iclik 0.1.6a0

Information criteria for composite likelihood models

IClik is a minimal package for evaluating composite likelihood models using Composite Likelihood AIC and BIC (CLAIC/CLBIC).

For a review of these information criteria, please see: Ng, C. T., & Joe, H. (2014). Model comparison with composite likelihood information criteria. Bernoulli, 20(4), 1738–1764. http://www.jstor.org/stable/43590422

This package is in development. Please let me know about any bugs or problems by raising an issue on GitHub.

Available information criteria

Composite Likelihood AIC (CLAIC)

The composite likelihood version of the Akaike information criterion (AIC) was proposed by Varin et al (2011). It is calculated as:

\begin{equation*} CLAIC = -2L_{CL}(\hat\theta_{CL}) + 2tr[\mathbf{J}(\hat\theta_{CL})\mathbf{H}^{-1}(\hat\theta_{CL})] \end{equation*}

Where \(\mathbf{J(\theta)}\) and \(\mathbf{H(\theta)}\) are the Jacobian and Hessian matrices of the likelihood function, and \(\hat\theta_{CL}\) represents the composite maximum likelihood estimate.

Reference: Varin, C., Reid, N., & Firth, D. (2011). AN OVERVIEW OF COMPOSITE LIKELIHOOD METHODS. Statistica Sinica, 21(1), 5–42. http://www.jstor.org/stable/24309261

Composite Likelihood BIC (CLBIC)

CLBIC, formulated by Gao and Song (2010), is similar to CLAIC, but adjusts for sample size n:

\begin{equation*} CLBIC = -2L_{CL}(\hat\theta_{CL}) + log(n) tr[\mathbf{J}(\hat\theta_{CL})\mathbf{H}^{-1}(\hat\theta_{CL})] \end{equation*}

Reference: Gao, X., & Song, P. X.-K. (2010). Composite Likelihood Bayesian Information Criteria for Model Selection in High-Dimensional Data. Journal of the American Statistical Association, 105(492), 1531–1540. http://www.jstor.org/stable/27920184

Installation

IClik is available via PyPi: pip install iclik.

Syntax

IClik is very easy to use, provided that you have a correctly formulated likelihood function. A simple example of how to use it is provided here.

Import claic:

from iclik.inform_crit import claic

First we need to define a composite likelihood function.

def f(params):
    """I'm a composite likelihood function"""
    x, y, z = params
    return x**2 + y**2 + z**2

Running IClik is then a one-liner:

claic(f, (1,2,3))

Output:

-26.000000000000004