bsts (version 0.9.8)

dirm: Dynamic intercept regression model

Description

A dynamic intercept regression is a regression model where the intercept term is a state space model. This model differs from bsts in that there can be multiple observations per time point.

Usage

dirm(formula,
     state.specification,
     data,
     prior = NULL,
     contrasts = NULL,
     na.action = na.pass,
     niter,
     ping = niter / 10,
     model.options = DirmModelOptions(),
     timestamps = NULL,
     seed = NULL,
     ...)

Value

An object of class bsts which is a list with the following components

coefficients

A niter by ncol(X) matrix of MCMC draws of the regression coefficients, where X is the design matrix implied by formula. This is only present if a model formula was supplied.

sigma.obs

A vector of length niter containing MCMC draws of the residual standard deviation.

The returned object will also contain named elements holding the MCMC draws of model parameters belonging to the state models. The names of each component are supplied by the entries in

state.specification. If a model parameter is a scalar, then the list element is a vector with niter elements. If the parameter is a vector then the list element is a matrix with

niter rows. If the parameter is a matrix then the list element is a 3-way array with first dimension niter.

Finally, if a model formula was supplied, then the returned object will contain the information necessary for the predict method to build the design matrix when a new prediction is made.

Arguments

formula

A formula, as you would supply to lm describing the regression portion of the relationship between y and X.

state.specification

A list with elements created by AddLocalLinearTrend, AddSeasonal, and similar functions for adding components of state. See the help page for state.specification.

The state specification describes the dynamic intercept term in the regression model.

data

An optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which dirm is called.

prior

A prior distribution for the regression component of the model, as created by SpikeSlabPrior. The prior for the time series component of the model will be specified during the creation of state.specification.

contrasts

An optional list containing the names of contrast functions to use when converting factors numeric variables in a regression formula. This argument works exactly as it does in lm. The names of the list elements correspond to factor variables in your model formula. The list elements themselves are the names of contrast functions (see help(contr.treatment) and the contrasts.arg argument to model.matrix.default). This argument can usually be omitted.

na.action

What to do about missing values. The default is to allow missing responses, but no missing predictors. Set this to na.omit or na.exclude if you want to omit missing responses altogether.

niter

A positive integer giving the desired number of MCMC draws.

ping

A scalar giving the desired frequency of status messages. If ping > 0 then the program will print a status message to the screen every ping MCMC iterations.

model.options

An object created by DirmModelOptions specifying the desired model options.

timestamps

The timestamp associated with each value of the response. This is most likely a Date or POSIXt. It is expected that there will be multiple observations per time point (otherwise 'bsts' should be used instead of 'dirm'), and thus the 'timestamps' argument will contain many duplicate values.

seed

An integer to use as the random seed for the underlying C++ code. If NULL then the seed will be set using the clock.

...

Extra arguments to be passed to SpikeSlabPrior (see the entry for the prior argument, above).

Author

Steven L. Scott

Details

The fitted model is a regression model with an intercept term given by a structural time series model. This is similar to the model fit by bsts, but it allows for multiple observations per time period.

Currently dirm only supports Gaussian observation errors, but look for that to change in future releases.

References

Harvey (1990), "Forecasting, structural time series, and the Kalman filter", Cambridge University Press.

Durbin and Koopman (2001), "Time series analysis by state space methods", Oxford University Press.

George and McCulloch (1997) "Approaches for Bayesian variable selection", Statistica Sinica pp 339--374.

See Also

bsts, AddLocalLevel, AddLocalLinearTrend, AddSemilocalLinearTrend, AddSeasonal AddDynamicRegression SpikeSlabPrior, SdPrior.

Examples

SimulateDirmData <- function(observation.sd = 1, trend.sd = .1,
                             time.dimension = 100, nobs.per.period = 3,
                             xdim = 4) {
  trend <- cumsum(rnorm(time.dimension, 0, trend.sd))
  total.sample.size <- nobs.per.period * time.dimension
  predictors <- matrix(rnorm(total.sample.size * xdim),
    nrow = total.sample.size)
  coefficients <- rnorm(xdim)
  expanded.trend <- rep(trend, each = nobs.per.period)
  response <- expanded.trend + predictors %*% coefficients + rnorm(
    total.sample.size, 0, observation.sd)
  timestamps <- seq.Date(from = as.Date("2008-01-01"),
                         len = time.dimension, by = "day")
  extended.timestamps <- rep(timestamps, each = nobs.per.period)
  return(list(response = response,
    predictors = predictors,
    timestamps = extended.timestamps,
    trend = trend,
    coefficients = coefficients))
}


data <- SimulateDirmData(time.dimension = 20)
ss <- AddLocalLevel(list(), data$response)

# In real life you'd want more than 50 MCMC iterations.
model <- dirm(data$response ~ data$predictors, ss, niter = 50,
  timestamps = data$timestamps)