stats (version 3.6.2)

simulate: Simulate Responses


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


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



an object representing a fitted model.


number of response vectors to simulate. Defaults to 1.


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.


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()).


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 \(IG(\mu_i, \lambda w_i)\) (see where \(\lambda\) is estimated by the inverse of the dispersion estimate for the fit. The variance is \(\mu_i^3/(\lambda w_i)\) and hence inversely proportional to the prior weights. The simulation is done by function rinvGauss from the SuppDists package, which must be installed.

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.


Run this code
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

## 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
## first set the RNG kind, then simulate, 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
# }

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