estimate {VLMCX}

Estimation of Variable Length Markov Chain with Exogenous Covariates

Description

Estimates the parameters of the multinomial logistic model in the VLMCX tree for each context in the tree.

Usage

estimate(VLMCXtree, y, X)

Arguments

VLMCXtree

a VLMCX tree

y

a "time series" vector (numeric, charachter, or factor)

X

Numeric matrix of predictors with rows corresponding to the y observations (over time) and columns corresponding to covariates.

Value

A tree from an object of type VLMCX. The tree contains the items

context

the context, or sequence of symbols.

alpha

a vector with coefficients corresponding to the intercept for the transition into the states in the state space of y.

beta

a 3 dimensional-array of estimated coefficients corresponding to [steps in the past, number of covariate, symbol (in the state space) to transition into].

child

list whose entries are nodes with the same structure.

Author(s)

Adriano Zanin Zambom <[e-mail]>

Examples

set.seed(1)
n = 4000
d = 2

X = cbind(rnorm(n), rnorm(n))
alphabet = 0:2 ### state space
y = sample(alphabet,2, replace = TRUE)
for (i in 3:n)
{
	if (identical(as.numeric(y[(i-1):(i-2)]), c(0,0)))
		value =  c(exp(-0.5 + -1*X[i-1,1] + 2.5*X[i-1,2]),      
		           exp(0.5 + -2*X[i-1,1] - 3.5*X[i-1,2]))
	else if (identical(as.numeric(y[(i-1):(i-2)]), c(0,1)))
		value = c(exp(-0.5),     exp(0.5))
	else
		value = c(runif(1,0,3), runif(1,0,3))


    prob = c(1,value)/(1 + sum(value)) ## compute probs with baseline state probability
    y[i] = sample(alphabet,1,prob=prob)
    
}
  

tree = NULL
tree$context = "x"  ## this is the root
tree$alpha = NULL
tree$beta = NULL
tree$child = list()
this_child = NULL
this_child$context = "0"
this_child$alpha = 0
this_child$child = list()
tree$child[[1]] = this_child

this_grandchild = NULL
this_grandchild$context = c(0, 0)
this_grandchild$alpha = 0
this_grandchild$beta = array(c(0,0,0,0),c(1, 2, 2)) ## steps, d, alphabet (state space)
this_grandchild$child = list()

tree$child[[1]]$child[[1]] = this_grandchild

this_other_grandchild = NULL
this_other_grandchild$context = c(0, 1)
this_other_grandchild$alpha = 0
this_other_grandchild$beta = NULL
this_other_grandchild$child = list()

tree$child[[1]]$child[[2]] = this_other_grandchild

estimate(tree, y, X)

fit = VLMCX(y, X, alpha.level = 0.0001, max.depth = 2, n.min = 15, trace = TRUE)
estimate(fit$tree, y, X)