# Estimation causal effect under Assumption 7 in Ding et al. (2011)

### Description

Estimation causal effect under Assumption 6 in Ding et al. (2011) when the second order moment of the error term is not constant.

### Usage

1 2 |

### Arguments

`Z` |
A vector of the randomization variable. |

`A` |
A vector of the first mediator: whether a patient receives antidepressant medication. |

`M` |
A vector of the second mediator: whether a patient receives mental health therapy. |

`Y` |
A vector of the outcome of interest. |

`X` |
A matrix of all the covariates. |

`polydegree` |
The order of the polynomial function. |

`step1` |
The result of the first step estimation from homo_IV1. |

`truncate` |
Truncate the estimated Omega using a positive constant. |

`select` |
Using AIC or BIC for variable selection in the polynomial regression, the default is null. |

### Details

For background of the problem, see Ding et al. (2011).

### Value

`beta` |
beta coefficients of Z, A, M and AM. |

`phat ` |
proportion of randomization to the treatment group. |

`residual` |
residuals of the first step regression. |

`se` |
standard errors of beta coefficients. |

`zvalue` |
z-vlues of the beta coefficients. |

`pvalue` |
p-values of the beta coefficients. |

`CI` |
confidence intervals of the beta coefficients. |

`COV` |
covariance matrix of the beta coefficients. |

`ser` |
robust version of standard errors of beta coefficients. |

`zvaluer` |
robust version of z-vlues of the beta coefficients. |

`pvaluer` |
robust version of p-values of the beta coefficients. |

`CIr` |
robust version of confidence intervals of the beta coefficients. |

`COVr` |
robust version of covariance matrix of the beta coefficients. |

`N` |
sample size |

`G` |
G is defined in Ding et al. (2010). |

`W` |
W is defined in Ding et al. (2010). |

`Omegahat` |
Omegahat is is defined in Ding et al. (2010). |

### Author(s)

Peng Ding <dingyunyiqiu@163.com>

### References

Ding, P., Geng, Z. and Zhou, X. H. (2011). Identifying Causal Effect for Multi-Component Intervention Using Instrumental Variable Method: with A Case Study of IMPACT Data. Technical Report.

### Examples

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