Understanding AIC Information Criterion: What You Need to Know

Understanding AIC Information Criterion: What You Need to Know

AIC (Akaike Information Criterion) is a statistical measure used to assess the goodness of fit of a statistical model. It is one of the most popular methods of model selection. When it comes to selecting an appropriate statistical model, it is crucial to ensure that the chosen model displays good fit, and AIC criterion measures this.

Introduction

When working with statistical models, it’s essential to use a model that accurately represents the data at hand. Selecting an inappropriate model can lead to incorrect conclusions and poor predictions. One way to achieve this goal is through the use of information criteria, such as AIC, criteria that measure the quality of fit of statistical models relative to each other. This article aims to provide a comprehensive understanding of AIC information criterion to help you select the most suitable model for your data.

What is AIC?

AIC is a statistical measure that compares how well a given model fits the data relative to other models. It was introduced by Hirotugu Akaike in 1973 and has since been widely used in various fields, including economics, psychology, and engineering.

AIC is defined as

AIC= -2ln(L) + 2K

where L is the likelihood function, and K is the number of estimated parameters in the model. The minimum value of AIC indicates the best-fitting model.

It’s important to note that AIC is only relevant for comparing models that leverage the same response variable. Additionally, AIC only provides relative measures of model quality, which means it cannot be used to compare models between different datasets.

How does AIC Work?

AIC considers two factors when assessing the quality of the model: model complexity and fit. This criterion aims to strike a balance between these factors, with the aim of identifying the best-fitting model.

To assess model fit and complexity, AIC considers the magnitude of the residuals or errors. The residual is the difference between the predicted values from the model and actual values. If the residual is small, it indicates good fit. However, complex models tend to fit the training data but perform poorly in data outside the sample range. Hence, accounting for model complexity is important when selecting models.

To determine the relative quality of two models, the difference between their respective AIC values is computed. A smaller difference implies that the model with the lower AIC value is relatively better than the other model.

Example

Suppose we fit two linear regression models to predict the weight of a person using the person’s height. Model 1 assumes that the relationship between height and weight is linear, while model 2 assumes that the relationship is quadratic.

Model 1:

Weight = B0 + B1* Height + Error

Model 2:

Weight = B0 + B1* Height + B2* Height^2 + Error

We can apply AIC to these models to identify the best fitting model. Suppose that Model 1 has an AIC of 50, while Model 2 has an AIC of 55. Since Model 1 has a lower AIC value, we can conclude that it is the better model.

Advantages of Using AIC

1. AIC can handle a wide range of models, including complex models with numerous variables.

2. AIC does not make any assumptions about the underlying distribution of the data and is robust to violations of the assumptions associated with other methods.

3. AIC provides a straightforward means of comparing model quality given the same response variable.

Disadvantages of Using AIC

There are a few limitations to using the AIC method. These include:

1. AIC is not suitable for comparing models that are based on different response variables.

2. The likelihood model used to compute AIC assumes that the observations are independent and identically distributed. Deviations from these assumptions may lead to incorrect conclusions.

3. AIC tends to select overly complex models, even when simpler models may fit the data almost as well.

Conclusion

AIC is an effective measure used to compare statistical models and determine the quality of fit relative to other models. While it has limitations, including its sensitivity to the number of instances, AIC remains one of the most popular selection criteria in practical applications. By understanding how AIC works and its advantages and limitations, you can make informed decisions when selecting a model for your data.