In regression model, we often want to describe the relationship between a
response variable and one or more input variables in terms of main effects
and interactions. To facilitate the specification of a regression model in
terms of the columns of a DataFrame, the DataFrames package provides a
Formula type, which is created by the ~ binary operator in Julia:
fm = Z ~ X + Y
A Formula object can be used to transform a DataFrame into a ModelFrame object:
df = DataFrame(X = randn(10), Y = randn(10), Z = randn(10)) mf = ModelFrame(Z ~ X + Y, df)
A ModelFrame object is just a simple wrapper around a DataFrame. For
modeling purposes, one generally wants to construct a ModelMatrix, which
constructs a Matrix{Float64} that can be used directly to fit a
statistical model:
mm = ModelMatrix(ModelFrame(Z ~ X + Y, df))
Note that mm contains an additional column consisting entirely of 1.0
values. This is used to fit an intercept term in a regression model.
In addition to specifying main effects, it is possible to specify interactions
using the & operator inside a Formula:
mm = ModelMatrix(ModelFrame(Z ~ X + Y + X&Y, df))
If you would like to specify both main effects and an interaction term at once,
use the * operator inside a Formula:
mm = ModelMatrix(ModelFrame(Z ~ X*Y, df))
The construction of model matrices makes it easy to formulate complex statistical models. These are used to good effect by the GLM Package.