B_est: Estimantion of unknown Markov-modulated linear regression...

In MMLR: Fitting Markov-Modulated Linear Regression Models

Description

This function is used to fit Markov-modulated linear regression models with two states of external environment. This function estimates Markov-modulated linear regression model parameters, using GLSM. Function uses the algorithm based on eigenvalues and eigenvectors decompositions.

Usage

B_est(tGiven, initState, X, Y, lambda, W = TRUE)

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).
Y	Vector of the responses Y, n – number of observations
lambda	Matrix with the known transition rates λ_{i,j}, (m x m), m – number of states
W	an optional logical variable indicating should vector of weights be used in the fitting process or not. If TRUE, matrix with weights is used (that is, inverse values to tGiven – observed times).

Details

Function calculates the following expression: , where vector of average sojourn times in each state $t_i$ is calculated using function Aver_soj_time, $t_i$ is an element of tGiven, $x_i$ is a vector of matrix X.

Value

Vector of estimated parameters β

Examples

lambda <- matrix(c(0, 0.33, 0.45, 0), nrow = 2, ncol = 2, byrow = TRUE)
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)
Y <- matrix(c (5.7, 9.9, 7.8, 14.5, 8.2, 14.5, 32.2, 3.8, 16.5, 7.7),nrow = 10, ncol = 1)
initState <- matrix (c(2,1,1,2,2,2,1,1,2,1),nrow = 10, ncol = 1)
B_est(tGiven,initState,Xtest,Y,lambda,W = 1)

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