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Fits one model and reports its inference table.

public static MultinomialLogitSummary Fit(ReadOnlySpan<double> design, ReadOnlySpan<int> response, int featureCount, MultinomialLogitOptions options = null)

Parameters — design is the regressors, row-major: featureCount values per row, with no constant column of your own. response is one category label per row: any integers, in any order, at least two distinct. featureCount is how many regressors each row carries. options chooses the intercept, the confidence level and Newton's budget and tolerance; null takes the reference's defaults.

Returns — MultinomialLogitSummary: the coefficients per non-reference category with their standard errors, z statistics, p-values and intervals, and the whole-model table.

Exceptions — ArgumentOutOfRangeException when featureCount is below one. ArgumentException when design is not a whole number of rows or response has another length, when the response holds fewer than two distinct labels, when no residual degree of freedom is left, or when the Hessian is not positive definite. A category the regressors separate perfectly and a regressor that is a combination of the others both land there; statsmodels returns NaN coefficients for the first and reports converged. InvalidOperationException when Newton spends its budget and MultinomialLogitOptions.ThrowOnNonConvergence says throw.

Example — the second category's equation, and the test against the constant-only model.

using Lodestar.Stats.Regression;

double[] design = [-0.8, -1.32, -0.25, 0.42, 1.14, 0.11, -0.55, -0.78, 0.75, 1.63, 0.27, -1.23,
                   -0.96, 1.6, 0.2, -1.73, -0.08, -1.16, -0.63, -0.49, -0.71, 0.55, -0.06, -0.59,
                   0.41, 0.83, -1.64, -0.26, -0.98, -0.17, -1.29, 0.02, -0.04, -0.3, -1.05, -0.4];
int[] response = [2, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 2,
                  0, 0, 2, 2, 2, 0, 2, 2, 1, 2, 2, 2];

MultinomialLogitSummary fit = MultinomialLogit.Fit(design, response, 1);

int reference = fit.Categories[0];                               // => 0
double slope = Math.Round(fit.Coefficients[1][1], 6);            // => -7.040761
double error = Math.Round(fit.StandardErrors[1][1], 6);          // => 2.76465
double ratio = Math.Round(fit.LikelihoodRatio, 6);               // => 33.328409

Coefficients[1] is the equation of Categories[2], label 2, against label 0: as the regressor rises, a row moves away from 2 towards 0.

Remarks — the categories are the labels sorted by value, and the smallest is the reference, as statsmodels sorts them. Relabelling while keeping the order changes nothing.

NullLogLikelihood is the closed form Σ nⱼ·log(nⱼ/n). statsmodels refits the constant-only model with an optimiser and lands up to 3e-10 from it, so PseudoRSquared and LikelihoodRatio agree with the reference to about that. The χ² tail amplifies the gap in LikelihoodRatioPValue to about 1e-8 (decision 0004).

ModelDegreesOfFreedom is (K − 1)·(J − 1) whether or not an intercept was fitted, where K is the number of columns fitted: the reference's df_model, which the likelihood-ratio p-value reads.

Applies to — net10.0, netstandard2.0.

See also — MultinomialLogitSummary, MultinomialLogitOptions.