Home › Stats-Regression › Multinomial logit

MultinomialLogitSummary

What a multinomial logit fit reports, at statsmodels parity.

public sealed class MultinomialLogitSummary

Properties:

• Categories: Categories is the distinct labels in ascending order; the first is the reference category.
• The coefficient table. Coefficients, StandardErrors, ZStatistics, PValues, ConfidenceLower and ConfidenceUpper are indexed by equation first, then by parameter. Equation j is Categories[j + 1] against Categories[0], and its first parameter is the intercept when one was fitted.
• The whole model:
  • LogLikelihood is the fitted log-likelihood.
  • NullLogLikelihood is the constant-only model's, in closed form.
  • PseudoRSquared is McFadden's 1 − LogLikelihood / NullLogLikelihood.
  • LikelihoodRatio is 2·(LogLikelihood − NullLogLikelihood), and LikelihoodRatioPValue its χ² tail on ModelDegreesOfFreedom.
  • Akaike and Bayesian count ModelDegreesOfFreedom + J − 1 parameters.
  • ModelDegreesOfFreedom is (K − 1)·(J − 1), and ResidualDegreesOfFreedom is n − ModelDegreesOfFreedom − (J − 1).
• The fit itself: HasIntercept, ConfidenceLevel, Converged and Iterations describe the fit that produced the table.

Example — the whole-model half of the table.

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 equations = fit.Coefficients.Count;       // => 2
int modelDegrees = fit.ModelDegreesOfFreedom; // => 2
int residualDegrees = fit.ResidualDegreesOfFreedom;  // => 32

Remarks — read Converged before the rest when ThrowOnNonConvergence was turned off: a table from a fit that spent its budget is plausible and wrong.

Applies to — net10.0, netstandard2.0.

See also — MultinomialLogit.Fit, MultinomialLogitOptions.