Combining bias and variance to produce total MSE for treatment effect

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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 bvmat.

biassq.mat

Matrix of squared biases, with a structure similar to errmat.

which.min.vec

Value of calibration index (row number for errmat) with minimum MSE.

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.