Stats Regression ivdesign

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IvDesign

An instrumental-variables problem's data: the response and its three row-major blocks with their widths.

public readonly ref struct IvDesign

Properties — Response is one value per row. Exogenous, Endogenous and Instruments are row-major blocks, ExogenousCount, EndogenousCount and InstrumentCount values per row: the regressors assumed uncorrelated with the error, the ones that are not, and the excluded instruments. Exogenous is empty and ExogenousCount zero when there are none. None of the blocks carries a constant column of its own: IvOptions.WithIntercept adds it.

Example — the same data described once and fitted twice.

using Lodestar.Stats.Regression;
using Lodestar.Stats.Regression.Instrumental;

double[] response = [3.1, 4.0, 5.2, 4.4, 6.9, 7.1, 6.0, 8.8, 9.1, 8.2, 10.7, 11.3];
double[] exogenous = [0.2, -1.0, 0.5, 1.3, -0.4, 0.9, -1.2, 0.1, 1.7, -0.6, 0.8, -0.3];
double[] endogenous = [1.0, 1.4, 2.1, 1.8, 3.0, 3.3, 2.6, 3.9, 4.2, 3.7, 4.9, 5.4];
double[] instruments =
    [0.9, 0.1, 1.5, -0.3, 2.2, 0.4, 1.7, 0.8, 3.1, -0.2, 3.3, 0.6,
     2.4, 1.1, 3.8, -0.5, 4.1, 0.9, 3.5, 0.2, 4.6, -0.1, 5.2, 0.7];

var design = new IvDesign(response, exogenous, 1, endogenous, 1, instruments, 2);

int rows = design.Response.Length;                  // => 12
double twoStage = InstrumentalVariables.TwoStageLeastSquares(design).Coefficients[2];  // => 1.9054825408…
double liml = InstrumentalVariables.Liml(design).Coefficients[2];                     // => 1.9021995…

Remarks — a ref struct, so the spans are read in place and a design lives no longer than the call it is passed to. The constructor checks nothing; the estimators refuse a block whose length is not its width times the rows, and fewer instruments than endogenous regressors.

Applies to — net10.0, netstandard2.0.

See also — InstrumentalVariables.