PF_forward_filter

Forward Particle Filter

Functions to only use the forward particle filter. Useful for log-likelihood evaluation though there is an \(O(d^2)\) variance of the estimate where \(d\) is the number of time periods. The number of particles specified in the control argument has no effect.

The function does not alter the .Random.seed to make sure the same rng.kind is kept after the call. See PF_EM for model details.

Usage
PF_forward_filter(x, N_fw, N_first, ...)

# S3 method for PF_EM PF_forward_filter(x, N_fw, N_first, seed, ...)

# S3 method for formula PF_forward_filter(x, N_fw, N_first, data, model = "logit", by, max_T, id, a_0, Q_0, Q, fixed_effects, control = PF_control(...), seed = NULL, trace = 0, G, theta, J, K, psi, phi, type = "RW", Fmat, ...)

# S3 method for data.frame PF_forward_filter(x, N_fw, N_first, formula, model = "logit", by, max_T, id, a_0, Q_0, Q, fixed_effects, control = PF_control(...), seed = NULL, trace = 0, fixed = NULL, random = NULL, G, theta, J, K, psi, phi, type = "RW", Fmat, order = 1, ...)

Arguments
x

an PF_EM or formula object.

N_fw

number of particles.

N_first

number of time zero particles to draw.

...

optional way to pass arguments to control.

seed

.GlobalEnv$.Random.seed to set. Not seed as in set.seed function. Can be used with the .Random.seed returned by PF_EM.

data

data.frame or environment containing the outcome and covariates.

model

either 'logit' for binary outcomes with the logistic link function, 'cloglog' for binary outcomes with the inverse cloglog link function, or 'exponential' for piecewise constant exponential distributed arrival times.

by

interval length of the bins in which parameters are fixed.

max_T

end of the last interval interval.

id

vector of ids for each row of the in the design matrix.

a_0

vector \(a_0\) for the initial coefficient vector for the first iteration (optional). Default is estimates from static model (see static_glm).

Q_0

covariance matrix for the prior distribution.

Q

initial covariance matrix for the state equation.

fixed_effects

values for the fixed parameters.

control

see PF_control.

trace

argument to get progress information. Zero will yield no info and larger integer values will yield incrementally more information.

G, theta, J, K, psi, phi

parameters for a restricted type = "VAR" model. See the vignette mentioned in 'Details' of PF_EM and the examples linked to in 'See Also'.

type

type of state model. Either "RW" for a [R]andom [W]alk or "VAR" for [V]ector [A]uto[R]egression.

Fmat

starting value for \(F\) when type = "VAR". See 'Details' in PF_EM.

formula

coxph like formula with Surv(tstart, tstop, event) on the left hand site of ~.

fixed

two-sided formula to be used with random instead of formula. It is of the form Surv(tstart, tstop, event) ~ x or Surv(tstart, tstop, event) ~ - 1 for no fixed effects.

random

one-sided formula to be used with fixed instead of formula. It is of the form ~ z.

order

order of the random walk.

Value

An object of class PF_clouds.

Methods (by class)

  • PF_EM: Forward particle filter using the estimates of an PF_EM call.

  • formula: Forward particle filter with formula input.

  • data.frame: Forward particle filter with data.frame data input as x instead of data. Can be used with fixed and random argument.

Warning

The function is still under development so the output and API may change.

Aliases
  • PF_forward_filter
  • PF_forward_filter.PF_EM
  • PF_forward_filter.formula
  • PF_forward_filter.data.frame
Examples
# NOT RUN {
# head-and-neck cancer study data. See Efron, B. (1988) doi:10.2307/2288857
is_censored <- c(
  6, 27, 34, 36, 42, 46, 48:51, 51 + c(15, 30:28, 33, 35:37, 39, 40, 42:45))
head_neck_cancer <- data.frame(
  id = 1:96,
  stop = c(
    1, 2, 2, rep(3, 6), 4, 4, rep(5, 8),
    rep(6, 7), 7, 8, 8, 8, 9, 9, 10, 10, 10, 11, 14, 14, 14, 15, 18, 18, 20,
    20, 37, 37, 38, 41, 45, 47, 47,
    2, 2, 3, rep(4, 4), rep(5, 5), rep(6, 5),
    7, 7, 7, 9, 10, 11, 12, 15, 16, 18, 18, 18, 21,
    21, 24, 25, 27, 36, 41, 44, 52, 54, 59, 59, 63, 67, 71, 76),
  event = !(1:96 %in% is_censored),
  group = factor(c(rep(1, 45 + 6), rep(2, 45))))

# fit model
set.seed(61364778)
ctrl <- PF_control(
  N_fw_n_bw = 500, N_smooth = 2500, N_first = 2000,
  n_max = 1, # set to one as an example
  n_threads = max(parallel::detectCores(logical = FALSE), 1),
  eps = .001, Q_tilde = as.matrix(.3^2), est_a_0 = FALSE)
pf_fit <- suppressWarnings(
  PF_EM(
    survival::Surv(stop, event) ~ ddFixed(group),
    data = head_neck_cancer, by = 1, Q_0 = 1, Q = 0.1^2, control = ctrl,
    max_T = 30))

# the log-likelihood in the final iteration
(end_log_like <- logLik(pf_fit))

# gives the same
fw_ps <- PF_forward_filter(
  survival::Surv(stop, event) ~ ddFixed(group), N_fw = 500, N_first = 2000,
  data = head_neck_cancer, by = 1, Q_0 = 1, Q = 0.1^2,
  a_0 = pf_fit$a_0, fixed_effects = -0.5370051,
  control = ctrl, max_T = 30, seed = pf_fit$seed)
all.equal(c(end_log_like), c(logLik(fw_ps)))

# will differ since we use different number of particles
fw_ps <- PF_forward_filter(
  survival::Surv(stop, event) ~ ddFixed(group), N_fw = 1000, N_first = 3000,
  data = head_neck_cancer, by = 1, Q_0 = 1, Q = 0.1^2,
  a_0 = pf_fit$a_0, fixed_effects = -0.5370051,
  control = ctrl, max_T = 30, seed = pf_fit$seed)
all.equal(c(end_log_like), c(logLik(fw_ps)))

# will differ since we use the final estimates
fw_ps <- PF_forward_filter(pf_fit, N_fw = 500, N_first = 2000)
all.equal(c(end_log_like), c(logLik(fw_ps)))
# }
Documentation reproduced from package dynamichazard, version 0.6.6, License: GPL-2

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