# Simulate Data from Structural Equation Model

### Description

Interprets the input graph as a structural equation model, generates random path coefficients, and simulates data from the model. This is a very bare-bones function and probably not very useful except for quick validation purposes (e.g. checking that an implied vanishing tetrad truly vanishes in simulated data). For more elaborate simulation studies, please use the lavaan package or similar facilities in other packages.

### Usage

1 2 | ```
simulateSEM(x, b.default = NULL, b.lower = -0.6, b.upper = 0.6, eps = 1,
N = 500, standardized = TRUE)
``` |

### Arguments

`x` |
the input graph, a DAG (which may contain bidirected edges). |

`b.default` |
default path coefficient applied to arrows for which no coefficient is defined in the model syntax. |

`b.lower` |
lower bound for random path coefficients, applied if |

`b.upper` |
upper bound for path coefficients. |

`eps` |
residual variance (only meaningful if |

`N` |
number of samples to generate. |

`standardized` |
whether a standardized output is desired (all variables have variance 1). If |

### Details

Data are generated in the following manner.
Each directed arrow is assigned a path coefficient that can be given using the attribute
"beta" in the model syntax (see the examples). All coefficients not set in this manner are
set to the `b.default`

argument, or if that is not given, are chosen uniformly
at random from the interval given by `b.lower`

and `b.upper`

(inclusive; set
both parameters to the same value for constant path coefficients). Each bidirected
arrow a <-> b is replaced by a substructure a <- L -> b, where L is an exogenous latent
variable. Path coefficients on such substructures are set to `sqrt(x)`

, where
`x`

is again chosen at random from the given interval; if `x`

is negative,
one path coefficient is set to `-sqrt(x)`

and the other to `sqrt(x)`

. All
residual variances are set to `eps`

.

### Value

Returns a data frame containing `N`

values for each variable in `x`

.

### Examples

1 2 3 4 | ```
## Simulate data with pre-defined path coefficients of -.6
g <- dagitty('dag{z -> x [beta=-.6] x <- y [beta=-.6] }')
x <- simulateSEM( g )
cov(x)
``` |