Simulate one or more responses from the distribution corresponding to a fitted model object.
an object representing a fitted model.
number of response vectors to simulate. Defaults to
an object specifying if and how the random number
generator should be initialized (‘seeded’).
additional optional arguments.
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
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
The methods for linear models fitted by
= "gaussian") assume that any weights which have been supplied are
inversely proportional to the error variance. For other GLMs the
simulate component of the
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
gamma.shape in package
MASS). The interpretation of weights is as multipliers to a
basic shape parameter, since dispersion is inversely proportional to
For an inverse gaussian GLM the model assumed is
IG(μ_i, λ w_i) (see
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.
Typically, a list of length
nsim of simulated responses. Where
appropriate the result can be a data frame (which is a special type of
"lm" method, the result is a data frame with an
"seed". If argument
attribute is the value of
.Random.seed before the
simulation was started; otherwise it is the value of the argument with
"kind" attribute with value
RNG about random number generation in R,
residuals for related methods;
lm for model fitting.
There are further examples in the ‘simulate.R’ tests file in the sources for package stats.
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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