Optimal Initial Values in Maximum Likelihood Estimation of Logistic Regression Models

Seksiri Niwattisaiwong ； Komsan Suriya

《International Journal of Intelligent Technologies and Applied Statistics》 11卷2期 (2018/06) Pp. 143-153

https://doi.org/10.6148/IJITAS.201806_11(2).0006

摘要

This study investigates an optimization for the initial values of parameters in maximum likelihood estimation of logistic regression models, questioning whether the default of initial values set at zero in statistical software packages is the best setting. By employing quadratic interpolation, a search for other initial values is performed to find some points that may yield higher log-likelihood values. Some alternative initial values that maximize the log-likelihood are discovered through the series of experiments using the Newton-Raphson algorithm for the maximum likelihood analysis of logistic regression functions without constant terms. However, the estimated parameters of independent variables are close to those estimated by statistical software. This means zero is not the optimal initial value of parameters in maximum likelihood estimation of logistic regression. Indeed, many statistical software packages, though having initial values defaulted at zero, have come with an improved inner process for the estimation algorithm; they are able to deliver the parameters for independent variables that yield accurate maximum log-likelihood values. Given the relatively reliable results, the use of statistical software in maximum likelihood estimation of logistic regression remains relevant.

關鍵字

Logistic regression model ； Maximum likelihood method ； Optimal initial values ； Parameter estimation ； Optimization