Finding multinomial logistic regression coefficients using Newton’s method

Instead of using Solver, we can use Property 3 of Basic Concepts of Multinomial Logistic Regression to calculate the mutinomial logistic regression coefficients. In order to demonstrate how to use Newton’s method we initialize the coefficients with the result from Solver shown in Figure 2 of Finding Multinomial Logistic Regression Coefficients using Solver and perform one iteration using the equation in Property 3 of Basic Concepts of Multinomial Logistic Regression,

Newton iteration multinomial logistic

Figure 1 – One iteration of Newton’s Method

The key formulas used in Figure 1 are shown in Figure 2.

Newton multinomial logistic formulas

Figure 2 – Key formulas from Figure 1

If we set the initial values of coefficients to zeros then we can use Newton’s Method to find the values of the multinomial logistic regression coefficients (e.g. using the MLogitCoeff supplemental function described in Finding Multinomial Logistic Regression Coefficients) as shown in the following figures.

Multinomial logistic regression Newton

Figure 3 – Multinomial logistic regression using Newton’s Method (part 1)

Multinomial Logistic Newton's Method

Figure 4 – Multinomial logistic regression using Newton’s Method (part 2)

Multinomial logistic parameters Newton

Figure 5 – Multinomial logistic regression using Newton’s Method (part 3)

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