power.z.mediation: Power Analysis for Indirect Effects in a Mediation Model (Z, Joint, and Monte Carlo Tests)

Description

Calculates power or sample size (only one can be NULL at a time) to test indirect effects in a mediation model (Z-Test, Joint Test, and Monte Carlo Interval Test). One can consider explanatory power of the covariates in the mediator and outcome model via specifying R-squared values accordingly. power.z.mediation() and power.z.med() are the same functions.

Formulas are validated using Monte Carlo simulations.

Usage

power.z.mediation(
  beta.a = NULL,
  beta.b = NULL,
  ab.ratio = 1,
  req.sign = "+",
  beta.cp = 0,
  sd.predictor = 1,
  sd.mediator = 1,
  sd.outcome = 1,
  r.squared.mediator = NULL,
  r.squared.outcome = NULL,
  n = NULL,
  power = NULL,
  alpha = 0.05,
  alternative = c("two.sided", "one.sided"),
  method = c("sobel", "aroian", "goodman", "joint", "monte.carlo"),
  n.simulation = 1000,
  n.draws = 1000,
  ceil.n = TRUE,
  verbose = 1,
  utf = FALSE
)
power.z.med(
  beta.a = NULL,
  beta.b = NULL,
  ab.ratio = 1,
  req.sign = "+",
  beta.cp = 0,
  sd.predictor = 1,
  sd.mediator = 1,
  sd.outcome = 1,
  r.squared.mediator = NULL,
  r.squared.outcome = NULL,
  n = NULL,
  power = NULL,
  alpha = 0.05,
  alternative = c("two.sided", "one.sided"),
  method = c("sobel", "aroian", "goodman", "joint", "monte.carlo"),
  n.simulation = 1000,
  n.draws = 1000,
  ceil.n = TRUE,
  verbose = 1,
  utf = FALSE
)

Value

parms: list of parameters used in calculation.
test: type of the statistical test ("Z-Test", "Joint Test", or "Monte Carlo Interval Test").
mean: mean of the alternative distribution.
sd: standard deviation of the alternative distribution.
null.mean: mean of the null distribution.
null.sd: standard deviation of the null distribution.
z.alpha: critical value(s).
power: statistical power \((1-\beta)\).
n: sample size.

Arguments

beta.a: regression coefficient for X -> M path. One can use standardized regression coefficient, but should keep sd.predictor = 1 and sd.mediator = 1 or leave them out as they are default specifications.
beta.b: regression coefficient for M -> Y path. One can use standardized regression coefficient, but should keep sd.mediator = 1 and sd.outcome = 1 or leave them out as they are default specifications.
ab.ratio: 'beta.a' / 'beta.b' ratio (can be negative) when minimum detectable effect is of interest (either beta.a or beta.b, or both).
req.sign: Sign of the indirect effect (beta.a * beta.b product), when minimum detectable effect is of interest (either beta.a or beta.b, or both)).
beta.cp: regression coefficient for X -> Y path (the direct path). One can use standardized regression coefficient, but should keep sd.predictor = 1 and sd.outcome = 1 or leave them out as they are default specifications.
sd.predictor: standard deviation of the predictor (X). For a binary predictor, sd.predictor = sqrt(p * (1 - p)) where p is the proportion of subjects in one of the groups.
sd.mediator: standard deviation of the mediator (M).
sd.outcome: standard deviation of the outcome (Y).
r.squared.mediator: R-squared value for the mediator model (M ~ X). The default is r.squared.mediator = beta.a ^ 2 * sd.predictor ^ 2 / sd.mediator ^ 2 assuming that X is the only predictor. Thus, an r.squared.mediator below this value will throw a warning. To consider other covariates in the mediator model provide a value greater than the default.
r.squared.outcome: R-squared value for the outcome model (Y ~ M + X). The default is r.squared.outcome = (beta.b ^ 2 * sd.mediator ^ 2 + beta.cp ^ 2 * sd.predictor ^ 2) / sd.outcome ^ 2 assuming that M and X are the only predictors. Thus, an r.squared.outcome below this value will throw a warning. To consider other covariates in the outcome model provide a value greater than the default.
n: integer; sample size.
power: statistical power, defined as the probability of correctly rejecting a false null hypothesis, denoted as \(1 - \beta\).
alpha: type 1 error rate, defined as the probability of incorrectly rejecting a true null hypothesis, denoted as \(\alpha\).
alternative: character; the direction or type of the hypothesis test: "two.sided" or "one.sided".
method: character; "sobel", "aroian", "goodman", "joint" or "monte.carlo". "joint" and "monte.carlo" methods can not be used for sample size calculation.
n.simulation: integer; number of replications (applies when method = "monte.carlo").
n.draws: integer; number of draws from the distribution of the path coefficients for each replication (applies when method = "monte.carlo").
ceil.n: logical; whether sample size should be rounded up. TRUE by default.
verbose: 1 by default (returns test, hypotheses, and results), if 2 a more detailed output is given (plus key parameters and definitions), if 0 no output is printed on the console.
utf: logical; whether the output should show Unicode characters (if encoding allows for it). FALSE by default.

Details

NOTE: The function pwrss.z.mediation() (or its alias pwrss.z.med()) are no longer supported. However, they will remain available as wrappers for the power.z.mediation function.

References

Aroian, L. A. (1947). The probability function of the product of two normally distributed variables. Annals of Mathematical Statistics, 18(2), 265-271.

Goodman, L. A. (1960). On the exact variance of products. Journal of the American Statistical Association, 55(292), 708-713.

MacKinnon, D. P., & Dwyer, J. H. (1993). Estimating mediated effects in prevention studies. Evaluation Review, 17(2), 144-158.

MacKinnon, D. P., Warsi, G., & Dwyer, J. H. (1995). A simulation study of mediated effect measures. Multivariate Behavioral Research, 30(1), 41-62.

Preacher, K. J., & Hayes, A. F. (2004). SPSS and SAS procedures for estimating indirect effects in simple mediation models. Behavior Research Methods, Instruments, & Computers, 36, 717-731.

Preacher, K. J., & Hayes, A. F. (2008). Asymptotic and resampling strategies for assessing and comparing indirect effects in multiple mediator models. Behavior Research Methods, 40, 879-891.

Sobel, M. E. (1982). Asymptotic intervals for indirect effects in structural equations models. In S. Leinhart (Ed.), Sociological methodology 1982 (pp. 290-312). Jossey-Bass.

Examples

Run this code

# with standardized coefficients

## statistical power
power.z.mediation(beta.a = 0.25,
            beta.b = 0.25,
            beta.cp = 0.10,
            n = 200)

## minimum required sample size
power.z.mediation(beta.a = 0.25,
            beta.b = 0.25,
            beta.cp = 0.10,
            power = 0.80)

## adjust for covariates in the outcome model
power.z.mediation(beta.a = 0.25,
            beta.b = 0.25,
            beta.cp = 0.10,
            r.squared.outcome = 0.50,
            power = 0.80)

# with binary predictor X such as treatment/control variable
# in this case standardized coefficients for path a and cp would be Cohen's d values

## statistical power
p <- 0.50 # proportion of subjects in one group
power.z.mediation(beta.a = 0.40,
            beta.b = 0.25,
            beta.cp = 0.10,
            sd.predictor = sqrt(p*(1-p)),
            n = 200)

## minimum required sample size
power.z.mediation(beta.a = 0.40,
            beta.b = 0.25,
            beta.cp = 0.10,
            sd.predictor = sqrt(p*(1-p)),
            power = 0.80)

## adjust for covariates in the outcome model
power.z.mediation(beta.a = 0.40,
            beta.b = 0.25, beta.cp = 0.10,
            r.squared.outcome = 0.50,
            sd.predictor = sqrt(p*(1-p)),
            power = 0.80)

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