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Fits least squares on the entity means, BetweenOLS(y, x).fit().

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

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

The second overload clusters the entities by the caller's labels, which must be constant within each entity.

Parameters — design is the panel. clusters is one label per row. options chooses the covariance and the intercept; null takes the reference's defaults.

Returns — a PanelSummary over one row per entity: ObservationCount is the entity count.

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 a cluster label varies inside an entity, or when the options ask for Driscoll-Kraay or for clusters by entity or period. ArgumentException naming design also when the rows times the parameters, or times the parameters plus one where no column is constant and the constant search appends one, are more cells than one array holds (#1614).

Example — the slope across entities rather than within them.

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.Between(design);

double slope = summary.Coefficients[1];      // => 2.686235759…
double error = summary.StandardErrors[1];    // => 0.1019030481…
int rows = summary.ObservationCount;         // => 4

Remarks — each entity counts once whatever its number of periods, as the reference weighs them. Clustered with no labels, each entity is its own cluster.

Applies to — net10.0, netstandard2.0.

See also — PanelRegression.FixedEffects.