R: Simulate Responses

simulate {stats} | R Documentation

## Simulate Responses

### Description

Simulate one or more responses from the distribution corresponding to a fitted model object.

### Usage

    simulate(object, nsim = 1, seed = NULL, ...)

### Arguments

`object` | an object representing a fitted model.
`nsim` | number of response vectors to simulate. Defaults to `1`.
`seed` | an object specifying if and how the random number generator should be initialized (‘seeded’). For the "lm" method, either `NULL` or an integer that will be used in a call to `set.seed` before simulating the response vectors. If set, the value is saved as the `"seed"` attribute of the returned value. The default, `NULL` will not change the random generator state, and return `.Random.seed` as the `"seed"` attribute, see ‘Value’.
`...` | additional optional arguments.

### Details

This is a generic function. Consult the individual modeling functions for details on how to use this function.

Package stats has a method for `"lm"` objects which is used for `lm` and `glm` fits. There is a method for fits from `glm.nb` in package MASS, and hence the case of negative binomial families is not covered by the `"lm"` method.

The methods for linear models fitted by `lm` or `glm(family = "gaussian")` assume that any weights which have been supplied are inversely proportional to the error variance. For other GLMs the (optional) `simulate` component of the `family` object is used—there is no appropriate simulation method for ‘quasi’ models as they are specified only up to two moments.

For binomial and Poisson GLMs the dispersion is fixed at one. Integer prior weights w_i can be interpreted as meaning that observation i is an average of w_i observations, which is natural for binomials specified as proportions but less so for a Poisson, for which prior weights are ignored with a warning.

For a gamma GLM the shape parameter is estimated by maximum likelihood (using function `gamma.shape` in package MASS). The interpretation of weights is as multipliers to a basic shape parameter, since dispersion is inversely proportional to shape.

For an inverse gaussian GLM the model assumed is IG(μ_i, λ w_i) (see https://en.wikipedia.org/wiki/Inverse_Gaussian_distribution) where λ is estimated by the inverse of the dispersion estimate for the fit. The variance is μ_i^3/(λ w_i) and hence inversely proportional to the prior weights. The simulation is done by function `rinvGauss` from the SuppDists package, which must be installed.

### Value

Typically, a list of length `nsim` of simulated responses. Where appropriate the result can be a data frame (which is a special type of list).

For the `"lm"` method, the result is a data frame with an attribute `"seed"`. If argument `seed` is `NULL`, the attribute is the value of `.Random.seed` before the simulation was started; otherwise it is the value of the argument with a `"kind"` attribute with value `as.list(RNGkind())`.

### See Also

`RNG` about random number generation in R, `fitted.values` and `residuals` for related methods; `glm`, `lm` for model fitting.

There are further examples in the ‘simulate.R’ tests file in the sources for package stats.

### Examples

    x <- 1:5
    mod1 <- lm(c(1:3, 7, 6) ~ x)
    S1 <- simulate(mod1, nsim = 4)
    ## repeat the simulation:
    .Random.seed <- attr(S1, "seed")
    identical(S1, simulate(mod1, nsim = 4))

    S2 <- simulate(mod1, nsim = 200, seed = 101)
    rowMeans(S2) # should be about the same as
    fitted(mod1)

    ## repeat identically:
    (sseed <- attr(S2, "seed")) # seed; RNGkind as attribute
    stopifnot(identical(S2, simulate(mod1, nsim = 200, seed = sseed)))

    ## To be sure about the proper RNGkind, e.g., after
    RNGversion("2.7.0")
    ## first set the RNG kind, then simulate
    do.call(RNGkind, attr(sseed, "kind"))
    identical(S2, simulate(mod1, nsim = 200, seed = sseed))

    ## Binomial GLM examples
    yb1 <- matrix(c(4, 4, 5, 7, 8, 6, 6, 5, 3, 2), ncol = 2)
    modb1 <- glm(yb1 ~ x, family = binomial)
    S3 <- simulate(modb1, nsim = 4)
    # each column of S3 is a two-column matrix.

    x2 <- sort(runif(100))
    yb2 <- rbinom(100, prob = plogis(2*(x2-1)), size = 1)
    yb2 <- factor(1 + yb2, labels = c("failure", "success"))
    modb2 <- glm(yb2 ~ x2, family = binomial)
    S4 <- simulate(modb2, nsim = 4)
    # each column of S4 is a factor

[Package stats version 4.0.5 Index]