method gave more precise coefficient estimates, so "What is the reason for substantive use of the 2-step method for model fitting?"…”