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Fits least squares with the chosen effects projected out, PanelOLS(y, x, entity_effects=…, time_effects=…).fit().

public static PanelSummary FixedEffects(PanelDesign design, PanelOptions options = null)

public static PanelSummary FixedEffects(PanelDesign design, ReadOnlySpan<int> clusters, PanelOptions options)

The second overload clusters by the caller's labels, alone or beside the entity or the period: its options must ask for PanelCovarianceType.Clustered.

Parameters — design is the response, the regressors and each row's entity and period, as a PanelDesign. clusters is one label per row. options chooses the effects, the covariance and the intercept; null takes the reference's defaults, which fit pooled least squares.

Returns — a PanelSummary whose PoolabilityTest is the F test that the effects are zero, null without effects.

Exceptions — ArgumentOutOfRangeException when ExogenousCount is below one or the confidence level is outside (0, 1). ArgumentException when a block's length is not its width times the rows, when two rows share an entity and a period, when no residual degree of freedom is left, when a Bartlett or Parzen bandwidth reaches past the periods, or when the options set a value this estimator does not read. ArgumentNullException when the clustered overload gets no options. ArgumentException too when clustering would run three ways. ArgumentException naming design also when the rows times the parameters plus one are more cells than one array holds, or when two-way effects need more dummy cells, rows by one fewer than the smaller side's levels, than one array holds (#1614).

Example — entity and time effects, clustered by entity.

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, new PanelOptions
{
    EntityEffects = true,
    TimeEffects = true,
    CovarianceType = PanelCovarianceType.Clustered,
    ClusterEntity = true,
});

double slope = summary.Coefficients[1];                 // => 1.804761904…
double error = summary.StandardErrors[1];               // => 0.1789687707…
int residualDf = summary.ResidualDegreesOfFreedom;      // => 8
double pooled = summary.PoolabilityTest!.Statistic;     // => 91.29621733…

Remarks — one effect is removed by demeaning; two are removed by demeaning the larger dimension and projecting out the other's dummies, as the reference does. With a constant the grand means go back in, so the constant survives. The effects count against the residual degrees of freedom, and against the covariance's scaling too — unless a single effect is nested in the clusters, which already absorb it: clustered by entity, entity effects are not counted twice.

Applies to — net10.0, netstandard2.0.

See also — PanelRegression.RandomEffects, PanelSummary.