Package dev.nm.stat.regression.linear.glm.quasi

Class QuasiGLMNewtonRaphson

  • All Implemented Interfaces:
    GLMFitting
    public class QuasiGLMNewtonRaphson
extends Object
implements GLMFitting
    The Newton-Raphson method is an iterative algorithm to estimate the β of the quasi GLM regression. It is a maximum likelihood method.
    See Also:
    • "P. J. MacCullagh and J. A. Nelder, "pp.327, An algorithm for fitting generalized linear models," in Generalized Linear Models, 2nd ed."
    • Wikipedia: Fitting

    • Constructor Detail

      • QuasiGLMNewtonRaphson

        public QuasiGLMNewtonRaphson​(double epsilon,
                             int maxIterations)
        Constructs an instance to run the Newton-Raphson method.
        Parameters:
        epsilon - a precision parameter: when a number |x| ≤ ε, it is considered 0
        maxIterations - the maximum number of iterations

    • Method Detail

      • fit

        public void fit​(GLMProblem problem,
                Vector beta0Initial)
        Description copied from interface: GLMFitting
        Fits a Generalized Linear Model.

        This method must be called before the three get methods.

        Specified by:
        fit in interface GLMFitting
        Parameters:
        problem - the generalized linear regression problem to be solved
        beta0Initial - initial guess for β^

      • betaHat

        public ImmutableVector betaHat()
        Description copied from interface: GLMFitting
        Gets the estimates of β, β^, as in
        E(Y) = μ = g-1(Xβ)
        Specified by:
        betaHat in interface GLMFitting
        Returns:
        β^

      • D

        public ImmutableMatrix D()
        Computes D.
        D = d(μ)/d(β) = (dμ/dη) * (dη/dβ)
        Returns:
        D

      • DVInv

        public ImmutableMatrix DVInv()
        Computes D / V(μ).
        Returns:
        D / V(μ)