Blog Posts on applied mathematics

Part 1: Ordered(Ordinal) Logistic Regression- Introduction by digital explorations on Mar 23, 2012Comment: draft! Use with caution! Final version will have this comment removed. Input data to ordinal logistic regression The response ordered categorical variable is assumed to have levels coded as 0, 1, ..., m-1. For example, in a Likert scale, SD(...

Python, Scipy:Multinomial logistic regression, determining coefficients with gradient vector and bfgs optimizer by digital explorations on Mar 16, 2012Latest update: March 17, 2012. I think the code is now correct. It was able to obtain the optimum value of the negative log likelihood function, using the gradient function and using the bfgs optimizer. We are very surprised that the former code in o...

Python, scipy: estimating multinomial logistic regression coefficients with lbfgs-b algorithm: Part 4 by digital explorations on Mar 14, 2012We continue from part 3, this time we use the limited memory bfgs bounded algorithm to determine the log likelihood coefficients of the multinomial or polytomous logistic regression model. The lbfgs algorithm is a fortran program written by Nocedal,...

Python, scipy:Multinomial logistic regression, a strange faulty implementation for determining coefficients with derivatives: Part 3 by digital explorations on Mar 12, 2012Computing the gradient vector for bfgs optimization with derivative Let us recall the formulas for the conditional probabilities of each level with reference level coded as zero. For simplicity , we assume that the response vector Y has three levels.

References for multinomial logistic regression by digital explorations on Mar 12, 2012I thought that the bfgs optimizer with a user specified gradient function (fprime) would be a fast method of solving the coefficients of the mlogit model. I may be wrong (gradient function is erroneous) but I have tried over and over again and the gr...

Python, scipy:Multinomial (polytomous, unordered) logistic regression: Part 1 by digital explorations on Mar 9, 2012Introduction We have written a Python module logistic.py and shown it in a previous post http://adorio-research.org/wordpress/?p=13229 for computing the coefficients of the basic logistic regression model which expects a dichotomous or binomial respo...

Python, scipy: basic logistic regression, updated with Null Deviance by digital explorations on Feb 28, 2012We are back to technical topics. Today we will discuss logistic regression, treating the most common case where the response or dependentb variable is a dichotomous, categorical variable. For example, one may have dead or alive, smoking or no smoking...

Python, scipy: basic logistic regression by digital explorations on Feb 28, 2012We are back to technical topics. Today we will discuss logistic regression, treating the most common case where the response or dependentb variable is a dichotomous, categorical variable. For example, one may have dead or alive, smoking or no smoking...

Python: Marquardt algorithm for nonlinear regression now at version 0.0.4! by digital explorations on Feb 5, 2012We have updated our old Python implementation of Marquardt algorithm for nonlinear least squares. The new version now offers three numerical derivative approximation formulas: Forward difference: Backward difference: Central difference: We have also...

Algebra: Solving inequalities involving absolute values by digital explorations on Dec 2, 2011We discuss the solution of inequalities involving absolute values where the inside expression is a linear function of x. Recall that the absolute value function is defined as For examples, |5| =|-5| = 5, |0|= 0. In the a...