The Factor Models
The way the x-variables (factors) are modeled to predict an expected value or probability is the subject of the factor side of the model.
The factors enter the prediction equation as a linear combination of x values and the parameters to be estimated. For a continuous response model, where i indexes the observations and j indexes the parameters, the assumed model for a typical observation, yi, is written
where
yi is the response
xij are functions of the data
εi is an unobservable realization of the random error
bj are unknown parameters to be estimated.
The way the x’s in the linear model are formed from the factor terms is different for each modeling type. The linear model x’s can also be complex effects such as interactions or nested effects. Complex effects are discussed in detail later.