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Sensitivity Analysis for Sample Size Planning From the AIPE Perspective for a Partial Correlation

Source: R/ss_aipe_partial_r_sensitivity.R
ss_aipe_partial_r_sensitivity.Rd

Quantifies how much misspecification of the population partial correlation distorts an AIPE-based sample size plan. The function constructs an \((J + 1) \times (J + 1)\) population covariance matrix whose implied partial correlation between \(Y\) and \(X_1\) (controlling for \(X_2, \ldots, X_J\)) equals true_rho, then on each replication draws an n-row sample from the corresponding multivariate normal distribution and computes the sample partial correlation and its Fisher's \(Z\) CI.

Usage

ss_aipe_partial_r_sensitivity(
  true_rho = NULL,
  estimated_rho = NULL,
  J,
  width,
  specified_N = NULL,
  conf_level = 0.95,
  assurance = NULL,
  G = 1000,
  print_iter = FALSE,
  save = FALSE,
  filename = "ss_aipe_partial_r_sensitivity_result.csv"
)

Arguments

true_rho

Population partial correlation between Y and \(X_1\) controlling for \(X_2, \ldots, X_J\); must lie in \((-1, 1)\).

estimated_rho

Planning value of the partial correlation passed to ss_aipe_partial_r; supply this or specified_N but not both.

J

Total number of predictors (so the partial correlation is between Y and one of the J predictors, partialing out the other \(J - 1\)). Must be at least 1.

width

Desired full width of the CI on the partial correlation.

specified_N

Sample size to evaluate (incompatible with estimated_rho).

conf_level

Confidence level (default 0.95).

assurance

Optional assurance probability passed to ss_aipe_partial_r.

G

Number of Monte Carlo replications (default 1000).

print_iter

Logical. Print iteration index per replication.

save

Logical. If TRUE write per-replication results to filename.

filename

Path used when save = TRUE.

Value

A data.frame with rows for the realized partial correlation, the interval width, the proportion of intervals at or below width, tail-specific and overall non-coverage of true_rho, and the input echoes, including assurance (present only when an assurance was supplied).

References

Kelley, K., & Maxwell, S. E. (2003). Sample size for multiple regression: Obtaining regression coefficients that are accurate, not simply significant. Psychological Methods, 8(3), 305–321. doi:10.1037/1082-989X.8.3.305

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

See also

ss_aipe_partial_r, ss_aipe_semipartial_r_sensitivity

design_consequences for what a chosen design delivers: power, the Type S (sign) and Type M (exaggeration) errors of the significance filter, and the expected confidence interval width.

Other AIPE sample size planning: ss_aipe_c_sensitivity(), ss_aipe_cliff_delta(), ss_aipe_cliff_delta_sensitivity(), ss_aipe_composite_sem(), ss_aipe_equivalence_r(), ss_aipe_equivalence_r_sensitivity(), ss_aipe_equivalence_smd(), ss_aipe_equivalence_smd_sensitivity(), ss_aipe_icc(), ss_aipe_icc_sensitivity(), ss_aipe_indirect_effect(), ss_aipe_indirect_effect_sensitivity(), ss_aipe_mixed_effects_sensitivity(), ss_aipe_omega_squared(), ss_aipe_omega_squared_sensitivity(), ss_aipe_partial_r(), ss_aipe_pcm_sensitivity(), ss_aipe_r(), ss_aipe_r_sensitivity(), ss_aipe_reliability_sensitivity(), ss_aipe_semipartial_r(), ss_aipe_semipartial_r_sensitivity()

Author

Ken Kelley kkelley@nd.edu

Examples

# Reduced replications and a wide target interval keep this fast.
set.seed(113)
ss_aipe_partial_r_sensitivity(
  true_rho = 0.40, estimated_rho = 0.40, J = 3, width = 0.40,
  G = 50, print_iter = FALSE
)
#>  term               value 
#>  mean_partial_r     0.413 
#>  median_partial_r   0.429 
#>  sd_partial_r       0.108 
#>  mean_ci_width      0.391 
#>  median_ci_width    0.39  
#>  sd_ci_width        0.0389
#>  pct_ci_less_w      0.58  
#>  pct_ci_miss_low    0.04  
#>  pct_ci_miss_high   0.02  
#>  total_type_I_error 0.06  
#>  total_N            72    
#>  J                  3     
#>  true_rho           0.4   
#>  estimated_rho      0.4   
#>  width              0.4   
#>  conf_level         0.95  
#> 
#> Confidence level: 95%