This
web-page (JavaScript program) computes the power of between-model
likelihood ratio tests, where
power is defined as the probability of rejecting the null hypothesis
when it is false. A description
of an analytical-numerical approximation approach can be found in:

Burnham, K.P., D.R. Anderson, G.C. White, C. Brownie and K.H. Pollock.
1987. Design and Analysis Methods for Fish Survival Experiments Based
on Release-Recapture. Am. Fish. Soc. Monogr. 5, pages 216, 289-295.

The basic idea: Given the alternative model, H_{a}, is true, what is the probability that
the likelihood-ratio test will reject the null model, H_{o}? If H_{o}
is true, the power of the test should equal the significance level
α.

Data should be generated by computing expected values under the alternative model
for specified sample sizes,
compute estimates under the alternative and null models, then compute a likelihood-ratio
test between models. The likelihood-ratio test will give you the
χ² value and
degrees of freedom needed for the power analysis.

Specifically, the χ²
value approximates the noncentrality parameter of a noncentral
χ²
distribution, from which power is directly obtained.

The formula used by the program is:

POWER = 1 - CHINC(
a, DF ,χ² )

where CHINC is the non-central χ² cdf
and a is the critical value for a chi-square distribution at level, α.