Package 'fitode' reference manual

Title:	Tools for Ordinary Differential Equations Model Fitting
Description:	Methods and functions for fitting ordinary differential equations (ODE) model in 'R'. Sensitivity equations are used to compute the gradients of ODE trajectories with respect to underlying parameters, which in turn allows for more stable fitting. Other fitting methods, such as MCMC (Markov chain Monte Carlo), are also available.
Authors:	Sang Woo Park [aut, cre] , Ben Bolker [aut]
Maintainer:	Sang Woo Park <[email protected]>
License:	GPL (>=2)
Version:	0.1.1.9000
Built:	2024-10-30 04:33:11 UTC
Source:	https://github.com/parksw3/fitode

Nicholson's blowfly data

Description

...

Usage

blowfly
blowfly

Format

A data frame containing 361 rows comprising:

eggs: number of eggs
nonemerging: ?
emerging: ?
deaths: ?
total: ?

Data from 1905 plague outbreak in Mumbai (formerly called Bombay)

Description

Plague death reports ...

Usage

bombay
bombay

Format

A data frame with 31 rows comprising:

week: week
mort: mortality

Extract model coefficients from fitode objects

Description

Extracts estimated parameters (either on response scales or link scales)

Usage

## S4 method for signature 'fitode'
coef(object, type = c("response", "links"))
## S4 method for signature 'fitode'
coef(object, type = c("response", "links"))

Arguments

`object`	fitode object
`type`	type of coefficients. The default (`type=response`) is on the response scale; this is the scale on which the model parameters are defined. Alternatively, `type=link` can be used to obtain parameters on the estimated scale.

Value

The estimated coefficients of the fitode object

Extract model coefficients from fitodeMCMC objects

Description

Extracts estimated parameters (median of the marginal posterior distributions)

Usage

## S4 method for signature 'fitodeMCMC'
coef(object)
## S4 method for signature 'fitodeMCMC'
coef(object)

Arguments

object

fitodeMCMC object

Value

The estimated median coefficients of the fitodeMCMC object

Calculate confidence intervals from fitode objects for model parameters and their transformations

Description

Calculate confidence intervals for model parameters and their transformations using (1) delta method, (2) profile likelihood, and (3) importance sampling.

Usage

## S4 method for signature 'fitode'
confint(
  object,
  parm,
  level = 0.95,
  method = c("delta", "profile", "impsamp", "wmvrnorm"),
  nsim = 1000,
  seed,
  ...
)
## S4 method for signature 'fitode'
confint(
  object,
  parm,
  level = 0.95,
  method = c("delta", "profile", "impsamp", "wmvrnorm"),
  nsim = 1000,
  seed,
  ...
)

Arguments

`object`	fitode object
`parm`	character vector specifying model parameters or list of formuals specifying transformations
`level`	the confidence level required
`method`	method for calculating confidence intervals
`nsim`	number of simulations to be used for importance sampling
`seed`	seed
`...`	extra arguments passed to profiling method

Value

The confidence intervals for model parameters and their transformations of the fitode object

Calculate credible intervals from fitodeMCMC objects for model parameters and their transformations

Description

Calculate credible intervals for model parameters and their transformations from posterior samples.

Usage

## S4 method for signature 'fitodeMCMC'
confint(object, parm, level = 0.95)
## S4 method for signature 'fitodeMCMC'
confint(object, parm, level = 0.95)

Arguments

`object`	fitodeMCMC object
`parm`	character vector specifying model parameters or list of formuals specifying transformations
`level`	the credible level required

Value

The credible intervals of the fitodeMCMC object

Fit ordinary differential equations model

Description

This function fits ordinary differential equations models to a uni- or multi-variate time series by maximum likelihood. It relies on sensitivity equations to compute gradients of the estimated trajectory with respect to model parameters. This allows one to use gradient-based optimization algorithms, which can provide more robust estimation.

Usage

fitode(
  model,
  data,
  start,
  tcol = "times",
  method = "BFGS",
  optimizer = "optim",
  link,
  fixed = list(),
  prior = list(),
  prior.density = TRUE,
  control = list(maxit = 1e+05),
  solver.opts = list(method = "rk4"),
  solver = ode,
  skip.hessian = FALSE,
  force.hessian = FALSE,
  use.ginv = TRUE,
  quietly = FALSE,
  trace = 0,
  ...
)
fitode(
  model,
  data,
  start,
  tcol = "times",
  method = "BFGS",
  optimizer = "optim",
  link,
  fixed = list(),
  prior = list(),
  prior.density = TRUE,
  control = list(maxit = 1e+05),
  solver.opts = list(method = "rk4"),
  solver = ode,
  skip.hessian = FALSE,
  force.hessian = FALSE,
  use.ginv = TRUE,
  quietly = FALSE,
  trace = 0,
  ...
)

Arguments

`model`	odemodel object
`data`	data frame with a time column and observation columns
`start`	named vector of starting parameter values
`tcol`	(character) time column
`method`	optimization method
`optimizer`	optimizer
`link`	named vector or list of link functions for model parameters
`fixed`	named vector or list of model parameters to fix and their values
`prior`	list of formulas specifying prior distributions
`prior.density`	(logical) should priors represent probability distributions?
`control`	see `optim`
`solver.opts`	options for ode integration. See `ode`
`solver`	ode solver
`skip.hessian`	skip hessian calculation
`force.hessian`	(logical) calculate the hessian numerically instead of taking the jacobian of the gradients based on sensitivity equations
`use.ginv`	(logical) use generalized inverse (`ginv`) to compute approximate vcov
`quietly`	suppress progress messages?
`trace`	print tracing info? (larger values = more verbose)
`...`	mle2 arguments

Value

An object of class “fitode” as described in fitode-class.

Class "fitode". Result of ode fitting based on Maximum Likelihood Estimation

Description

Class "fitode". Result of ode fitting based on Maximum Likelihood Estimation

Slots

call: (languge) The call to fitode
model: odemodel object
data: the time series data
coef: estimated parameters
vcov: estimated variance-covariance matrix
min: minimum negative log-likelihood
mle2: mle2 object
link: list of link functions for model parameters
fixed: list of fixed parameters
prior: list of priors

Methods

coef: signature(object = "fitode"): Extract coefficients.
confint: signature(object = "fitode"): Caculate confidence intervals from the delta method, profile likelihood, or importance sampling.
logLik: signature(object = "fitode"): Extract log-likelihood.
plot: signature(object = "fitode"): Plot estimated trajectories and the associated confidence intervals.
predict: signature(object = "fitode"): Predict estimated trajectories and the associated confidence intervals from the delta method or importance sampling.
profile: signature(object = "fitode"): Calculate likelihood profile.
show: signature(object = "fitode"): Display object briefly.
stdEr: signature(object = "fitode"): Calculate standard errors.
summary: signature(object = "fitode"): Generate object summary.
vcov: signature(object = "fitode"): Extract variance-covariance matrix.

Fit ordinary differential equations model using MCMC

Description

This function fits ordinary differential equations models to a uni- or multi-variate time series by MCMC using the Metropolis-Hastings update rule. It searches through the parameter space on link scales, which can provide more efficient posterior sampling.

Usage

fitodeMCMC(
  model,
  data,
  start,
  tcol = "times",
  proposal.vcov,
  prior = list(),
  chains = 1,
  iter = 2000,
  burnin = iter/2,
  thin = 1,
  refresh = max(iter/10, 1),
  prior.only = FALSE,
  link,
  fixed = list(),
  solver.opts = list(method = "rk4"),
  solver = ode,
  ...
)
fitodeMCMC(
  model,
  data,
  start,
  tcol = "times",
  proposal.vcov,
  prior = list(),
  chains = 1,
  iter = 2000,
  burnin = iter/2,
  thin = 1,
  refresh = max(iter/10, 1),
  prior.only = FALSE,
  link,
  fixed = list(),
  solver.opts = list(method = "rk4"),
  solver = ode,
  ...
)

Arguments

`model`	ode model
`data`	data frame with time column and observation column
`start`	named vector of starting parameter values
`tcol`	time column
`proposal.vcov`	variance-covariance matrix of a multivariate normal proposal distribution
`prior`	list of formulas specifying prior distributions
`chains`	(numeric) number of chains
`iter`	(numeric) number of iterations per chain
`burnin`	(numeric) number of burnin interations
`thin`	(numeric) thining interval between consecutive observations
`refresh`	(numeric) refresh interval
`prior.only`	(logical) sample from prior distribution only?
`link`	named vector or list of link functions for model parameters
`fixed`	named vector or list of model parameters to fix and their values
`solver.opts`	options for ode integration. See `ode`
`solver`	ode solver
`...`	additional arguments (unused)

Value

An object of class “fitodeMCMC” as described in fitodeMCMC-class.

Class "fitodeMCMC". Result of ode fitting based on Markov Chain Monte Carlo (MCMC)

Description

Class "fitodeMCMC". Result of ode fitting based on Markov Chain Monte Carlo (MCMC)

Slots

call: (languge) The call to fitodeMCMC
model: odemodel object
data: the time series data
coef: estimated parameters (posterior median)
vcov: estimated variance-covariance matrix
mcmc: mcmc.list object containing posterior samples
lp: mcmc.list object containing log-posterior values of posterior samples
link: list of link functions for model parameters
fixed: list of fixed parameters
prior: list of priors
details: a list containing miscellaneous objects for internal uses

Methods

coef: signature(object = "fitodeMCMC"): Extract median of the posterior.
confint: signature(object = "fitodeMCMC"): Caculate credible intervals from the posterior.
plot: signature(object = "fitodeMCMC"): Plot estimated trajectories and the associated confidence intervals.
predict: signature(object = "fitodeMCMC"): Predict estimated trajectories and the associated confidence intervals from the posterior.
show: signature(object = "fitodeMCMC"): Display object briefly.
stdEr: signature(object = "fitodeMCMC"): Calculate standard errors of the posterior.
summary: signature(object = "fitodeMCMC"): Generate object summary.
vcov: signature(object = "fitodeMCMC"): Extract variance-covariance matrix of the posterior.

Constructor method of "odemodel" class

Description

Constructor method of "odemodel" class

Usage

## S4 method for signature 'odemodel'
initialize(
  .Object,
  name,
  model,
  observation,
  initial,
  par,
  link,
  diffnames,
  keep_sensitivity = TRUE,
  call
)
## S4 method for signature 'odemodel'
initialize(
  .Object,
  name,
  model,
  observation,
  initial,
  par,
  link,
  diffnames,
  keep_sensitivity = TRUE,
  call
)

Arguments

`.Object`	object
`name`	name of the model
`model`	ode model
`observation`	observation model
`initial`	initial values
`par`	model parameters
`link`	link functions for parameters (log links are used as default)
`diffnames`	optional character vector specifying the names of a variable for which the consecutive difference needs to be calculated
`keep_sensitivity`	(logical) maintain the Jacobian as a part of the model object?
`call`	original function call

Value

An object of class “odemodel” as described in odemodel-class.

Examples

SI_model <- odemodel(
    name = "SI",
    model = list(
        S ~ - beta*S*I/N,
        I ~ beta*S*I/N - gamma*I
    ),
    observation = list(
        susceptible ~ dnorm(mean=S, sd=sigma1),
        infected ~ dnorm(mean=I, sd=sigma2)
    ),
    initial = list(
        S ~ N * (1 - i0),
        I ~ N * i0
    ),
    par = c("beta", "gamma", "N", "i0", "sigma1", "sigma2"),
    link = c(i0="logit")
)
SI_model <- odemodel(
    name = "SI",
    model = list(
        S ~ - beta*S*I/N,
        I ~ beta*S*I/N - gamma*I
    ),
    observation = list(
        susceptible ~ dnorm(mean=S, sd=sigma1),
        infected ~ dnorm(mean=I, sd=sigma2)
    ),
    initial = list(
        S ~ N * (1 - i0),
        I ~ N * i0
    ),
    par = c("beta", "gamma", "N", "i0", "sigma1", "sigma2"),
    link = c(i0="logit")
)

Extract log-likelihood

Description

Extract log-likelihood of a fit

Usage

## S4 method for signature 'fitode'
logLik(object)
## S4 method for signature 'fitode'
logLik(object)

Arguments

object

fitode object

Value

The log-likelihood of the fitode object

Class representing log-likelihood models used to fit ode models

Description

Class representing log-likelihood models used to fit ode models

Slots

name: name of the distribution
expr: an expression specifying the model
observation: observation variable name
mean: mean variable name
par: additional parameter names
grad: the gradient with respect to the parameters

1918 Philadelphia flu data set

Description

1918 Philadelphia flu data set

Usage

phila1918
phila1918

Format

A data frame with 122 rows comprising:

date: date
mort: mortality

Internal function for plotting methods

Description

Internal function for plotting methods

Usage

plot_internal(
  pred,
  data,
  onepage = TRUE,
  xlim,
  ylim,
  xlabs,
  ylabs,
  col.traj = "black",
  lty.traj = 1,
  col.conf = "black",
  lty.conf = 4,
  add = FALSE,
  ...
)
plot_internal(
  pred,
  data,
  onepage = TRUE,
  xlim,
  ylim,
  xlabs,
  ylabs,
  col.traj = "black",
  lty.traj = 1,
  col.conf = "black",
  lty.conf = 4,
  add = FALSE,
  ...
)

Arguments

`pred`	prediction objects
`data`	observed data
`onepage`	(logical) print all figures on one page?
`xlim`	x coordinates range
`ylim`	y coordinates range
`xlabs`	a label for the x axis
`ylabs`	a label for the y axis
`col.traj`	colour of the estimated trajectory
`lty.traj`	line type of the estimated trajectory
`col.conf`	colour of the confidence intervals
`lty.conf`	line type of the confidence intervals
`add`	add to another plot?
`...`	additional arguments to be passed on to the plot function

Plot a fitode object

Description

Plot a fitode object

Usage

## S4 method for signature 'fitode,missing'
plot(
  x,
  level,
  data,
  which,
  method = c("delta", "impsamp", "wmvrnorm"),
  onepage = TRUE,
  xlim,
  ylim,
  xlabs,
  ylabs,
  col.traj = "black",
  lty.traj = 1,
  col.conf = "black",
  lty.conf = 4,
  add = FALSE,
  nsim = 1000,
  ...
)
## S4 method for signature 'fitode,missing'
plot(
  x,
  level,
  data,
  which,
  method = c("delta", "impsamp", "wmvrnorm"),
  onepage = TRUE,
  xlim,
  ylim,
  xlabs,
  ylabs,
  col.traj = "black",
  lty.traj = 1,
  col.conf = "black",
  lty.conf = 4,
  add = FALSE,
  nsim = 1000,
  ...
)

Arguments

`x`	fitode object
`level`	the confidence level required
`data`	(FIXME)
`which`	which to plot
`method`	confidence interval method
`onepage`	(logical) print all figures on one page?
`xlim`	x coordinates range
`ylim`	y coordinates range
`xlabs`	a label for the x axis
`ylabs`	a label for the y axis
`col.traj`	colour of the estimated trajectory
`lty.traj`	line type of the estimated trajectory
`col.conf`	colour of the confidence intervals
`lty.conf`	line type of the confidence intervals
`add`	add to another plot?
`nsim`	number of simulations for mvrnorm, wmvrnorm methods
`...`	additional arguments to be passed on to the plot function

Value

No return value, called for side effects

Examples

load(system.file("doc_examples", "SIR_mort.rda", package = "fitode"))
plot(SIR_mort_fit)
load(system.file("doc_examples", "SIR_mort.rda", package = "fitode"))
plot(SIR_mort_fit)

Plot a fitodeMCMC object

Description

Plot a fitodeMCMC object

Usage

## S4 method for signature 'fitodeMCMC,missing'
plot(
  x,
  level,
  data,
  which,
  onepage = TRUE,
  xlim,
  ylim,
  xlabs,
  ylabs,
  col.traj = "black",
  lty.traj = 1,
  col.conf = "black",
  lty.conf = 4,
  add = FALSE,
  ...
)
## S4 method for signature 'fitodeMCMC,missing'
plot(
  x,
  level,
  data,
  which,
  onepage = TRUE,
  xlim,
  ylim,
  xlabs,
  ylabs,
  col.traj = "black",
  lty.traj = 1,
  col.conf = "black",
  lty.conf = 4,
  add = FALSE,
  ...
)

Arguments

`x`	fitodeMCMC object
`level`	the confidence level required
`data`	(FIXME)
`which`	which to plot
`onepage`	(logical) print all figures on one page?
`xlim`	x coordinates range
`ylim`	y coordinates range
`xlabs`	a label for the x axis
`ylabs`	a label for the y axis
`col.traj`	colour of the estimated trajectory
`lty.traj`	line type of the estimated trajectory
`col.conf`	colour of the confidence intervals
`lty.conf`	line type of the confidence intervals
`add`	add to another plot?
`...`	additional arguments to be passed on to the plot function

Value

No return value, called for side effects

Prediction function for fitode objects

Description

Computes estimated trajectories and their confidence intervals (using either the delta method or importance sampling).

Usage

## S4 method for signature 'fitode'
predict(
  object,
  level,
  times,
  method = c("delta", "impsamp", "wmvrnorm"),
  nsim = 1000
)
## S4 method for signature 'fitode'
predict(
  object,
  level,
  times,
  method = c("delta", "impsamp", "wmvrnorm"),
  nsim = 1000
)

Arguments

`object`	fitode object
`level`	the confidence level required
`times`	time vector to predict over. Default is set to the time frame of the data.
`method`	confidence interval method. Default is set to Delta method.
`nsim`	number of simulations for mvrnorm, wmvrnorm methods

Value

The estimated trajectories and their confidence intervals of the fitode object

Prediction function for fitodeMCMC objects

Description

Computes estimated trajectories and their credible intervals. The estimated trajectories are obtained by taking the median trajectories from the posterior samples.

Usage

## S4 method for signature 'fitodeMCMC'
predict(object, level, times, simplify = TRUE)
## S4 method for signature 'fitodeMCMC'
predict(object, level, times, simplify = TRUE)

Arguments

`object`	fitodeMCMC object
`level`	the credible level required
`times`	time vector to predict over. Default is set to the time frame of the data.
`simplify`	(logical) simplify output to return estimated trajectories and their credible intervals? If `simplify=FALSE`, all posterior trajectories will be returned

Value

Estimated trajectories and their credible intervals of the fitodeMCMC object

Class representing prior models used to fit ode models

Description

Class representing prior models used to fit ode models

Slots

name: name of the distribution
expr: an expression specifying the model
observation: observation variable name
par: additional parameter names
keep_grad: keep gradient?
grad: the gradient with respect to the parameters

Profile fitode objects

Description

Profile fitode objects

Usage

## S4 method for signature 'fitode'
profile(fitted, which = 1:p, alpha = 0.05, trace = FALSE, ...)
## S4 method for signature 'fitode'
profile(fitted, which = 1:p, alpha = 0.05, trace = FALSE, ...)

Arguments

`fitted`	fitted model object
`which`	which parameter(s) to profile? (integer value)
`alpha`	critical level
`trace`	trace progress of computations?
`...`	additional arguments passed to mle2 profiling method

Value

The log-likelihood profile of the fitode object

Data from 2014 Sierra Leone Ebola epidemic

Description

Ebola case reports ...

Usage

SierraLeone2014
SierraLeone2014

Format

A data frame with 67 rows comprising:

times: decimal dates (year + fraction of year)
confirmed: confirmed cases

Internal function for simulation models

Description

Simulates deterministic trajectories and propagates observation error

Usage

simulate_internal(
  model,
  times,
  parms,
  y,
  solver.opts = list(method = "rk4"),
  solver = ode,
  observation = TRUE,
  nsim = 1,
  seed = NULL
)
simulate_internal(
  model,
  times,
  parms,
  y,
  solver.opts = list(method = "rk4"),
  solver = ode,
  observation = TRUE,
  nsim = 1,
  seed = NULL
)

Arguments

`model`	odemodel object
`times`	time vector
`parms`	named vector of parameter values
`y`	initial values
`solver.opts`	options for ode solver
`solver`	ode solver (must take y, times, func, and parms arguments)
`observation`	(logical) propagate observation error?
`nsim`	number of simulations
`seed`	seed

simulate fitode objects

Description

simulate fitode objects

Usage

## S4 method for signature 'fitode'
simulate(object, nsim = 1, seed = NULL, times, parms, y, observation = TRUE)
## S4 method for signature 'fitode'
simulate(object, nsim = 1, seed = NULL, times, parms, y, observation = TRUE)

Arguments

`object`	fitode object
`nsim`	number of simulations
`seed`	random-number seed
`times`	time vector
`parms`	named vector of parameter values
`y`	initial values
`observation`	(logical) propagate observation error?

Value

The numerical simulation of the object

simulate model objects

Description

simulate model objects

Usage

## S4 method for signature 'odemodel'
simulate(
  object,
  nsim = 1,
  seed = NULL,
  times,
  parms,
  y,
  solver.opts = list(method = "rk4"),
  solver = ode,
  observation = TRUE
)
## S4 method for signature 'odemodel'
simulate(
  object,
  nsim = 1,
  seed = NULL,
  times,
  parms,
  y,
  solver.opts = list(method = "rk4"),
  solver = ode,
  observation = TRUE
)

Arguments

`object`	odemodel object
`nsim`	number of simulations
`seed`	random-number seed
`times`	time vector
`parms`	named vector of parameter values
`y`	initial values
`solver.opts`	options for ode solver
`solver`	ode solver (must take y, times, func, and parms arguments)
`observation`	(logical) propagate observation error?

Value

The numerical simulation of the object

Extract standard error from fitode objects

Description

Calculates standard error by taking the square root of the diagonal matrix

Usage

## S4 method for signature 'fitode'
stdEr(x, type = c("response", "links"))
## S4 method for signature 'fitode'
stdEr(x, type = c("response", "links"))

Arguments

`x`	fitode object
`type`	type of standard error. The default (`type=response`) is on the response scale; this is the scale on which the model parameters are defined. Alternatively, `type=link` can be used to obtain standard errors on the estimated scale.

Value

The standard error of the fitode object

Extract standard error from fitodeMCMC objects

Description

Calculates standard error by taking the square root of the diagonal of the variance-covariance matrix

Usage

## S4 method for signature 'fitodeMCMC'
stdEr(x)
## S4 method for signature 'fitodeMCMC'
stdEr(x)

Arguments

`x`	fitodeMCMC object

Value

The standard error of the fitodeMCMC object

Summarize fitode object

Description

Summarize fitode objects; returns estimate, standard error, and confidence intervals

Usage

## S4 method for signature 'fitode'
summary(object)
## S4 method for signature 'fitode'
summary(object)

Arguments

object

fitode object

Value

The summary of the fitode object

Summarize fitodeMCMC object

Description

Summarize fitodeMCMC object; returns estimate, standard error, credible intervals, effective sample sizes, and gelman-rubin diagnostic

Usage

## S4 method for signature 'fitodeMCMC'
summary(object)
## S4 method for signature 'fitodeMCMC'
summary(object)

Arguments

object

fitodeMCMC object

Value

The summary of the fitodeMCMC object

Tumor growth data

Description

...

Usage

tumorgrowth
tumorgrowth

Format

A data frame containing 14 rows comprising:

day
volume

Update fitode fits

Description

Update fitode fits

Usage

## S4 method for signature 'fitode'
update(object, observation, initial, par, link, ...)
## S4 method for signature 'fitode'
update(object, observation, initial, par, link, ...)

Arguments

`object`	fitode objects
`observation`	observation model
`initial`	initial values
`par`	model parameters
`link`	link functions for parameters (log links are used as default)
`...`	additional arguments to be passed to fitode

Value

An object of class “fitode” as described in fitode-class.

Update fitodeMCMC fits

Description

Update fitodeMCMC fits

Usage

## S4 method for signature 'fitodeMCMC'
update(object, observation, initial, par, link, ...)
## S4 method for signature 'fitodeMCMC'
update(object, observation, initial, par, link, ...)

Arguments

`object`	fitodeMCMC objects
`observation`	observation model
`initial`	initial values
`par`	model parameters
`link`	link functions for parameters (log links are used as default)
`...`	additional arguments to be passed to fitode

Value

An object of class “fitode” as described in fitodeMCMC-class.

Extract variance-covariance matrix from fitode objects

Description

Extracts variance-covariance matrix (either on response scales or link scales)

Usage

## S4 method for signature 'fitode'
vcov(object, type = c("response", "links"))
## S4 method for signature 'fitode'
vcov(object, type = c("response", "links"))

Arguments

`object`	fitode object
`type`	type of covariance matrix. The default (`type=response`) is on the response scale; this is the scale on which the model parameters are defined. Alternatively, `type=link` can be used to obtain the covariance matrix on the estimated scale.

Value

The variance-covariance matrix of the fitode object

Extract variance-covariance matrix from fitodeMCMC objects

Description

Calculates variance-covariance matrix from posterior samples

Usage

## S4 method for signature 'fitodeMCMC'
vcov(object)
## S4 method for signature 'fitodeMCMC'
vcov(object)

Arguments

object

fitodeMCMC object

Value

The variance-covariance matrix of the fitodeMCMC object

Package 'fitode'

Help Index

Nicholson's blowfly data

Description

Usage

Format

Data from 1905 plague outbreak in Mumbai (formerly called Bombay)

Description

Usage

Format

Extract model coefficients from fitode objects

Description

Usage

Arguments

Value

Extract model coefficients from fitodeMCMC objects

Description

Usage

Arguments

Value

Calculate confidence intervals from fitode objects for model parameters and their transformations

Description

Usage

Arguments

Value

Calculate credible intervals from fitodeMCMC objects for model parameters and their transformations

Description

Usage

Arguments

Value

Fit ordinary differential equations model

Description

Usage

Arguments

Value

See Also

Class "fitode". Result of ode fitting based on Maximum Likelihood Estimation

Description

Slots

Methods

See Also

Fit ordinary differential equations model using MCMC

Description

Usage

Arguments

Value

See Also

Class "fitodeMCMC". Result of ode fitting based on Markov Chain Monte Carlo (MCMC)

Description

Slots

Methods

Constructor method of "odemodel" class

Description

Usage

Arguments

Value

Examples

Extract log-likelihood

Description

Usage

Arguments

Value

Class representing log-likelihood models used to fit ode models

Description

Slots

1918 Philadelphia flu data set

Description

Usage

Format

Internal function for plotting methods

Description

Usage

Arguments

Plot a fitode object

Description

Usage

Arguments

Value

Examples

Plot a fitodeMCMC object