Using Logistic Regression to Predict the Probability That Individual ‘Honeycrisp’ Apples Will Develop Bitter Pit

Abstract

‘Honeycrisp’ is a popular apple cultivar, but it is prone to several disorders, especially bitter pit. Previously reported models for predicting bitter pit are biased, indicating that the models are missing one or more important predictor variables. To identify additional variables that may improve bitter pit prediction, a study was undertaken to investigate the influence of canopy position, spur characteristics, and individual fruit characteristics on bitter pit development. ‘Honeycrisp’ trees from two orchards over 2 years provided four combinations of orchards and years. Fruits were sampled from spurs at different canopy positions and with varying bourse shoot lengths and numbers of fruits and leaves. Following cold storage, bitter pit was assessed in three ways: 1) bitter pit severity was recorded as the number of pits per fruit, 2) bitter pit was recorded as a binomial response (yes, no) for each fruit, and 3) the incidence of bitter pit was recorded as the proportion of fruit developing bitter pit. As a result of the high fruit-to-fruit variation, bitter pit severity was associated with canopy position or spur characteristics to a lesser extent than bitter pit incidence. Bitter pit incidence was generally greater for fruits developing on spurs with only one fruit and spurs from the lower canopy. Binomial data were analyzed with a generalized linear mixed model. Fruit harvested from trees with heavy crop loads, and those developing on spurs with multiple fruit and spurs with long bourse shoots had the lowest probability of developing bitter pit. Regardless of how bitter pit was assessed, bitter pit related positively to fruit weight (FW), but the relationship usually depended on other variables such as canopy position, fruit per spur, and leaves per spur. The advantages of fitting binomial data with logistic regression models are discussed.

Keywords

• binary analysis
• bourse shoots
• calcium disorders
• canopy position
• fruit weight
• malus ×domestica
• roc curves
• spur characteristics