sim_dgp: Simulating from a data generating process

Description

This function can be used to generate data from a data generating process for SDM, SAR, SEM, and SLX type models.

Usage

sim_dgp(
  n,
  tt,
  rho,
  beta1 = c(),
  beta2 = c(),
  beta3 = c(),
  sigma2,
  n_neighbor = 4,
  W = NULL,
  do_symmetric = FALSE,
  intercept = FALSE,
  spatial_error = FALSE
)

Value

A list with the generated $X$, $Y$ and $W$ and a list of parameters.

Arguments

n: Number of spatial observations $n$.
tt: Number of time observations $T$.
rho: The true $\rho$ parameter
beta1: Vector of dimensions $k_1 \times 1$. Provides the values for $\beta_1$ Defaults to c(). Note: has to be of same length as $\beta_2$.
beta2: Vector of dimensions $k_1 \times 1$. Provides the values for $\beta_2$ Defaults to c(). Note: has to be of same length as $\beta_1$.
beta3: Vector of dimensions $k_2 \times 1$. Provides the values for $\beta_3$ Defaults to c().
sigma2: The true $\sigma^2$ parameter for the DGP. Has to be a scalar larger than zero.
n_neighbor: Number of neighbors for the generated $n \times n$ spatial weight $W$ matrix. Defaults to 4.
W: Exogeneous spatial weight matrix for the data generating process. Defaults to NULL, in which case a nearest neighbor matrix with n_neighbor will be generated.
do_symmetric: Should the generated spatial weight matrix be symmetric? (default: FALSE)
intercept: Should the first column of $Z$ be an intercept? Defaults to FALSE. If intercept = TRUE, $\beta_3$ has to be at least of length 1.
spatial_error: Should a spatial error model be constructed? Defaults to FALSE.

Details

For the SDM, SAR, and SLX models the generated spatial panel model takes the form

$$ Y = \rho W Y + X \beta_1 + W X \beta_2 + Z \beta_3 + \epsilon, $$

with $\epsilon \sim N(0,I_n\sigma^2)$.

For the SEM model the generated spatial panel model takes the form

$$ Y = X \beta_1 + W X \beta_2 + Z \beta_3 + \epsilon, $$

with $\epsilon \sim N(0,(I_n - \rho W)\sigma^2)$.

The function generates the $N \times 1$ vector $Y$. The elements of the explanatory variable matrices $X$ ($N \times k_1$) and $Z$ ($N \times k_2$) are randomly generated from a Gaussian distribution with zero mean and unity variance ($N(0,1)$).

The non-negative, row-stochastic $n$ by $n$ matrix $W$ is constructed using a k-nearest neighbor specification based on a randomly generated spatial location pattern, with coordinates sampled from a standard normal distribution.

Values for the parameters $\beta_1$, $\beta_2$, and $\beta_3$, as well as $\rho$ and $\sigma^2$ have to be provided by the user. The length of $\beta_1$ and $\beta_2$ have to be equal.

A spatial Durbin model (SDM) is constructed if $\rho$ is not equal to zero, spatial_error is FALSE, and $\beta_1$, $\beta_2$, and $\beta_3$ are all supplied by the user.
A spatial autoregressive model is constructed if $\rho$ is not equal to zero, spatial_error is FALSE, and only $\beta_3$ is supplied by the user.
An SLX type model is constructed if $\rho$ is equal to zero, spatial_error is FALSE, and $\beta_1$, $\beta_2$ are supplied by the user.
An SEM type model is constructed if spatial_error is TRUE and either only $\beta_3$ or $\beta_1$, $\beta_2$, and $\beta_3$ are supplied by the user.

Examples

Run this code

# SDM data generating process
dgp_dat = sim_dgp(n =20, tt = 10, rho = .5, beta1 = c(1,-1),
                  beta2 = c(0,.5),beta3 = c(.2),sigma2 = .5)

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