Xreg: Preparing data for parameter estimation procedure

In MMLR: Fitting Markov-Modulated Linear Regression Models

Description

Regressors matrix formation taking into account observation times and initial states. Kronecker product is used.

Usage

Xreg(tGiven, initState, X, lambda)

Arguments

tGiven	Vector of the observed times (n x 1), n – number of observations
initState	Vector of the initial states (n x 1), n – number of observations
X	Matrix of predictors (n x k), n - number of observations, k - number of columns (k - 1 - number of regressors).
lambda	Matrix with the known transition rates λ_{i,j}, (m x m), m – number of states

Details

Function calculates the following expression , where vector of average sojourn times in each state is calculated using function Aver_soj_time.

Value

Matrix (n x 2k)

Examples

Xtest <- cbind(rep_len(1,10),c(2,5,7,3,1,1,2,2,3,6), c(5,9,1,2,3,2,3,5,2,2))
tGiven <- matrix (c(6,4.8,1,2.6,6.4,1.7,2.9,4.4,1.5,3.4), nrow = 10, ncol = 1)
initState <- matrix (c(2,1,1,2,2,2,1,1,2,1),nrow = 10, ncol = 1)
lambda <- matrix(c(0, 0.33, 0.45, 0), nrow = 2, ncol = 2, byrow = TRUE)
Xreg(tGiven, initState, Xtest, lambda)

MMLR documentation built on Jan. 9, 2020, 5:06 p.m.