Sensitivity Analysis for Sample Size Planning From the AIPE Perspective for an Indirect Effect

Quantifies how much misspecification of the population mediation path coefficients \(a\) and \(b\) distorts an AIPE-based sample size plan for the indirect effect \(ab\). On each replication the function simulates a three-variable mediation system \(X \to M \to Y\) of size n with population path coefficients true_a and true_b, fits the two regressions of M on X and Y on M and X, computes the sample indirect effect \(\hat a \hat b\), and forms the interval the plan targeted: the symmetric Wald interval from the delta method standard error (method = "closed_form") or the Monte Carlo interval (method = "monte_carlo"), matching ss_aipe_indirect_effect.

Usage

ss_aipe_indirect_effect_sensitivity(
  true_a = NULL,
  true_b = NULL,
  estimated_a = NULL,
  estimated_b = NULL,
  width,
  specified_N = NULL,
  method = c("closed_form", "monte_carlo"),
  conf_level = 0.95,
  B = 5000L,
  G = 1000,
  print_iter = FALSE,
  save = FALSE,
  filename = "ss_aipe_indirect_effect_sensitivity_result.csv"
)

Arguments

true_a: Population path coefficient a (from X to M); the data generating value.
true_b: Population path coefficient b (from M to Y after controlling for X); the data generating value.
estimated_a, estimated_b: Path coefficients used to plan the study (passed to ss_aipe_indirect_effect). Supply both or neither (if neither, supply specified_N).
width: Desired full width of the CI on \(ab\).
specified_N: Sample size to evaluate (incompatible with estimated_a / estimated_b).
method: One of "closed_form" (default) or "monte_carlo"; the interval computed on each replication, also forwarded to the planner when the sample size is planned from estimated_a and estimated_b. A planning call with method = "monte_carlo" runs the planner's a priori Monte Carlo search at its default G, so it takes a few seconds.
conf_level: Confidence level (default 0.95).
B: Number of Monte Carlo draws used for the indirect-effect CI when method = "monte_carlo" (default 5000).
G: Number of outer simulation replications (default 1000).
print_iter: Logical.
save: Logical. Save per-replication CSV.
filename: Path used when save = TRUE.

Value

A data.frame with rows for mean / median / SD of \(\hat a \hat b\) and the CI width, the proportion of intervals at or below width, tail-specific and overall non-coverage of the population value true_a * true_b, and the input echoes.

References

Preacher, K. J., & Kelley, K. (2011). Effect size measures for mediation models: Quantitative strategies for communicating indirect effects. Psychological Methods, 16(2), 93–115. doi:10.1037/a0022658

Tofighi, D., & Kelley, K. (2020). Improved inference in mediation analysis: Introducing the model-based constrained optimization procedure. Psychological Methods, 25, 496–515. doi:10.1037/met0000259

Maxwell, S. E., Delaney, H. D., & Kelley, K. (2027). Designing experiments and analyzing data: A model comparison perspective (4th ed.). Routledge.

Author

Ken Kelley kkelley@nd.edu

Examples

# Reduced replications and a wide target width keep this fast.
set.seed(113)
ss_aipe_indirect_effect_sensitivity(
  true_a = 0.4, true_b = 0.3,
  estimated_a = 0.4, estimated_b = 0.3,
  width = 0.40, method = "closed_form",
  G = 50, print_iter = FALSE
)
#>  term               value
#>  mean_ab            0.128
#>  median_ab          0.134
#>  sd_ab              0.107
#>  mean_ci_width      0.435
#>  median_ci_width    0.434
#>  sd_ci_width        0.149
#>  pct_ci_less_w      0.42 
#>  pct_ci_miss_low    0    
#>  pct_ci_miss_high   0.1  
#>  total_type_I_error 0.1  
#>  total_N            27   
#>  true_a             0.4  
#>  true_b             0.3  
#>  true_ab            0.12 
#>  estimated_a        0.4  
#>  estimated_b        0.3  
#>  width              0.4  
#>  conf_level         0.95 
#> 
#> Confidence level: 95%