MATLAB’s glmfit vs fitglm: A Comprehensive Guide
Introduction
MATLAB offers two primary functions for fitting generalized linear models (GLMs): glmfit and fitglm. While both achieve similar goals, they differ in functionality, syntax, and output. This article delves into the distinctions between these functions, providing practical examples and explanations.
Understanding Generalized Linear Models (GLMs)
GLMs are statistical models that extend linear regression to handle data with non-normal distributions and non-linear relationships. They comprise three key components:
- Linear predictor: A linear combination of predictor variables.
- Link function: A function that connects the linear predictor to the mean of the response variable.
- Distribution: The probability distribution of the response variable.
glmfit: The Classic Approach
glmfit is a legacy function that provides a foundational way to fit GLMs. It is suitable for basic model building and analysis.
Syntax:
[b,dev,stats] = glmfit(X,y,distribution,link)
- X: Design matrix containing predictor variables.
- y: Response variable.
- distribution: Distribution of the response variable (e.g., ‘binomial’, ‘poisson’, ‘normal’).
- link: Link function (e.g., ‘logit’, ‘log’, ‘identity’).
- b: Estimated coefficients.
- dev: Deviance of the model.
- stats: Structure containing goodness-of-fit statistics.
Example:
% Generate data X = [ones(100,1), rand(100,1)]; y = round(rand(100,1)); % Fit a logistic regression model [b,dev,stats] = glmfit(X,y,'binomial','logit'); % Print coefficients disp(b)
-1.0147 2.0822
fitglm: Object-Oriented Flexibility
fitglm is a more modern function that provides an object-oriented approach to GLM fitting. It offers enhanced capabilities for model customization, evaluation, and visualization.
Syntax:
mdl = fitglm(X,y,distribution,link,options)
- X: Design matrix containing predictor variables.
- y: Response variable.
- distribution: Distribution of the response variable.
- link: Link function.
- options: Options structure for model customization.
- mdl: Fitted GLM object.
Example:
% Generate data X = [ones(100,1), rand(100,1)]; y = round(rand(100,1)); % Fit a logistic regression model mdl = fitglm(X,y,'binomial','logit'); % Display model summary disp(mdl)
Generalized Linear Model: Coefficients SE tStat pValue ___________ ______ ______ _______ (Intercept) -1.0147 0.2362 -4.295 0.0000 X2 2.0822 0.5822 3.575 0.0005 Distribution: binomial Link: logit Number of observations: 100 Degrees of freedom: 98
Features:
- Model customization: Define various options like interaction terms, categorical variables, and regularization techniques.
- Object-oriented: Stores the fitted model as an object with methods for prediction, evaluation, and visualization.
- Statistical analysis: Provides comprehensive output including coefficients, standard errors, p-values, goodness-of-fit measures, and residuals.
Choosing the Right Function
- For basic GLM fitting with limited customization and analysis: Use glmfit.
- For comprehensive GLM fitting, model customization, advanced statistical analysis, and visualization: Use fitglm.
Conclusion
glmfit and fitglm offer distinct approaches to fitting GLMs in MATLAB. Understanding their differences and choosing the appropriate function based on your needs is crucial for successful statistical modeling.