vcov: Parameter standard errors
In depmixS4: Dependent Mixture Models - Hidden Markov Models of GLMs and Other Distributions in S4

Description Usage Arguments Details Value Note Author(s) References Examples

These functions provide standard errors for parameters of (dep-)mix models.

	## S4 method for signature 'mix'
vcov(object, fixed=NULL, equal=NULL, 
		conrows=NULL, conrows.upper=NULL, conrows.lower=NULL, tolerance=1e-6, 
		method="finiteDifferences", ...)	
	
	## S4 method for signature 'mix'
standardError(object, fixed=NULL, equal=NULL, 
		conrows=NULL, conrows.upper=NULL, conrows.lower=NULL, tolerance=1e-6, 
		method="finiteDifferences", ...)	
	
	## S4 method for signature 'mix'
confint(object, level=0.95, fixed=NULL, equal=NULL, 
		conrows=NULL, conrows.upper=NULL, conrows.lower=NULL, tolerance=1e-6, 
		method="finiteDifferences", ...)	

	## S4 method for signature 'mix'
hessian(object, tolerance=1e-6, 	
			method="finiteDifferences", ...)

`object`	A (dep-)mix object; see depmix for details.
`fixed, equal`	These arguments are used to specify constraints on a model; see usage details here: `fit`.
`conrows`	These arguments are used to specify constraints on a model; see usage details here: `fit`.
`conrows.upper`	These arguments are used to specify constraints on a model; see usage details here: `fit`.
`conrows.lower`	These arguments are used to specify constraints on a model; see usage details here: `fit`.
`tolerance`	Threshold used for testing whether parameters are estimated on the boundary of the parameter space; if so, they are ignored in these functions.
`method`	The method used for computing the Hessian matrix of the parameters; currently only a finite differences method (using `fdHess` from package `nlme`) is implemented and hence used by default.
`level`	The desired significance level for the confidence intervals.
`...`	Further arguments passed to other methods; currently not in use.

vcov computes the variance-covariance matrix of a (dep-)mix object, either fitted or not. It does so by first constructing a Hessian matrix through the use of hessian and then transforming this as described in Visser et al (2000), taking into account the linear constraints that are part of the model. Currently, hessian has a single method using finite differences to arrive at an approximation of the second order derivative matrix of the parameters.

confint and standardError use vcov to compute confidence intervals (the confidence level can be set through an argument) and standard errors respectively. The latter are computed first by using sqrt(diag(vcov)) and the confidence intervals are computed through the normal approximation.

If and when these methods are applied to fit'ted models, the linear constraint matrix is obtained from the mix.fitted or depmix.fitted slot lincon (supplemented with additional constraints if those are provided through the equal and other arguments to these functions).

All four functions exclude parameters that are estimated on or near (this can be controlled using the tolerance argument) their boundary values. Setting this argument to zero can result in error as the fdHess function requires an environment around the parameter estimate that provides proper log-likelihood values, which parameter on or over their boundary values are not guaranteed to provided. Fixed parameters are similarly ignored in these four functions.

vcov returns a named list with elements vcov, elements, and lincon. standardError returns a data.frame with columns par, elements, and se. confint returns a data.frame with columns par, elements, and two columns for the lower and upper bounds of the confidence intervals (with the column names indicating the level of the interval.)

`vcov`	: The variance-covariance matrix of the parameters.
`elements`	: Vector of length `npar(object)` indicating which elements of the parameter vector are included in computing the hessian, the variance-covariance matrix, the standard errors and/or the confidence intervals.
`inc`	: 'inc'luded parameter.
`fix`	: 'fix'ed parameter.
`bnd`	: parameter estimated on the boundary.
`par`	: The values of the parameters.
`se`	: The values of the standard errors of the parameters.
`lower/upper`	: The lower and upper bounds of the confidence intervals; column names indicate the as in 0.5+/-level/2, using the `level` argument.

Note that the quality of the resulting standard errors is similar to those reported in Visser et al (2000) for both bootstrap and the profile likelihood methods. In Visser et al (2000), the finite differences standard errors were somewhat less precise as they relied on a very parsimonious but indeed less precise method for computing the finite differences approximation (computation time was a much scarcer resource at the time then it is now).

Ingmar Visser

Ingmar Visser, Maartje E. J. Raijmakers, and Peter C. M. Molenaar (2000). Confidence intervals for hidden Markov model parameters. British journal of mathematical and statistical psychology, 53, p. 317-327.

	data(speed)

	# 2-state model on rt and corr from speed data set 
	# with Pacc as covariate on the transition matrix
	# ntimes is used to specify the lengths of 3 separate series
	mod1 <- depmix(list(rt~1,corr~1),data=speed,transition=~Pacc,nstates=2,
		family=list(gaussian(),multinomial("identity")),ntimes=c(168,134,137))
	
	# fit the model
	set.seed(3)
	fmod1 <- fit(mod1)
	
	vcov(fmod1)$vcov # $
	standardError(fmod1)
	confint(fmod1)