Stats Regression ivsummary

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IvSummary

An instrumental-variables fit's inference table and diagnostics, as linearmodels reports them.

public sealed class IvSummary

Properties — the per-coefficient lists run constant, exogenous, endogenous: Coefficients, StandardErrors, TStatistics, PValues, ConfidenceLower and ConfidenceUpper. CovarianceType, Debiased, Bandwidth (the kernel's, as given or as chosen, else null) and ConfidenceLevel echo how they were computed. HasConstant says whether the regressors hold a constant, which centres RSquared; AdjustedRSquared and ResidualDegreesOfFreedom follow. ModelTest is the joint test that every coefficient but the constant is zero, a WaldTest. Kappa is the k-class parameter, null for GMM. FirstStage holds one IvFirstStage per endogenous regressor. Overidentification is Sargan's test for 2SLS and LIML and Hansen's J for GMM, null when the model is just identified.

Example — the whole-model half of the table.

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);

IvSummary summary = InstrumentalVariables.TwoStageLeastSquares(
    design, new IvOptions { Debiased = true });

double fit = summary.RSquared;                   // => 0.9961817721…
double overall = summary.ModelTest!.Statistic;   // => 1414.83778…
int? denominator = summary.ModelTest.DenominatorDegreesOfFreedom;  // => 9
double exogenousP = summary.PValues[1];          // => 0.3990498032…

Remarks — p-values are the precise tail. The reference computes 2 − 2·cdf, which returns zero below 1e-16; this returns the tail itself, and the two agree to 1e-15 absolute. Under Debiased the model test is an F and the coefficients read Student's t with ResidualDegreesOfFreedom; otherwise a χ² and the normal.

Applies to — net10.0, netstandard2.0.

See also — InstrumentalVariables, IvFirstStage.