# Combining bias and variance to produce total MSE for treatment effect

### Description

Combining normalized bias and variance over a range of values for omitted R-squared to produce normalized MSE.

### Usage

1 | ```
mlr.combine.bias.variance(tr, bvmat, orsq.min = 0.001, orsq.max = 1, n.orsq = 100)
``` |

### Arguments

`tr` |
Binary treatment indicator vector (1=treatment, 0=control), whose coefficient in the linear regression model is TE. |

`bvmat` |
Matrix of bias and variances. First column must be bias, and second column must be variance. Each row corresponds to a different ‘calibration index’ or scenario, which we want to compare and find the best among them. |

`orsq.min` |
Minimum omitted R-squared used for combining bias and variance. |

`orsq.max` |
Maximum omitted R-squared. |

`n.orsq` |
Number of values for omitted R-squared generated in the vector. |

### Value

A list with the following elements:

`orsq.vec` |
Vector of omitted R-squared values used for combining bias and variance. |

`errmat` |
Matrix of MSE, with each row corresponding to an omitted R-squared value, and each column for a value of calibration index, i.e. one row if |

`biassq.mat` |
Matrix of squared biases, with a structure similar to |

`which.min.vec` |
Value of calibration index (row number for |

### Author(s)

Alireza S. Mahani, Mansour T.A. Sharabiani

### References

Link to a draft paper, documenting the supporting mathematical framework, will be provided in the next release.