ABSTRACT
In Section 5.2.7, the PCB in the fish model was fitted using a categorical predictor to indicate fish size. By using the categorical predictor size, the data set is divided into two groups, one with observations of large fish and one with observations of small fish. Initially, a simple linear regression model using only year as the predictor (equation 5.2 on page 127) was used. This model assumes that the relationship between log(PCB) and the two predictors (year, and Len.c) is the same for all fish. In Section 5.2.7, separate models were fit for small and large fish (equation 5.4, page 142). The underlying assumption is that the log(PCB) relationship is now size-specific. When a factor or categorical variable is used, the data set exhibits a multilevel structure. Each datum not only represents a single observation, but also belongs to a group. Using a categorical variable to describe each datum’s group association leads to models describing group-specific relationships. The two models represented in equation 5.4 are fitted separately except that a common model residual standard error is assumed. This view of data structure as multilevel or hierarchical is often scientifically necessary.
