Introduction

In social sciences, health sciences, and fields like banking and insurance, logistic regression remains a popular method for prediction and inference, especially when the outcome variable is binary. Logistic regression, a specific case of generalized linear models (GLMs), owes its popularity partly to its explainability and straightforward interpretation.

Logistic regression employs the logit link function, which maps probabilities to a linear combination of predictors. However, the logit link is not always the most suitable choice for certain situations.

Alternative link functions such as probit and cloglog (complementary log-log), which also belong to the exponential family, offer potential advantages. Although this article does not delve deeply into the mechanics of probit and cloglog, we emphasize their consideration in applied research since they are readily available in most statistical software packages. Let us compare the three link functions using a practical real-world dataset and analysis.

Dataset Overview

The analysis is based on data collected from 500 newborns at a London hospital. Each infant was evaluated for low birth weight (defined as less than 2500 grams). The binary outcome variable, lowbw, is coded as:

  • lowbw = 1: Low birth weight
  • lowbw = 0: Normal birth weight

Potential Influencing Factors The dataset includes the following predictors:

  • Sex of the infant (sex): 1 = Male, 2 = Female

  • Gestational age (weeks): Measured in weeks.

  • Mother’s age (age): Recorded in years.

  • Maternal hypertension (hyp): 1 = Mother has hypertension, 0 = Mother does not have hypertension

Objective

The goal is to examine the impact of maternal age and hypertension on the likelihood of low birth weight. Specifically, we aim to determine how these factors contribute to the probability of a newborn weighing less than 2500 grams.
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