Type: Package
Title: Tools for Ordinary Differential Equations Model Fitting
Version: 0.1.1
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.
License: GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
Depends: R (≥ 4.0), bbmle
Imports: deSolve, Deriv, MASS, numDeriv, mvtnorm, coda, methods
Suggests: knitr, ggplot2, testthat (≥ 3.0.0)
VignetteBuilder: knitr
Encoding: UTF-8
LazyData: true
RoxygenNote: 7.1.2
Config/testthat/edition: 3
NeedsCompilation: no
Packaged: 2022-10-26 16:53:41 UTC; swp2
Author: Sang Woo Park ORCID iD [aut, cre], Ben Bolker ORCID iD [aut]
Maintainer: Sang Woo Park <swp2@princeton.edu>
Repository: CRAN
Date/Publication: 2022-10-29 08:50:05 UTC

S4 generic for evaluating an object

Description

S4 generic for evaluating an object

Usage

Eval(object, ...)

Arguments

object

an R object

...

further arguments passed to methods

Value

The result of evaluating the object.

Evaluate the log-likelihood model

Description

Evaluate the log-likelihood model

Usage

## S4 method for signature 'loglik.ode'
Eval(object, observation, mean, par = NULL, ...)

Arguments

object

loglik.ode object

observation

observations

mean

mean values

par

additional parameters

...

other values if required

Value

numeric

Data from 2014 Sierra Leone Ebola epidemic

Description

Ebola case reports ...

Usage

SierraLeone2014

Format

A data frame with 67 rows comprising:

times

decimal dates (year + fraction of year)

confirmed

confirmed cases

S4 generic for transforming an object

Description

S4 generic for transforming an object

Usage

Transform(object, ...)

Arguments

object

an R object

...

further arguments passed to methods

Value

The result of transforming the object.

Transform the model

Description

Transform the model

Usage

## S4 method for signature 'loglik.ode'
Transform(
  object,
  transforms = NULL,
  name,
  observation = "X",
  mean,
  par,
  keep_grad = TRUE
)

Arguments

object

loglik.ode object

transforms

list of formulas specifying transformations

name

name of the log-likelihood model

observation

observation variable name

mean

mean variable name

par

additional parameter names

keep_grad

maintain the gradient as part of the model

Value

loglik.ode object

Transform the model

Description

Transform the model

Usage

## S4 method for signature 'odemodel'
Transform(
  object,
  transforms,
  observation,
  initial,
  par,
  link,
  keep_sensitivity
)

Arguments

object

odemodel object

transforms

list of formulas specifying transformations

observation

observation model

initial

initial values

par

model parameters

keep_sensitivity

(logical) maintain the Jacobian as part of the model

Value

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

Transform the prior model

Description

Transform the prior model

Usage

## S4 method for signature 'prior.ode'
Transform(
  object,
  transforms = NULL,
  name,
  observation = "X",
  par,
  keep_grad = TRUE
)

Arguments

object

object

transforms

list of formulas specifying transformations

name

name of the log-likelihood model

observation

observation variable name

par

additional parameter names

keep_grad

maintain the gradient as part of the model

Value

An object of class “prior.ode” as described in prior.ode-class.

Description

Apply link functions to model parameters – for fitode internal usage. type=linkfun applies link functions; type=linkinv applies inverse link functions; type=mu.eta returns derivative of inverse link functions

Usage

apply_link(par, linklist, type = c("linkfun", "linkinv", "mu.eta"))

Arguments

par

named vector of parameter values

linklist

list containing linkfun, linkinv, and mu.eta for each link

type

string specifying which function should be applied

Value

vector of parameter values with link transformations

See Also

make.link

Nicholson's blowfly data

Description

...

Usage

blowfly

Format

A data frame containing 361 rows comprising:

eggs

number of eggs

nonemerging

?

emerging

?

deaths

?

total

?

Description

Check link functions for model parameters – for fitode internal usage

Usage

check_link(model, link)

Arguments

model

odemodel object

link

named vector specifying link functions

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"))

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)

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,
  ...
)

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)

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

Taylor expansion of digamma(a+b) for a>>b

Description

Taylor expansion of digamma(a+b) for a>>b

Usage

dfun(x, y, mag = 1e+08)

Arguments

x

first argument

y

second argument

mag

cutoff magnitude for switching approximations

Value

numeric

Taylor expansion of trigamma(a+b) (?) for a>>b

Description

Taylor expansion of trigamma(a+b) (?) for a>>b

Usage

dfun2(x, y, mag = 1e+08, focal = "x")

Arguments

x

first argument

y

second argument

mag

cutoff magnitude for switching approximations

Value

numeric

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,
  ...
)

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?

...

mle2 arguments

Value

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

See Also

mle2

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

See Also

mle2-class

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,
  ...
)

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

Fix parameters of an ODE model

Description

Fix parameters of an ODE model to a constant value by transforming the model (using Transform() function)

Usage

fixpar(model, fixed)

Arguments

model

odemodel object

fixed

named vector or list of model parameters to fix

S4 generic for computing a gradient

Description

S4 generic for computing a gradient

Usage

grad(object, ...)

Arguments

object

an R object

...

further arguments passed to methods

Value

The gradient of the object.

Evaluate the gradient of a likelihood model

Description

Evaluate the gradient of a likelihood model

Usage

## S4 method for signature 'loglik.ode'
grad(object, observation, mean, par, ...)

Arguments

object

loglik.ode object

observation

observations

mean

mean values

par

additional parameters

...

other values if required

Value

a list with each element as a partial derivative values

Evaluate the gradients of a model

Description

Evaluate the gradients of a model

Usage

## S4 method for signature 'odemodel'
grad(object, state, par)

Arguments

object

odemodel object

state

state

par

parameter values

S4 generic for computing a hessian

Description

S4 generic for computing a hessian

Usage

hessian(object, ...)

Arguments

object

an R object

...

further arguments passed to methods

Value

The hessian of the object.

The initializer for loglik.ode

Description

The initializer for loglik.ode

Usage

## S4 method for signature 'loglik.ode'
initialize(
  .Object,
  name,
  model,
  observation = "X",
  mean,
  par = NULL,
  keep_grad = TRUE
)

Arguments

.Object

object

name

name of the distribution

model

formula specifying the disstribution

observation

observation variable name

mean

mean variable name

par

additional parameter names

keep_grad

maintain the gradient as part of the model

Value

An object of class “loglik.ode” as described in loglik.ode-class.

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
)

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")
)

the initializer for prior.ode

Description

the initializer for prior.ode

Usage

## S4 method for signature 'prior.ode'
initialize(
  .Object,
  name,
  model,
  observation = "X",
  par = NULL,
  keep_grad = TRUE
)

Arguments

.Object

object

name

name of the distribution

model

the formula specifying the model

observation

observation variable name

par

additional parameter names

keep_grad

maintain the gradient as part of the model

Value

An object of class “prior.ode” as described in prior.ode-class.

Constructor for solution.ode class

Description

Constructor for solution.ode class

Usage

## S4 method for signature 'solution.ode'
initialize(
  .Object,
  y,
  times,
  model,
  parms,
  solver.opts = list(method = "rk4"),
  solver = ode
)

Arguments

.Object

object

y

initial values

times

time vector

model

ode model

parms

parameters of the solution

solver.opts

options for ode solver

solver

ode solver (must take y, times, func, and parms as arguments)

Value

An object of class “solution.ode” as described in solution.ode-class.

S4 generic for computing a jacobian

Description

S4 generic for computing a jacobian

Usage

jacobian(object, ...)

Arguments

object

an R object

...

further arguments passed to methods

Value

The jacobian of the object.

Evaluate the jacobian of the gradients

Description

Evaluate the jacobian of the gradients

Usage

## S4 method for signature 'odemodel'
jacobian(object, state, par, type = c("initial", "state", "par"))

Arguments

object

odemodel object

state

state

par

parameter values

type

state of par?

Extract log-likelihood

Description

Extract log-likelihood of a fit

Usage

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

Arguments

object

fitode object

Value

The log-likelihood of the fitode object

Calculate the derivative of the log-likelihood function

Description

Calculate the derivative of the log-likelihood function with respect to model parameters using sensitivity equations and chain rule

Usage

logLik.sensitivity(
  parms,
  model,
  data,
  solver.opts = list(method = "rk4"),
  solver = ode,
  return.NLL = TRUE,
  return.traj = FALSE
)

Arguments

parms

named vector of parameter values

model

odemodel object

data

data

solver.opts

options for the ode solver (see ode)

solver

ode solver

return.NLL

(logical) return negative log-likelihood

return.traj

(logical) return estimated trajectory

Value

a vector of nll and derivative of nll with respect to model parameters (or a list containing (1) the estimated traejctory and (2) a vector of nll and its derivatives)

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

Make a list containing log prior density and its gradient

Description

Make a list containing log prior density and its gradient

Usage

make_prior(model, link, prior, prior.density = TRUE, keep_grad = TRUE)

Arguments

model

model.ode object

link

link

prior

list of formulas

prior.density

(logical) does this represent a probability density?

keep_grad

(logical) keep gradient?

Calculate the derivative of the mean expression

Description

Calculate the derivative of an expression with respect to model parameters using sensitivity equations and chain rule

Usage

ode.sensitivity(
  model,
  parms,
  times,
  solver.opts = list(method = "rk4"),
  solver = ode
)

Arguments

model

odemodel object

parms

named vector of parameter values

times

time window for which the model should be solved

solver.opts

options for the ode solver (see ode)

solver

ode solver

solve ode models

Description

solve ode models

Usage

ode.solve(
  model,
  times,
  parms,
  y,
  solver.opts = list(method = "rk4"),
  solver = ode
)

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 as arguments)

Value

An object of class “solution.ode” as described in solution.ode-class.

Class "odemodel" representing ode models

Description

Class "odemodel" representing ode models

Create a new odemodel

Usage

odemodel(...)

Slots

name

name of the model

gfun

gradient function

grad

list of gradients

observation

list of observation models

initial

list of expressions representing the initial values

state

state variables

par

parameters

link

link functions for parameters (log links are used as default)

diffnames

character vector specifying the names of a variable for which the consecutive difference needs to be calculated

call

original function call

jacobian.initial

Jacobian of initial values with respect to its parameters

jacobian.state

Jacobian with respect to its states

jacobian.par

Jacobian with repsect to its parameters

loglik

list of log-likelihood functions

expr

expressions for true trajectories

expr.sensitivity

sensitivity of the expressions with respect to state variables and parameters

keep_sensitivity

(logical) keep sensitivity equations?

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,
  ...
)

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

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,
  ...
)

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

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,
  ...
)

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

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
)

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)

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, ...)

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

Select a log-likelihood model

Description

Select a log-likelihood model

Usage

select_model(
  dist = c("ols", "dnorm", "dnorm2", "dpois", "dnbinom", "dnbinom1", "dgamma",
    "dlnorm")
)

Arguments

dist

conditional distribution of reported data (dnorm, dnorm2, dpois, dnbinom, dnbinom1, dgamma)

Select a prior model

Description

Select a prior model

Usage

select_prior(
  family = c("dnorm", "dgamma", "dbeta", "dlnorm"),
  link = c("identity", "log", "logit"),
  prior.density = TRUE,
  keep_grad = TRUE
)

Arguments

family

prior distribution type

link

link

prior.density

(logical) keep the Jacobian of transformations?

keep_grad

(logical) keep gradients?

Description

Set up link functions for model parameters – for fitode internal usage; assumes log-link by default if link functions are not specified

Usage

set_link(link, par)

Arguments

link

named list or vector of strings specifying link functions

par

(character) model parameters

Value

list of strings specifying link functions for each model parameter

See Also

make.link

Show fitode objects

Description

Show fitode objects

Usage

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

Arguments

object

fitode object

Value

No return value, called for side effects

Show fitodeMCMC object

Description

Show fitodeMCMC object

Usage

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

Arguments

object

fitodeMCMC object

Value

No return value, called for side effects

Show the model

Description

Show the model

Usage

## S4 method for signature 'odemodel'
show(object)

Arguments

object

odemodel object

Value

No return value, called for side effects

simulate fitode objects

Description

simulate fitode objects

Usage

## 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
)

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

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
)

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

Class "solution.ode". Result of solving ode modeld with/without sensitivity equations

Description

Class "solution.ode". Result of solving ode modeld with/without sensitivity equations

Slots

name

name of the model

y

initial values

times

time vector

model

ode model

parms

parameters of the solution

solution

solution of the model

sensitivity

partial derivative of each state variable with respect to the parameters

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"))

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)

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)

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)

Arguments

object

fitodeMCMC object

Value

The summary of the fitodeMCMC object

See Also

effectiveSize gelman.diag

Tumor growth data

Description

...

Usage

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, ...)

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, ...)

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"))

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)

Arguments

object

fitodeMCMC object

Value

The variance-covariance matrix of the fitodeMCMC object