Comparison of linear regression models considering heteroscedasticity of fruits and flower buds of highbush blueberry cultivated in Chile
2013
Ávila, Julio | Salvo, Sonia | Muñoz, Carlos
To suitably manage the logistics of blueberry production, predictions of the potential yield to be obtained from harvest must be made months in advance. One way to estimate this yield is by predicting the number of fruits to be harvested, which depends on the number of flower buds available after pruning. The number of flower buds per plant is the most explanatory variable for the number of fruits (Salvo et al., 2012). This relationship is highly linear; nevertheless, as the number of buds increases, the prediction error for the fruits increases as well (Salvo et al., 2011). This effect is known as heteroscedasticity, and it negatively affects predictions using linear methods. To control this effect, three models were compared: constant variance, nonconstant variance and transformed variables with constant variance. The model of nonconstant variance uses a variance function (σ2y⌢2θ), and its parameters were estimated using the generalised least squares model. With these considerations, the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC) and log-likelihood statistics were reduced between 1 and 10% compared to the constant–variance model. In contrast, the transformed variables model fit the data well but did not fulfil the theoretical error assumptions. Another relevant aspect is that the nonconstant variance model decreased the residual variance on the order of 90% and fulfilled all theoretical error assumptions. Using this model, blueberry producers can obtain more precise fruit predictions, thereby reducing the uncertainty of planning the harvest logistics months in advance.
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