Generate the Sampling Distribution of Regression Parameters Using the Monte Carlo Method for Data with Missing Values

Usage

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

Arguments

object: Object of class lm.
mi: Object of class mids (output of mice::mice()), object of class amelia (output of Amelia::amelia()), or a list of multiply imputed data sets.
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.

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 ("MCMI").

Details

Multiple imputation is used to deal with missing values in a data set. The vector of parameter estimates and the corresponding sampling covariance matrix are estimated for each of the imputed data sets. Results are combined to arrive at the pooled vector of parameter estimates and the corresponding sampling covariance matrix. The pooled estimates are then used to generate the sampling distribution of regression parameters. See MC() for more details on the Monte Carlo method.

References

Dudgeon, P. (2017). Some improvements in confidence intervals for standardized regression coefficients. Psychometrika, 82(4), 928–951. 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. doi:10.1207/s15327906mbr3901_4

Pesigan, I. J. A., & Cheung, S. F. (2023). Monte Carlo confidence intervals for the indirect effect with missing data. Behavior Research Methods. 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. doi:10.1080/19312458.2012.679848

Author

Ivan Jacob Agaloos Pesigan

Examples

# Data ---------------------------------------------------------------------
data("nas1982", package = "betaMC")
nas1982_missing <- mice::ampute(nas1982)$amp # data set with missing values

# Multiple Imputation
mi <- mice::mice(nas1982_missing, m = 5, seed = 42, print = FALSE)

# Fit Model in lm ----------------------------------------------------------
## Note that this does not deal with missing values.
## The fitted model (`object`) is updated with each imputed data
## within the `MCMI()` function.
object <- lm(QUALITY ~ NARTIC + PCTGRT + PCTSUPP, data = nas1982_missing)

# Monte Carlo --------------------------------------------------------------
mc <- MCMI(
  object,
  mi = mi,
  R = 100, # use a large value e.g., 20000L for actual research
  seed = 0508
)
mc
#> Call:
#> MCMI(object = object, mi = mi, R = 100, seed = 508)
#> The first set of simulated parameter estimates
#> and model-implied covariance matrix.
#> 
#> $coef
#> [1] 0.08360573 0.18269795 0.15525578
#> 
#> $sigmasq
#> [1] 20.30319
#> 
#> $vechsigmacapx
#> [1] 3712.8505  609.1971  635.5153  332.2336  201.1010  549.9604
#> 
#> $sigmacapx
#>           [,1]     [,2]     [,3]
#> [1,] 3712.8505 609.1971 635.5153
#> [2,]  609.1971 332.2336 201.1010
#> [3,]  635.5153 201.1010 549.9604
#> 
#> $sigmaysq
#> [1] 117.1189
#> 
#> $sigmayx
#> [1] 520.3821 142.8529 175.2580
#> 
#> $sigmacap
#>          [,1]      [,2]     [,3]     [,4]
#> [1,] 117.1189  520.3821 142.8529 175.2580
#> [2,] 520.3821 3712.8505 609.1971 635.5153
#> [3,] 142.8529  609.1971 332.2336 201.1010
#> [4,] 175.2580  635.5153 201.1010 549.9604
#> 
#> $pd
#> [1] TRUE
#> 
# The `mc` object can be passed as the first argument
# to the following functions
#   - BetaMC
#   - DeltaRSqMC
#   - DiffBetaMC
#   - PCorMC
#   - RSqMC
#   - SCorMC