Multilevel modeling in food science: A case study on heat-induced ascorbic acid degradation kinetics

Area of Science:

• Analytical Chemistry
• Chemical Kinetics
• Statistical Modeling

Background:

• Experimental results often exhibit variation due to repetitions.
• Traditional analysis methods like averaging or complete pooling can obscure valuable information about this variation.
• Alternative methods include no-pooling, complete pooling, and partial pooling.

Purpose of the Study:

• To compare different methods of analyzing experimental repetitions, specifically averaging, complete pooling, no-pooling, and partial pooling.
• To apply multilevel modeling with partial pooling to characterize variation in experimental data.
• To evaluate the predictive accuracy of different kinetic models for ascorbic acid degradation.

Main Methods:

• Multilevel modeling was employed, utilizing partial pooling to partition variance across different levels (measurements, groups, clusters).
• A case study involving the heat-induced isothermal degradation of ascorbic acid with 15 repetitions was analyzed.
• Bayesian analysis was performed to visualize posterior distributions of parameters and assess model predictive accuracy.

Main Results:

• Averaging and complete pooling methods significantly underestimated variation.
• The no-pooling technique overestimated variation.
• Partial pooling, as implemented in multilevel modeling, provided a more accurate representation of variation by partitioning it across levels.
• The multilevel model with an estimated reaction order demonstrated superior predictive accuracy compared to other models.

Conclusions:

• Multilevel modeling is a preferred approach for analyzing experimental data with inherent variation, offering better characterization of uncertainties.
• Bayesian analysis enhances multilevel modeling by providing insights into parameter behavior and focusing on predictive accuracy.
• The study highlights the sensitivity of ascorbic acid kinetics to experimental conditions and the effectiveness of multilevel modeling in capturing this variability.