## Advanced Statistics - Biology 6030 |

## Bowling Green State University, Fall 2017 |

The **negative log-likelihood** is the negative log of the probability of an observed response. Minimizing the negative of a log-likelihood function thus produces maximum likelihood estimates for a particular effect.

First, the negative log-likelihood (i.e., uncertainty) is calculated for the case where no model is assumed (e.g., the probabilities are estimated at equal and fixed background rates). Then the negative log-likelihood (or uncertainty) is calculated after fitting the model.

The difference of these two negative log-likelihoods is the reduction due to fitting the model. Two times this value is the likelihood-ratio Chi-square test statistic. An advantage of the log-likelihood ratios is that log-likelihood terms are additive (see replicated goodness of fit tests).

An advantage of the log-likelihood ratios is that log-likelihood terms are additive (see replicated goodness of fit tests). Log-likelihood ratio can be used to assesses Goodness of Fit (G-test), similar to ChiΧ^{2} =Σ [(observed - expected)^{2}/expected]

G = -2Σ[observed * ln(observed/expected)]

The ratio refers to the maximum value of the likelihood function under the constraint of the null hypothesis to the maximum without that constraint.

last modified: 3/18/08

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