DMAR (version 1.0.0)

ss_power_indirect_effect: Sample Size Planning for Power for the Indirect (Mediation) Effect

Description

Power, or the sample size required for a desired power, for the test of the indirect effect \(a b\) in the simple mediation model, with paths specified in standardized metric (unit-variance \(X\), \(M\), and \(Y\)). The default test is joint significance (the indirect effect is declared when both \(\hat a\) and \(\hat b\) are individually significant), which tracks the resampling tests' power closely and far exceeds the Sobel test in small samples (Fritz & MacKinnon, 2007); the Sobel normal-theory test is available for comparison. This is the power counterpart of the accuracy in parameter estimation (AIPE) planner ss_aipe_indirect_effect, and the planning complement of the analysis function mediate.

Usage

ss_power_indirect_effect(
  a,
  b,
  c_prime = 0,
  desired_power = NULL,
  N = NULL,
  alpha_level = 0.05,
  method = c("joint_significance", "sobel")
)

Value

A tidy data.frame with

necessary_N (or specified_N), actual_power (the power to detect the indirect effect, the quantity the sample size is planned against), the component powers (power_a, power_b;

NA for the Sobel method), the paths (a, b,

c_prime), the implied indirect_effect, and

alpha_level. The method is recorded in the "method"

attribute. The result carries the dmar_ss_power class, so

tidy reports the sample size and the power to detect the indirect effect, and glance adds the component powers and the planning inputs.

Arguments

a

Standardized \(X \to M\) path.

b

Standardized \(M \to Y\) path, holding \(X\).

c_prime

Standardized direct effect of \(X\) on \(Y\) holding \(M\). Defaults to 0; it enters only through the residual variance of \(Y\).

desired_power

Desired power; supply this to solve for \(N\).

N

Total sample size; supply this to evaluate the realized power. Specify exactly one of desired_power and N. This is the total sample size.

alpha_level

Two-sided Type I error rate for each component test. Defaults to 0.05.

method

"joint_significance" (default) or "sobel".

Author

Ken Kelley [email protected]

Details

With unit-variance variables, the large-sample standard errors are \(\mathrm{se}_a = \sqrt{(1 - a^2)/N}\) and \(\mathrm{se}_b = \sqrt{\sigma^2_{e_Y} / [N (1 - a^2)]}\) with \(\sigma^2_{e_Y} = 1 - (b^2 + c'^2 + 2 a b c')\). Because \(\hat a\) and \(\hat b\) are asymptotically independent in this model, the joint significance power is the product of the two component powers; the Sobel power refers \(ab / \mathrm{se}_{ab}\) (first-order delta method, via the same variance as var_indirect_effect) to the normal. The joint-significance component powers use the exact noncentral t (with \(n - 2\) and \(n - 3\) degrees of freedom), so its only approximations are the population standard errors and component independence; the tests validate the result against raw-data simulation. A specified parameter combination must be admissible (positive residual variances), or the function stops.

References

Fritz, M. S., & MacKinnon, D. P. (2007). Required sample size to detect the mediated effect. Psychological Science, 18(3), 233--239. tools:::Rd_expr_doi("10.1111/j.1467-9280.2007.01882.x")

MacKinnon, D. P., Lockwood, C. M., Hoffman, J. M., West, S. G., & Sheets, V. (2002). A comparison of methods to test mediation and other intervening variable effects. Psychological Methods, 7(1), 83--104. tools:::Rd_expr_doi("10.1037/1082-989X.7.1.83")

See Also

mediate to analyze the study this plans; ss_aipe_indirect_effect to plan for confidence interval width instead of detection; design_consequences for what the chosen design delivers.

Other mediation: mediate(), mediation_mbco()

Other sample size for power: power_fisher_exact(), ss_aipe_mixed_effects(), ss_power_R2(), ss_power_R2_sensitivity(), ss_power_c(), ss_power_c_ancova(), ss_power_composite_ancova(), ss_power_composite_ancova_2group(), ss_power_composite_anova(), ss_power_composite_factorial_ancova(), ss_power_composite_factorial_ancova_het(), ss_power_composite_factorial_anova(), ss_power_composite_sem(), ss_power_contrast(), ss_power_equivalence_c(), ss_power_factorial_ancova(), ss_power_factorial_anova(), ss_power_mixed_effects(), ss_power_one_way_anova(), ss_power_pcm(), ss_power_r(), ss_power_rc(), ss_power_reg_coef(), ss_power_reg_coef_sensitivity(), ss_power_rm_anova(), ss_power_sc(), ss_power_sem(), ss_power_smd(), ss_power_split_plot_anova()

Examples

# Fritz and MacKinnon's (2007) running scenario (a = b = .39). The
# joint significance approximation returns necessary_N = 65; raw-data
# simulation puts the power at N = 65 nearer .77 and reaches .80 near
# N = 70, which is why Fritz and MacKinnon's simulation-based table
# reports a somewhat larger requirement.
ss_power_indirect_effect(a = .39, b = .39, desired_power = .80)

# A near-zero a path against a larger b: the weak link drives the requirement.
ss_power_indirect_effect(a = .14, b = .39, desired_power = .80)

# Realized power at a given N, and the Sobel comparison (always lower).
ss_power_indirect_effect(a = .39, b = .39, N = 75)
ss_power_indirect_effect(a = .39, b = .39, N = 75, method = "sobel")