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,
  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
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] 4.207593e-05
p_mediation(50, a=sqrt(.35), b=sqrt(.35), cprime=.39, dichotomous.X=TRUE)
#> [1] 4.246959e-09

# return analysis model
p_mediation(50, a=sqrt(.35), b=sqrt(.35), cprime=.39, return_analysis=TRUE)
#> lavaan 0.7-3 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
#>                                                       
#>   Browne's residual (NT model-based) test             
#>   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 × 11
#>   VARIABLE     n    mean     trim  median    sd   IQR     skew   kurt   min
#>   <fct>    <dbl>   <dbl>    <dbl>   <dbl> <dbl> <dbl>    <dbl>  <dbl> <dbl>
#> 1 X         1000 -0.0216  0.00440 0.0150   1.99  2.66 -0.139    0.147 -7.05
#> 2 M         1000 -0.0211 -0.00806 0.00147  2.03  2.69 -0.00522  0.243 -6.57
#> 3 Y         1000  0.105   0.0775  0.0595   3.06  4.02  0.0700  -0.150 -9.32
#> # ℹ 1 more variable: max <dbl>

# two-step regression-based estimates (not used)
lm(M ~ X, data=dat) |> coef()       # a
#>  (Intercept)            X 
#> -0.003213948  0.829169267 
lm(Y ~ M + X, data=dat) |> coef()   # b and cprime
#> (Intercept)           M           X 
#>  0.09293029 -0.78280809  0.21877855 
lm(Y ~ X, data=dat) |> coef()       # c = cprime + a*b
#> (Intercept)           X 
#>  0.09544619 -0.43030186 

# 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 × 11
#>   VARIABLE     n   mean   trim median    sd   IQR   skew   kurt    min   max
#>   <fct>    <dbl>  <dbl>  <dbl>  <dbl> <dbl> <dbl>  <dbl>  <dbl>  <dbl> <dbl>
#> 1 X         2000  2      2      2      2.00  4    0      -2.00    0     4   
#> 2 M         2000  1.62   1.61   1.61   1.98  3.13 0.0347 -0.744  -4.27  7.27
#> 3 Y         2000 -0.672 -0.687 -0.691  2.91  3.73 0.0308  0.189 -11.1  10.2 

# two-step regression-based estimates (not used)
lm(M ~ X, data=dat) |> coef()       # a
#> (Intercept)           X 
#>  0.05529227  0.78392957 
lm(Y ~ M + X, data=dat) |> coef()   # b and cprime
#> (Intercept)           M           X 
#>  0.07316201 -0.71660675  0.20905105 
lm(Y ~ X, data=dat) |> coef()       # c = cprime + a*b
#> (Intercept)           X 
#>   0.0335392  -0.3527182 

# \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 × 6
#>       n       a       b cprime sig.level power
#>   <dbl>   <dbl>   <dbl>  <dbl>     <dbl> <lgl>
#> 1    50 0.59161 0.59161   0.39      0.05 NA   
#> 
#> Estimate of power: 0.997
#> 95% Confidence Interval: [0.994, 1.000]
#> Execution time (H:M:S): 00:00:23

  # 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 × 6
#>       n       a       b cprime sig.level power
#>   <dbl>   <dbl>   <dbl>  <dbl>     <dbl> <dbl>
#> 1    NA 0.59161 0.59161   0.39      0.05  0.95
#> 
#> Estimate of n: 50.0
#> 95% Confidence Interval: [NA, NA]
#> Execution time (H:M:S): 00:25:54

# }

p-value from three-variable mediation analysis simulation

Usage

Arguments

Value

See also

Author

Examples