Relevance To Chi-squared Fitting
Often, one wishes to select amongst competing models where the likelihood functions assume that the underlying errors are normally distributed (with mean zero) and independent. This assumption leads to model fitting.
For fitting, the likelihood is given by
- ,
where C is a constant independent of the model used, and dependent only on the use of particular data points. i.e. it does not change if the data do not change.
The AIC is therefore given by . As only differences in AIC are meaningful, the constant C can be ignored, allowing us to take for model comparisons. This form is often convenient, because most model-fitting programs produce as a statistic for the fit.
Another convenient form arises if the σi are assumed to be identical and the residual sum of squares (RSS) is available. Then we get AIC = n ln(RSS/n) + 2k + C, where again C can be ignored in model comparisons.
Read more about this topic: Akaike Information Criterion
Famous quotes containing the words relevance to, relevance and/or fitting:
“... whatever men do or know or experience can make sense only to the extent that it can be spoken about. There may be truths beyond speech, and they may be of great relevance to man in the singular, that is, to man in so far as he is not a political being, whatever else he may be. Men in the plural, that is, men in so far as they live and move and act in this world, can experience meaningfulness only because they can talk with and make sense to each other and to themselves.”
—Hannah Arendt (1906–1975)
“The most striking fault in work by young or beginning novelists, submitted for criticism, is irrelevance—due either to infatuation or indecision. To direct such an author’s attention to the imperative of relevance is certainly the most useful—and possibly the only—help that can be given.”
—Elizabeth Bowen (1899–1973)
“Eccentricity gives misfits a way of fitting in.”
—Mason Cooley (b. 1927)