Generalized Linear Model Part 2

MSE or Mean Squared Error

The square difference between an observation’s actual (target) and model’s fitted (estimated) values.

Squared-Loss or L² - Loss

MAE or Mean Absolute Error

The absolute difference between an observation’s actual (target) and model’s fitted (estimated) values

Absolute Loss or L¹ - Loss

RMSE or Root Mean Squared Error

The root of the mean squared error

MAPE or Mean Absolute Percentage Error

Measures the accuracy of predictions

Used the loss function in Regression Problems

The difference between MAE and MSE

MSE and RMSE are more sensitive and are affected more by more significant errors. They also both take into account Outliers

Conversely, MAE is less affected by larger errors as it gives equal weight to all errors. It focuses on the direction and consistency of the errors and is not affected by the presence of outliers.

Formula for MSE

Formula for MAE

Formula for MAPE

R² in Linear Regression

Calculated based on Residual Sum of Squares (SSR) and Total Sum of the Square (SST).

This approach relies on having continuous, normally distributed, dependent variables and residuals.

R² om GLM

Used since its error do not have to be normally distributed and dependent variables do not have to be continuous.

Pseudo R-Squared

Used for comparison

Used when comparing this to another of the same data, predicting the same outcome

The higher this is the better the model.

Commonly Used are: Efron’s, Mc Fadden’s, Nagekerke, Cox and Snell’s.

Used of Measures | Predictability and Accuracy

RMSE, MSE, MAE, and MAPE

Used for Measures | Explainability

Pseudo R-Squared

Identity Link

The mean of Y increases by B₁ when we increase x by 1 unit

Logarithmic Link

For every increase in X the mean of Y is multiplied by e^B₁

Inverse Link