HMMHSMM (version 0.1.0)

HMMVarianceMatrix: Variance-Covariance Matrix for Hidden Markov Models

Description

Computes an approximate variance-covariance matrix of the parameter estimates from a fitted Hidden Markov Model (HMM) using a numerical Hessian of the log-likelihood. This function reformulates the HMM as a special case of a Hidden Semi-Markov Model (HSMM) with geometric dwell-time distributions, and calls HSMMVarianceMatrix.

Usage

HMMVarianceMatrix(x, HMM, obsdist, h = 1e-5, method = "central",
                  verbose = TRUE)

Value

A variance-covariance matrix of the HMM parameter estimates, computed as the inverse of the observed information matrix (negative Hessian of the log-likelihood), adjusted to be positive-definite.

Arguments

x

Numeric vector. The observed data sequence.

HMM

A fitted HMM object (typically the output from findmleHMM), containing estimated parameters Pi, delta, and observation parameters.

obsdist

Character string. Observation distribution. Supported distributions: "norm", "pois", "weibull", "nbinom", "exp", "gamma", "lnorm", "gev", "ZInormal", "ZIgamma".

h

Numeric. Step size for finite-difference approximation of the Hessian. Default is 1e-5.

method

Character string. Method for numerical Hessian computation. Options are "central" (default, central differences) or "forward" (forward differences).

verbose

Logical, if TRUE (default), progress messages are printed to the console. Set to FALSE to suppress informational output.

Author

Aimee Cody

Details

This function is a wrapper around HSMMVarianceMatrix, treating an HMM as a special case of an HSMM with geometric dwell-time distributions. The Hessian is computed numerically, inverted, and adjusted for positive-definiteness to provide a variance-covariance matrix for the estimated parameters.

See Also

generateHMM, for simulating HMM data. HSMMVarianceMatrix, for the general hidden semi-Markov case. confintHMM, for bootstrap confidence intervals of HMM parameters.
findmleHMM, for fitting Hidden Markov Models.

Examples

# Example with 2-state Normal HMM
J <- 2
Pi <- matrix(c(0.9, 0.1,
               0.2, 0.8), nrow = 2, byrow = TRUE)
delta <- c(0.5, 0.5)
obspar <- list(mean = c(0, 3), sd = c(1, 1))
# Simulate data
sim_data <- generateHMM(n = 100, J = J, obsdist = "norm",
                        obspar = obspar, Pi = Pi, delta = delta)
# Fit HMM
HMM_fit <- findmleHMM(x = sim_data$x, J = J,
                      obsdist = "norm", obspar = obspar,
                      Pi = Pi, delta = delta)
# Compute variance-covariance matrix
vcov_matrix <- HMMVarianceMatrix(x = sim_data$x, HMM = HMM_fit,
                                 obsdist = "norm")
vcov_matrix