Non-linear regression models in the management of accumulated production of parchment coffee in Peru

Abstract

Parchment coffee results from washing the coffee cherry, and its production has achieved a significant increase in the coffee-growing regions of Peru. Knowing the production pattern of this grain is essential to help coffee producers make decisions in the economic and social sector. As growth curves generally have sigmoidal behavior, which is well fit by non-linear models, this study aimed to model the cumulative production pattern of parchment coffee as a function of time (in months) in the year 2022, comparing the fit of the non-linear Logistic, Gompertz and von Bertalanffy models. The cumulative national production, and production of the departments of Huánuco and San Martín, in Peru, were analyzed. Data used to fit the models were obtained from the Ministry of Development and Irrigation (MIDAGRI) of Peru. To check the assumptions of normality, homoscedasticity, and independence of residuals, the Shapiro-Wilk, Breusch-Pagan, and Durbin-Watson tests were used, respectively. The model parameters were estimated using the least squares method using the Gauss-Newton algorithm in the R software. The goodness-of-fit of the models was tested using goodness-of-fit measures such as Coefficient of Determination (R2), Residual Standard Deviation (RSD), Akaike Information Criterion (AIC), and nonlinearity measures. Based on the models’ goodness-of-fit measures, the Gompertz model with a first-order autoregressive error term (AR1) fit best to national production data, and the Logistic model was the most suitable for describing the production of the departments of Huánuco, and San Martín.