# simulate

##### Simulate Responses

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
\(IG(\mu_i, \lambda w_i)\) (see
https://en.wikipedia.org/wiki/Inverse_Gaussian_distribution)
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.

##### 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

`library(stats)`

```
# NOT RUN {
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
# }
```

*Documentation reproduced from package stats, version 3.6.0, License: Part of R 3.6.0*