Description Usage Arguments Details Value Note Author(s) References See Also Examples

View source: R/powerMediation.R

Calculate sample size for testing mediation effect based on Sobel's test.

1 2 3 4 5 6 7 8 9 10 | ```
ssMediation.Sobel(power,
theta.1a,
lambda.a,
sigma.x,
sigma.m,
sigma.epsilon,
n.lower = 1,
n.upper = 1e+30,
alpha = 0.05,
verbose = TRUE)
``` |

`power` |
power of the test. |

`theta.1a` |
regression coefficient for the predictor in the linear regression linking
the predictor |

`lambda.a` |
regression coefficient for the mediator in the linear regression linking
the predictor |

`sigma.x` |
standard deviation of the predictor. |

`sigma.m` |
standard deviation of the mediator. |

`sigma.epsilon` |
standard deviation of the random error term
in the linear regression linking
the predictor |

`n.lower` |
lower bound of the sample size. |

`n.upper` |
upper bound of the sample size. |

`alpha` |
type I error rate. |

`verbose` |
logical. |

The sample size is for testing the null hypothesis *θ_1λ=0*
versus the alternative hypothesis *θ_{1a}λ_a\neq 0*
for the linear regressions:

*
m_i=θ_0+θ_{1a} x_i + e_i, e_i\sim N(0, σ^2_e)*

*
y_i=γ+λ_a m_i+ λ_2 x_i + ε_i, ε_i\sim N(0, σ^2_{ε})
*

Test statistic is based on Sobel's (1982) test:

*
Z=\frac{\hat{θ}_{1a}\hat{λ_a}}{\hat{σ}_{θ_{1a}λ_a}}
*

where *\hat{σ}_{θ_{1a}λ_a}* is the estimated standard deviation
of the estimate *\hat{θ}_{1a}\hat{λ_a}* using multivariate
delta method:

*
σ_{θ_{1a}λ_a}=√{θ_{1a}^2σ_{λ_a}^2+λ_a^2σ_{θ_{1a}}^2}
*

and
*σ_{θ_{1a}}^2=σ_e^2/(nσ_x^2)* is the
variance
of the estimate *\hat{θ}_{1a}*, and
*σ_{λ_a}^2=σ_{ε}^2/(nσ_m^2(1-ρ_{mx}^2))*
is the variance
of the estimate *\hat{λ_a}*, *σ_m^2* is the variance of the
mediator *m_i*.

From the linear regression *m_i=θ_0+θ_{1a} x_i+e_i*, we have the
relationship *σ_e^2=σ_m^2(1-ρ^2_{mx})*. Hence, we can simply
the variance *σ_{θ_{1a}, λ_a}* to

*
σ_{θ_{1a}λ_a}=√{θ_{1a}^2\frac{σ_{ε}^2}{nσ_m^2(1-ρ_{mx}^2)}+λ_a^2\frac{σ_{m}^2(1-ρ_{mx}^2)}{nσ_x^2}}*

`n ` |
sample size. |

`res.uniroot ` |
results of optimization to find the optimal sample size. |

The test is a two-sided test. For one-sided tests, please double the
significance level. For example, you can set `alpha=0.10`

to obtain one-sided test at 5% significance level.

Weiliang Qiu stwxq@channing.harvard.edu

Sobel, M. E.
Asymptotic confidence intervals for indirect effects in structural equation models.
*Sociological Methodology*. 1982;13:290-312.

`powerMediation.Sobel`

,
`testMediation.Sobel`

1 2 3 | ```
ssMediation.Sobel(power=0.8, theta.1a=0.1701, lambda.a=0.1998,
sigma.x=0.57, sigma.m=0.61, sigma.epsilon=0.2,
alpha = 0.05, verbose = TRUE)
``` |

```
[1] 324.5108
```

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