Regression Options

By default, the regression models for the CCA , PCR , MLR and GCM are fitted under the assumption that the predictands are normally distributed. In some cases that assumption may be invalid. For example, precipitation data are generally positively skewed. There are options to fit regression models that assume alternative data distributions. These alternative regression models are called Generalised Linear Models (GLMs) .

The following options are available:

• Ordinary least squares regression : appropriate for Y-data that are normally distributed. In most cases it is reasonable to assume that temperature data are normally distributed. This assumption is also reasonable for large rainfall amounts (e.g., seasonal averages for non-arid areas and seasons).
• Logistic regression : appropriate for Y-data that represent yes/no outcomes, or for Y-data that are probabilities. For example, the predictand may be the occurrence of an extreme event, and the Y-data are recorded as a 0 if the event did not occur, and 1 if the event did occur.
• Binomial regression : appropriate for Y-data that represent counts with upper and lower limits. For example, the predictand may be the number of days with no rainfall over a fixed period.
• Poisson regression : appropriate for Y-data that represent counts with no upper limit. For example, the predictand may be the number of storms over a fixed period.
• Gamma regression : appropriate for Y-data that have a lower limit of 0 and are positively skewed. For example, the predictand may be the amount of rainfall.