Log-Link and Logistic Regression
By definition, linear regression models specify a linear relationship between the predictor variables in the model and the outcome variable under study. In linear regression, each one-unit difference in a predictor variable is associated with some constant difference in the mean value of the outcome variable. In many instances, the assumption of a linear relationship between two characteristics is reasonable. However, there are circumstances in which nonlinear relationships might be expected. For example, the HIV viral load, a measure of disease severity, grows exponentially over time among untreated patients, such that each week the viral load may be 10% greater than it was the previous week. This growth pattern motivates evaluation of the relative change (or percent change) in the HIV viral load.