MATLAB provides powerful tools for statistical analysis and modeling, particularly for fitting generalized linear models (GLMs). The two primary functions available for this purpose are glmfit and fitglm . While both functions can be used to fit generalized linear models, they differ in terms of functionality, flexibility, and ease of use. This article explores these differences in detail, complete with technical explanations and examples.

Understanding Generalized Linear Models (GLMs)

Generalized Linear Models are a broad class of models that include linear regression, logistic regression, Poisson regression, and many others. GLMs consist of three components:

1. Random Component: Specifies the probability distribution of the response variable.
2. Systematic Component: A linear predictor that is a function of the explanatory variables.
3. Link Function: Connects the expected value of the response variable to the linear predictor.

glmfit

: Function Overview

The glmfit function in MATLAB is a low-level function used for fitting generalized linear models. It provides flexibility in terms of model specification but requires more detailed inputs from the user. Here's a basic usage example:

• Flexibility: Allows specification of distribution ('normal', 'binomial', 'Poisson', etc.) and link function ('identity', 'logit', 'probit', etc.).
• Output Details: Outputs coefficient estimates, deviance, and a structure containing standard errors, t-statistics, and p-values.
• Customization: More parameters can be passed for further customization such as offset and weights.
• Ease of Use: Simplifies the model fitting process using high-level syntax and automatic handling of design matrices.
• Integrated Functionality: Works seamlessly with MATLAB tables and supports formula syntax for model specification.
• Enhanced Output: Returns a CompactGeneralizedLinearModel object with methods for prediction, diagnostics, and visualization.
• Fine-Grained Control: When you need precise control over the model specification, such as when using non-standard link functions or distributions.
• Programming Efficiency: If you are comfortable with MATLAB's matrix operations and seek a lightweight function for execution speed.
• Older Scripts: For backward compatibility with older MATLAB codebases.
• Exploratory Data Analysis: When rapid iteration and experimentation are needed, especially with dataset tables.
• Rich Model Output: If you require easy access to model properties, diagnostics, and prediction functions.
• Integration with Other Tools: When leveraging MATLAB's broader data analysis and visualization capabilities.