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PanelSummary

A panel fit's inference table and diagnostics, as linearmodels reports them.

public sealed class PanelSummary

Properties — the per-coefficient lists run constant, then regressors: Coefficients, StandardErrors, TStatistics, PValues, ConfidenceLower and ConfidenceUpper. CovarianceType, Debiased, Bandwidth (Driscoll-Kraay's, as given or as chosen, else null) and ConfidenceLevel echo how they were computed. HasConstant says whether the regressors hold a constant. ObservationCount is the regression's rows — entities for between, differences for first-difference — and EntityCount and PeriodCount the panel's. ResidualDegreesOfFreedom follows. RSquared is the regression's own; RSquaredWithin, RSquaredBetween and RSquaredOverall apply the coefficients to the entity-demeaned rows, the entity means and the rows as given. ModelTest is the homoskedastic F that every coefficient but the constant is zero, RobustModelTest the same under the chosen covariance, and PoolabilityTest fixed effects' F that the effects are zero, all WaldTests or null. ResidualVariance, EffectsVariance and Rho are the variance decomposition, for fixed and random effects; Theta is random effects' per-entity weight.

Example — the whole-model half of pooled least squares.

using Lodestar.Stats.Regression;
using Lodestar.Stats.Regression.Panel;

int[] entities = [1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4];
int[] periods = [2020, 2021, 2022, 2023, 2020, 2021, 2022, 2023, 2020, 2021, 2022, 2023, 2020, 2021, 2022, 2023];
double[] x = [0.5, 1.1, 1.9, 2.4, 1.2, 1.8, 2.9, 3.1, -0.3, 0.4, 0.8, 1.6, 2.0, 2.2, 3.1, 3.9];
double[] y = [2.1, 3.0, 4.2, 4.9, 4.4, 5.1, 6.8, 7.0, 0.2, 1.3, 1.7, 3.1, 6.1, 6.3, 7.9, 9.2];

var design = new PanelDesign(y, x, 1, entities, periods);

PanelSummary summary = PanelRegression.FixedEffects(design);

double overall = summary.RSquaredOverall;          // => 0.9287034786…
double between = summary.RSquaredBetween;          // => 0.9588515532…
double within = summary.RSquaredWithin;            // => 0.8127574405…
double f = summary.ModelTest!.Statistic;           // => 182.3630164…
int entityCount = summary.EntityCount;             // => 4

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 tests are F and the coefficients read Student's t with ResidualDegreesOfFreedom; otherwise χ² and the normal.

The per-coefficient lists are the fit's own arrays, taken and exposed as they are, not copied: a caller casting one back to its array and writing to it changes this summary, and every holder of the same array (#1305).

Applies to — net10.0, netstandard2.0.

See also — PanelRegression, PanelOptions.