p-value from three-variable mediation analysis simulation

Simple 3-variable mediation analysis simulation to test the hypothesis that X -> Y is mediated by the relationship X -> M -> Y. Currently, M and Y are assumed to be continuous variables with Gaussian errors, while X may be continuous or dichotomous.

Usage

p_mediation(
  n,
  a,
  b,
  cprime,
  dichotomous.X = FALSE,
  two.tailed = TRUE,
  method = "wald",
  sd.X = 1,
  sd.Y = 1,
  sd.M = 1,
  gen_fun = gen_mediation,
  return_analysis = FALSE,
  ...
)

gen_mediation(
  n,
  a,
  b,
  cprime,
  dichotomous.X = FALSE,
  sd.X = 1,
  sd.Y = 1,
  sd.M = 1,
  ...
)

Arguments

n: total sample size unless dichotomous.X = TRUE, in which the value represents the size per group
a: regression coefficient for the path X -> M
b: regression coefficient for the path M -> Y
cprime: partial regression coefficient for the path X -> Y
dichotomous.X: logical; should the X variable be generated as though it were dichotomous? If TRUE then n represents the sample size per group
two.tailed: logical; should a two-tailed or one-tailed test be used?
method: type of inferential method to use. Default uses the Wald (a.k.a., Sobel) test
sd.X: standard deviation for X
sd.Y: standard deviation for Y
sd.M: standard deviation for M
gen_fun: function used to generate the required two-sample data. Object returned must be a data.frame with the columns "DV" and "group". Default uses gen_mediation to generate conditionally Gaussian distributed samples. User defined version of this function must include the argument ...
return_analysis: logical; return the analysis object for further extraction and customization?
...: additional arguments to be passed to gen_fun. Not used unless a customized gen_fun is defined

Value

a single p-value

Author

Phil Chalmers rphilip.chalmers@gmail.com

Examples


# joint test H0: a*b = 0
p_mediation(50, a=sqrt(.35), b=sqrt(.35), cprime=.39)
#> [1] 0.0002565864
p_mediation(50, a=sqrt(.35), b=sqrt(.35), cprime=.39, dichotomous.X=TRUE)
#> [1] 5.341437e-07

# return analysis model
p_mediation(50, a=sqrt(.35), b=sqrt(.35), cprime=.39, return_analysis=TRUE)
#> lavaan 0.6-21 ended normally after 1 iteration
#> 
#>   Estimator                                         ML
#>   Optimization method                           NLMINB
#>   Number of model parameters                         5
#> 
#>   Number of observations                            50
#> 
#> Model Test User Model:
#>                                                       
#>   Test statistic                                 0.000
#>   Degrees of freedom                                 0

# data generation properties
N <- 1000
dat <- gen_mediation(n = N, a = .8, b = -.7, cprime = .2,
           sd.X = 2, sd.Y = 3, sd.M = 2)
descript(dat) # specific SDs
#> # A tibble: 3 × 12
#>   VARS      n    mean    trim    sd    skew    kurt    min   P25     P50   P75
#>   <fct> <dbl>   <dbl>   <dbl> <dbl>   <dbl>   <dbl>  <dbl> <dbl>   <dbl> <dbl>
#> 1 X      1000  0.0345  0.0448  1.97 -0.0649 -0.169   -6.50 -1.24  0.0504  1.33
#> 2 M      1000 -0.0307 -0.0224  2.02 -0.0261 -0.184   -5.57 -1.43  0.0151  1.34
#> 3 Y      1000  0.0812  0.0713  2.98  0.0223 -0.0146 -10.3  -1.87 -0.0236  2.18
#> # ℹ 1 more variable: max <dbl>

# two-step regression-based estimates (not used)
lm(M ~ X, data=dat) |> coef()       # a
#> (Intercept)           X 
#> -0.05822562  0.79561851 
lm(Y ~ M + X, data=dat) |> coef()   # b and cprime
#> (Intercept)           M           X 
#>  0.05258074 -0.69532842  0.21069509 
lm(Y ~ X, data=dat) |> coef()       # c = cprime + a*b
#> (Intercept)           X 
#>  0.09306667 -0.34252107 

# same properties, but dichotomous X variable
dat <- gen_mediation(n = N, a = .8, b = -.7, cprime = .2,
           sd.X = 2, sd.Y = 3, sd.M = 2, dichotomous.X = TRUE)
descript(dat) # specific SDs
#> # A tibble: 3 × 12
#>   VARS      n   mean   trim    sd    skew    kurt   min     P25    P50   P75
#>   <fct> <dbl>  <dbl>  <dbl> <dbl>   <dbl>   <dbl> <dbl>   <dbl>  <dbl> <dbl>
#> 1 X      2000  2      2      2.00  0      -2.00    0     0       2      4   
#> 2 M      2000  1.58   1.59   2.00 -0.0107 -0.858  -3.75 -0.0453  1.56   3.23
#> 3 Y      2000 -0.720 -0.709  2.95 -0.0104 -0.0973 -9.56 -2.74   -0.669  1.26
#> # ℹ 1 more variable: max <dbl>

# two-step regression-based estimates (not used)
lm(M ~ X, data=dat) |> coef()       # a
#> (Intercept)           X 
#> -0.02934882  0.80493087 
lm(Y ~ M + X, data=dat) |> coef()   # b and cprime
#> (Intercept)           M           X 
#>  0.01563743 -0.61796916  0.12075761 
lm(Y ~ X, data=dat) |> coef()       # c = cprime + a*b
#> (Intercept)           X 
#>  0.03377409 -0.37666484 

# \donttest{

  # power to detect mediation
  p_mediation(n=50, a=sqrt(.35), b=sqrt(.35), cprime=.39) |>
    Spower(parallel=TRUE, replications=1000)
#> 
#> ── Spower Results ──────────────────────────────────────────────────────────────
#> 
#> Design conditions:
#> 
#> # A tibble: 1 × 4
#>       n cprime sig.level power
#>   <dbl>  <dbl>     <dbl> <lgl>
#> 1    50   0.39      0.05 NA   
#> 
#> Estimate of power: 0.997
#> 95% Confidence Interval: [0.994, 1.000]
#> Execution time (H:M:S): 00:00:22

  # sample size estimate for .95 power
  p_mediation(n=interval(50,200), a=sqrt(.35), b=sqrt(.35), cprime=.39) |>
    Spower(power=.95, parallel=TRUE)
#> 
#> ── Spower Results ──────────────────────────────────────────────────────────────
#> 
#> Design conditions:
#> 
#> # A tibble: 1 × 4
#>       n cprime sig.level power
#>   <dbl>  <dbl>     <dbl> <dbl>
#> 1    NA   0.39      0.05  0.95
#> 
#> Estimate of n: 51.0
#> 95% Confidence Interval: [NA, NA]
#> Execution time (H:M:S): 00:23:41

# }

p-value from three-variable mediation analysis simulation

Usage

Arguments

Value

See also

Author

Examples