Class OrderedRegression<E1 extends Enum<E1> & IntegerValuedEnum>

java.lang.Object
microsim.statistics.regression.OrderedRegression<E1>
Type Parameters:
E1 - event type.
All Implemented Interfaces:
IDiscreteChoiceModel

public class OrderedRegression<E1 extends Enum<E1> & IntegerValuedEnum> extends Object implements IDiscreteChoiceModel
Ordered Discrete Variable Models.

Let y define a discrete valued set {y_0,y_1,..., y_n}. Each y_i is an indicator variable for discrete value i, where higher values of i reflect some natural ordering of the set.

ystar = Xb + e

y_j = 1 if cut_j-1 < ystar <= cut_j and 0 otherwise.

P(y_j=1|X) = P(cut_j-1<ystar).P(ystar<=cut_j) = (1 - P(ystar<=cut_j-1)).P(ystar<=cut_j)

= P(ystar<=cut_j) - P(ystar<=cut_j).P(ystar<=cut_j-1) = P(ystar<=cut_j) - P(ystar<=cut_j-1) = F(cut_j-Xb) - F(cut_j-1-Xb)

NB: P(ystar<=cut_j).P(ystar<=cut_j-1) = P(ystar<=cut_j-1) because cut_j-1 <= cut_j

Author:
Justin van de Ven