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Inference

Ivan Jacob Agaloos Pesigan

Source: vignettes/inference.Rmd
inference.Rmd

The following presents an example of how to use the functions in this package to generate confidence intervals for the indirect effect for the model fitted in the Model Fitting article.

Arguments

Variables Values Notes
R 20000 Number of Monte Carlo replications.
B 5000 Number of bootstrap samples.

Monte Carlo Method

Maximum Likelihood 

mc_ml <- MCML(
  fit_ml,
  R = R
)
mc_ml
#>        0.05%         0.5%         2.5%        97.5%        99.5%       99.95% 
#> -0.014833023 -0.000230099  0.009405113  0.123442323  0.150985676  0.187875583

Multiple Imputation

The two versions are based on the pooled covariance matrix used. vcov uses the total covariance matrix \(\mathbf{V}_{T}\) while vcov_tilde uses the adjusted total covariance matrix \(\tilde{\mathbf{V}}_{T}\).

mc_mi <- MCMI(
  fit_mi,
  R = R
)
mc_mi
#>                   0.05%          0.5%        2.5%     97.5%     99.5%    99.95%
#> vcov       -0.012533766 -0.0008536301 0.008771913 0.1244398 0.1533265 0.2002091
#> vcov_tilde -0.009596199  0.0010447389 0.010266007 0.1212220 0.1455933 0.1754708

Nonparametric Bootstrapping

Maximum Likelihood Nested within Nonparametric Bootstrap (NB(ML)) 

nb_ml <- NBML(
  data_missing,
  B = B,
  mplus_bin = mplus_bin
)
nb_ml
#>    Lower .5% Lower 2.5% Lower 5% Estimate Upper 5% Upper 2.5% Upper .5%
#> bc     0.002      0.012    0.018    0.056    0.127      0.142     0.171
#> pc    -0.001      0.008    0.013    0.056    0.114      0.129     0.160

Multiple Imputation

Multiple Imputation Nested Within Nonparametric Bootstrap (NB(MI)) 

nb_mi <- NBMI(
  data_missing,
  data_mi,
  B = B,
  m = m,
  mplus_bin = mplus_bin
)
nb_mi
#>           0.05%         0.5%        2.5%     97.5%     99.5%    99.95%
#> bc -0.008599074  0.002197657 0.012710451 0.1431757 0.1785678 0.2054530
#> pc -0.010897738 -0.001965398 0.007835137 0.1283433 0.1575050 0.2002295

Nonparametric Bootstrap Nested Within Multiple Imputation (MI(NB)) 

mi_nb <- MINB(
  data_mi,
  B = B
)
mi_nb
#>          0.05%          0.5%        2.5%     97.5%     99.5%    99.95%
#> bc -0.01025972  0.0026119888 0.012309673 0.1409874 0.1730426 0.2142799
#> pc -0.01551219 -0.0008570296 0.008490644 0.1295344 0.1604574 0.2014387

Joint Significance Test

The JointSigML() and JointSigMI() functions return 1 for a significant result and 0 otherwise. Note that the output vector’s name corresponds to the alpha level. The default value of alpha is alpha = c(0.05, 0.01, 0.001).

Maximum Likelihood 

joint_ml <- JointSigML(
  fit_ml
)
joint_ml
#>  0.05  0.01 0.001 
#>     1     1     0

Multiple Imputation

The two versions are based on the two types of pooled covariance matrices \(\mathbf{V}_{T}\) and \(\tilde{\mathbf{V}}_{T}\).

joint_mi <- JointSigMI(
  fit_mi
)
joint_mi
#>            0.05 0.01 0.001
#> vcov          1    1     0
#> vcov_tilde    1    1     0

Results

Here is a summary of the \(95\%\) confidence intervals.

ci <- rbind(
  mc_ml[c(3, 4)],
  mc_mi[, c(3, 4)],
  nb_ml[, c(2, 6)],
  nb_mi[, c(3, 4)],
  mi_nb[, c(3, 4)]
)
rownames(ci) <- c(
  "MC.FIML",
  "MC.MI",
  "MC.MI.ADJ",
  "NBBC(FIML)",
  "NBPC(FIML)",
  "NBBC(MI)",
  "NBPC(MI)",
  "MI(NBBC)",
  "MI(NBPC)"
)
knitr::kable(ci)
2.5% 97.5%
MC.FIML 0.0094051 0.1234423
MC.MI 0.0087719 0.1244398
MC.MI.ADJ 0.0102660 0.1212220
NBBC(FIML) 0.0120000 0.1420000
NBPC(FIML) 0.0080000 0.1290000
NBBC(MI) 0.0127105 0.1431757
NBPC(MI) 0.0078351 0.1283433
MI(NBBC) 0.0123097 0.1409874
MI(NBPC) 0.0084906 0.1295344