Application of Linear Mixed Model in Longitudinal Study to Optimize Effect of Ultrasound on Color of Minimally Processed Granny Smith Apple

This study aims to identify and optimize ultrasonic bath process parameters to improve the quality of minimally processed apples during storage. Specifically, it investigates how exposure time and power affect the browning index over time using a longitudinal (time-dependent) approach. To capture the complexity of food quality changes during storage, a linear mixed model (LMM) was employed, accounting for both fixed effects and random variation among samples. The adopted experimental design was a 22 with 3 replications, treating storage time (ST) and quadratic storage time (QST) as covariates. The LMM fitting is improved when random intercept and slope are included in the model. The estimated variance of the random effect associated with the intercept and storage time was 3,79 and 0,13, respectively. The results also revealed significant interactions between linear and quadratic time and process factors, as well as a notable interaction between process factors (p=0,032), where power exhibited a buffering effect on exposure time. The optimal process parameters are 400 W and 3 minutes. Given the correlation between repeated measurements and the biological variability of the samples, identifying the optimal combination of process parameters was crucial for improving the quality attributes of perishable, short-shelf-life food products. Compared to traditional models, LMM provides more precise and accurate results.