betaMC (version 1.3.3)

MC: Generate the Sampling Distribution of Regression Parameters Using the Monte Carlo Method

Description

Generate the Sampling Distribution of Regression Parameters Using the Monte Carlo Method

Usage

MC(
  object,
  R = 20000L,
  type = "hc3",
  g1 = 1,
  g2 = 1.5,
  k = 0.7,
  decomposition = "eigen",
  pd = TRUE,
  tol = 1e-06,
  fixed_x = FALSE,
  seed = NULL
)

Value

Returns an object of class mc which is a list with the following elements:

call

Function call.

args

Function arguments.

lm_process

Processed lm object.

scale

Sampling variance-covariance matrix of parameter estimates.

location

Parameter estimates.

thetahatstar

Sampling distribution of parameter estimates.

fun

Function used ("MC").

Arguments

object

Object of class lm.

R

Positive integer. Number of Monte Carlo replications.

type

Character string. Sampling covariance matrix type. Possible values are "mvn", "adf", "hc0", "hc1", "hc2", "hc3", "hc4", "hc4m", and "hc5". type = "mvn" uses the normal-theory sampling covariance matrix. type = "adf" uses the asymptotic distribution-free sampling covariance matrix. type = "hc0" through "hc5" uses different versions of heteroskedasticity-consistent sampling covariance matrix.

g1

Numeric. g1 value for type = "hc4m".

g2

Numeric. g2 value for type = "hc4m".

k

Numeric. Constant for type = "hc5"

decomposition

Character string. Matrix decomposition of the sampling variance-covariance matrix for the data generation. If decomposition = "chol", use Cholesky decomposition. If decomposition = "eigen", use eigenvalue decomposition. If decomposition = "svd", use singular value decomposition.

pd

Logical. If pd = TRUE, check if the sampling variance-covariance matrix is positive definite using tol.

tol

Numeric. Tolerance used for pd.

fixed_x

Logical. If fixed_x = TRUE, treat the regressors as fixed. If fixed_x = FALSE, treat the regressors as random.

seed

Integer. Seed number for reproducibility.

Author

Ivan Jacob Agaloos Pesigan

Details

Let the parameter vector of the unstandardized regression model be given by $$ \boldsymbol{\theta} = \left\{ \mathbf{b}, \sigma^{2}, \mathrm{vech} \left( \boldsymbol{\Sigma}_{\mathbf{X}\mathbf{X}} \right) \right\} $$ where \(\mathbf{b}\) is the vector of regression slopes, \(\sigma^{2}\) is the error variance, and \( \mathrm{vech} \left( \boldsymbol{\Sigma}_{\mathbf{X}\mathbf{X}} \right) \) is the vector of unique elements of the covariance matrix of the regressor variables. The empirical sampling distribution of \(\boldsymbol{\theta}\) is generated using the Monte Carlo method, that is, random values of parameter estimates are sampled from the multivariate normal distribution using the estimated parameter vector as the mean vector and the specified sampling covariance matrix using the type argument as the covariance matrix. A replacement sampling approach is implemented to ensure that the model-implied covariance matrix is positive definite.

References

Dudgeon, P. (2017). Some improvements in confidence intervals for standardized regression coefficients. Psychometrika, 82(4), 928–951. tools:::Rd_expr_doi("10.1007/s11336-017-9563-z")

MacKinnon, D. P., Lockwood, C. M., & Williams, J. (2004). Confidence limits for the indirect effect: Distribution of the product and resampling methods. Multivariate Behavioral Research, 39(1), 99-128. tools:::Rd_expr_doi("10.1207/s15327906mbr3901_4")

Pesigan, I. J. A., & Cheung, S. F. (2024). Monte Carlo confidence intervals for the indirect effect with missing data. Behavior Research Methods. tools:::Rd_expr_doi("10.3758/s13428-023-02114-4")

Preacher, K. J., & Selig, J. P. (2012). Advantages of Monte Carlo confidence intervals for indirect effects. Communication Methods and Measures, 6(2), 77–98. tools:::Rd_expr_doi("10.1080/19312458.2012.679848")

See Also

Other Beta Monte Carlo Functions: BetaMC(), DeltaRSqMC(), DiffBetaMC(), MCMI(), PCorMC(), RSqMC(), SCorMC()

Examples

# Data ---------------------------------------------------------------------
data("nas1982", package = "betaMC")

# Fit Model in lm ----------------------------------------------------------
object <- lm(QUALITY ~ NARTIC + PCTGRT + PCTSUPP, data = nas1982)

# MC -----------------------------------------------------------------------
mc <- MC(
  object,
  R = 100, # use a large value e.g., 20000L for actual research
  seed = 0508
)
mc
# The `mc` object can be passed as the first argument
# to the following functions
#   - BetaMC
#   - DeltaRSqMC
#   - DiffBetaMC
#   - PCorMC
#   - RSqMC
#   - SCorMC