Linear Regression and Generalized Linear Models (GLM) are both statistical methods used for understanding the relationship between variables. Understanding the difference between GLM and Linear Regression is essential for accurate model selection, tailored to data types and research questions. It’s crucial for predicting diverse outcomes, ensuring valid statistical inference, and is vital in interdisciplinary research. In this blog, we will learn about the differences between Linear Regression and GLM by delving into their distinct characteristics, suitable applications, and the importance of choosing the right model based on data type and research objective.
Linear Regression and Generalized Linear Models (GLM) are two closely related statistical methods used for modeling the relationship between a dependent variable (response) and one or more independent variables (predictors). Here are the definitions for both GLM and Linear Regression:
The following is the list of key differences between GLM and Linear Regression:
Aspect | Linear Regression | Generalized Linear Models (GLM) |
---|---|---|
Response Variable Type | Continuous and normally distributed. | Can be various types: continuous, binary, count, etc. |
Relationship with Independent Variables | Linear relationship assumed. | Relationship defined by a link function, can be non-linear. |
Error Distribution | Errors are normally distributed with constant variance (homoscedasticity). | Distribution of errors can vary, not restricted to normal. Includes Poisson, binomial, etc. |
Model Flexibility | Less flexible, suitable for datasets where the response variable has a linear relationship with predictors. | More flexible, can model a wide range of data types and relationships. |
Use Cases | Suitable for predicting values where the response is a continuous measure (e.g., house prices). | Suitable for cases like binary outcomes (logistic regression), count data (Poisson regression), etc. |
Assumptions | Assumes linearity, homoscedasticity, and independence of errors. | More general, does not assume normal distribution of errors, and can handle heteroscedasticity. |
Link Function | No link function (identity link is implied). | Uses a link function to relate the mean of the response variable to the linear predictor (e.g., logit link for logistic regression). |
Python code | sklearn.linear_model.LinearRegression, statsmodels.api.OLS | sklearn.linear_model.LogisticRegression (for GLM with logistic link), statsmodels.api.GLM, statsmodels.api.Logit |
R code | lm() | glm() |
When deciding between Generalized Linear Models (GLM) and Linear Regression, consider the following three key points:
These criteria are fundamental in guiding the choice between GLM and Linear Regression, ensuring the selection of the most appropriate model for your data analysis needs.
Here are two unique examples for each, where GLM and Linear Regression would be most appropriate. These examples illustrate situations where the inherent characteristics of the data and the nature of the relationship between variables make either Linear Regression or GLM the more suitable choice for analysis.
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