pwrss.z.med {pwrss}

Indirect Effect in Mediation Analysis (z, Joint, and Monte Carlo Tests)

Description

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

Formulas are validated using Monte Carlo simulation.

Usage

pwrss.z.med(a, b, cp = 0,
            sdx = 1, sdm = 1, sdy = 1,
            r2m.x = a^2 * sdx^2 / sdm^2,
            r2y.mx = (b^2 * sdm^2 + cp^2 * sdx^2) / sdy^2,
            n = NULL, power = NULL, alpha = 0.05,
            alternative = c("not equal", "less", "greater"),
            mc = TRUE, nsims = 1000, ndraws = 1000,
            verbose = TRUE)

Arguments

a

expected regression coefficient for X -> M path. One can use standardized regression coefficient, but should keep sdx = 1 and sdm = 1 or leave them out as they are default specifications

b

expected regression coefficient for M -> Y path. One can use standardized regression coefficient, but should keep sdm = 1 and sdy = 1 or leave them out as they are default specifications

cp

expected regression coefficient for X -> Y path (the direct path). One can use standardized regression coefficient, but should keep sdx = 1 and sdy = 1 or leave them out as they are default specifications

sdx

expected standard deviation of the predictor (X). For a binary predictor, sdx = sqrt(p*(1-p)) wherep is the proportion of subjects in one of the groups

sdm

expected standard deviation of the mediator (M)

sdy

expected standard deviation of the outcome (Y)

r2m.x

expected R-squared value for the mediator model (M ~ X). The default is r2m.x = a^2 * sdx^2 / sdm^2 assuming that X is the only predictor. Thus, an r2m.x below this value will throw a warning. To consider other covariates in the mediator model provide a value greater than the default

r2y.mx

expected R-squared value for the outcome model (Y ~ M + X). The default is r2y.mx = (b^2 * sdm^2 + cp^2 * sdx^2) / sdy^2 assuming that M and X are the only predictors. Thus, an r2y.mx below this value will throw a warning. To consider other covariates in the outcome model provide a value greater than the default

n

total sample size

power

statistical power (1-\beta)

alpha

probability of type I error

alternative

direction of the hypothesis test: "not equal", "greater", "less". It applies to all tests (for path 'a', 'b', and the indirect effect) and typically specified as "not equal". If path 'a' and 'b' have the opposite signs there will be a warning for "greater" or "less" tests (it can be ignored)

mc

logical; if TRUE, statistical power is based on monte carlo simulation

nsims

number of replications (applies when mc = TRUE)

ndraws

number of draws from the distribution of the path coefficients for each replication (applies when mc = TRUE)

verbose

if FALSE no output is printed on the console

Value

parms

list of parameters used in calculation

test

type of the statistical test (z test)

ncp

non-centrality parameter

power

statistical power (1-\beta)

n

total sample size

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

# with standardized coefficients

## statistical power
pwrss.z.med(a = 0.25, b = 0.25, cp = 0.10,
            alpha = 0.05, n = 200, mc = TRUE)

## minimum required sample size
pwrss.z.med(a = 0.25, b = 0.25, cp = 0.10,
            alpha = 0.05, power = 0.80)

## adjust for covariates in the outcome model
pwrss.z.med(a = 0.25, b = 0.25, cp = 0.10,
            r2y.mx = 0.50,
            alpha = 0.05, 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
pwrss.z.med(a = 0.40, b = 0.25, cp = 0.10,
            sdx = sqrt(p*(1-p)),
            alpha = 0.05, n = 200, mc = TRUE)

## minimum required sample size
pwrss.z.med(a = 0.40, b = 0.25, cp = 0.10,
            sdx = sqrt(p*(1-p)),
            alpha = 0.05, power = 0.80)

## adjust for covariates in outcome model
pwrss.z.med(a = 0.40, b = 0.25, cp = 0.10,
            r2y.mx = 0.50, sdx = sqrt(p*(1-p)),
            alpha = 0.05, power = 0.80)