msm (version 1.4)

qmatrix.msm: Transition intensity matrix

Description

Extract the estimated transition intensity matrix, and the corresponding standard errors, from a fitted multi-state model at a given set of covariate values.

Usage

qmatrix.msm(x, covariates="mean", sojourn=FALSE,
            ci=c("delta","normal","bootstrap","none"), cl=0.95,
            B=1000, cores=NULL)

Arguments

x

A fitted multi-state model, as returned by msm.

covariates

The covariate values at which to estimate the intensity matrix. This can either be: the string "mean", denoting the means of the covariates in the data (this is the default), the number 0, indicating that all the covariat

sojourn

Set to TRUE if the estimated sojourn times and their standard errors should also be returned.

ci

If "delta" (the default) then confidence intervals are calculated by the delta method, or by simple transformation of the Hessian in the very simplest cases. Normality on the log scale is assumed.

If "normal", t

cl

Width of the symmetric confidence interval to present. Defaults to 0.95.

B

Number of bootstrap replicates, or number of normal simulations from the distribution of the MLEs.

cores

Number of cores to use for bootstrapping using parallel processing. See boot.msm for more details.

Value

• A list with components:
• estimate
  Estimated transition intensity matrix.
• SE
  Corresponding approximate standard errors.
• L
  Lower confidence limits
• U
  Upper confidence limits
• Or if ci="none", then qmatrix.msm just returns the estimated transition intensity matrix.

  If sojourn is TRUE, extra components called sojourn, sojournSE, sojournL and sojournU are included, containing the estimates, standard errors and confidence limits, respectively, of the mean sojourn times in each transient state.

  The default print method for objects returned by qmatrix.msm presents estimates and confidence limits. To present estimates and standard errors, do something like

  qmatrix.msm(x)[c("estimates","SE")]

Details

Transition intensities and covariate effects are estimated on the log scale by msm. A covariance matrix is estimated from the Hessian of the maximised log-likelihood.

A more practically meaningful parameterisation of a continuous-time Markov model with transition intensities $q_{rs}$ is in terms of the mean sojourn times $-1 / q_{rr}$ in each state $r$ and the probabilities that the next move of the process when in state $r$ is to state $s$, $-q_{rs} / q_{rr}$.

See Also

pmatrix.msm, sojourn.msm, deltamethod, ematrix.msm