---
title: "Information Criteria"
canonical: "https://modelassist.epixanalytics.com/space/EA/26586582/Information%20Criteria"
format: markdown
---
Information criteria are metrics that exist to help with selecting the 'best fitting' model when there are multiple 'candidate' models that have been fitted to data.

<span style="color: #222222">The conceptual thinking, and the math, behind the IC's is as follows:</span>

1. <span style="color: #222222">First, the IC's are based on </span><span style="color: #222222">[MLE methods](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575336)</span><span style="color: #222222">, and therefore measure how likely it is that the observed data came from the fitted model (e.g. a distribution, copula or time-series);</span>
2. <span style="color: #222222">Second, all IC's also have a term that 'penalizes' for the number of parameters that are used in the model that is fitted to the data. The idea here is that that, everything else being equal, a model that has fewer parameters (a simpler model) is preferable to a model that has many parameters and is therefore more complex.</span>

  


Compared to other [Goodness of Fit (GOF)](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575329) statistics, information criteria were developed later, but IC are generally preferred to other GOF statistics because:

1. Information criteria can be used when fitting distributions, copulas and time series to historical data (the [other GOF statistics](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575330) can only be used when fitting distributions to data);
2. Information criteria have a more intuitive and probabilistic interpretation than other GOF statistics;
3. Everything else being equal, information criteria prefer simpler models compared to more complex models

  


While there are many different IC's, the three most common are:

1. Akaike information criterion<span style="color: #222222"> (AIC)</span>
2. <span style="color: #222222">Bayesian information criterion (BIC), which is also called the Schwarz information criterion</span>
3. Hannan–Quinn information criterion, which is an alternative to the Akaike and Bayesian criterion

  


While Information Criteria are calculated by most software packages, understanding the calculations and steps to obtain MLE estimates, and how to calculate three different IC's, can help in interpreting them. Therefore, in the following Excel model, a Gamma distribution is fitted to a data set using an MLE approach. In addition, the model also shows how all three of the above mentioned IC's are calculated.

![LLH_Fit_and_ICs.xls]()