## Understanding AIC: What is Information Criterion and How Does It Work?

Information criterion is a term that is widely used in statistical analysis to determine the best model fit for a given set of data. Essentially, it provides a way to measure the tradeoff between model complexity and accuracy. One of the most commonly used information criteria is the Akaike Information Criterion (AIC), which was developed by the Japanese statistician Hirotsugu Akaike in the 1970s. In this article, we will be discussing what AIC is and how it works.

## What is AIC?

AIC is a mathematical formula that measures the quality of a statistical model based on how well it fits the data and the number of parameters used in the model. Simply put, AIC is a measure of the goodness of fit of a model, adjusted for the number of parameters used.

The basic idea behind AIC is to find the model that not only fits the data well but also has the fewest parameters. This is because a model that is too complex may overfit the data, which means that it will fit the noise in the data as well as the signal. On the other hand, a model that is too simple may underfit the data, which means that it will not capture the important patterns and relationships in the data.

## How does AIC work?

AIC works by penalizing models that have more parameters. The formula for AIC is:

AIC = -2*log(L) + 2*k

where ‘L’ is the likelihood of the data given the model, and ‘k’ is the number of parameters in the model. The lower the AIC value, the better the model.

In practice, AIC is often used to compare several candidate models and choose the one with the lowest AIC value. To do this, one calculates the AIC value for each model and then selects the one with the lowest AIC value. This is known as model selection.

However, it is important to note that AIC is not an absolute measure of goodness of fit. Rather, it is a way to compare models and choose the one that provides the best balance of simplicity and fit.

## Examples

To illustrate AIC, let’s consider an example. Suppose we have a set of data points and we want to fit a polynomial to the data. We can fit polynomials of different degrees and then calculate the AIC value for each model. The model with the lowest AIC value is the best fit.

For instance, let’s say we fit polynomials of degree 1, 2, 3, and 4 and obtain the following AIC values: 100, 80, 120, and 150. The model with the lowest AIC value is the quadratic polynomial (degree 2) with an AIC value of 80. This means that the quadratic model provides the best fit to the data, while still being relatively simple.

## Conclusion

In conclusion, AIC is a useful tool in statistical analysis that can help researchers choose the best model fit for a given set of data. By balancing the complexity of the model with its accuracy, AIC provides a way to avoid overfitting or underfitting and find the best fit for the data. Understanding AIC is essential for anyone working with statistical models, and its application can be used in a variety of fields, including medicine, engineering, and social sciences.