AIC.moc: Information criterions for MOC models.
In moc: General Nonlinear Multivariate Finite Mixtures

Description Usage Arguments Details Value Note Author(s) References See Also

View source: R/moc.R

AIC.moc generates a table of \log(Likelihood), AIC, BIC, ICL-BIC and entropy values along with the degrees of freedom of multiple moc objects.

logLik returns an object of class logLik containing the \log(Likelihood), degrees of freedom and number of observations.

loglike.moc computes the \log(Likelihood) of a moc object evaluated at the supplied parameters values, contrary to logLik above which uses the estimated parameter values. It gives the option to re-evaluate the model in which case the supplied parameter values are used as new starting values.

entropy is a generic method to compute the entropy of sets of probabilities.

The entropy of a set of k probabilities (p_1,…,p_k) is computed as entropy = - Sum_i( p_i * \log(p_i) ), it reaches its minimum of 0 when one of the p_i=1 (minimum uncertainty) and its maximum of \log(k) when all probabilities are equal to p_i = 1/k (maximum uncertainty). Standardized entropy is just entropy/\log(k) which lies in the interval [0,1]. The total and mean mixture entropy are the weighted sum and mean of the mixture probabilities entropy of all subjects. These are computed for both the prior (without knowledge of the response patterns) and the posterior mixture probabilities (with knowledge of the responses).

The default method entropy.default compute entropy and standardized entropy of a set of probabilities.

entropy.moc generates a table containing weighted total and mean standardized entropy of prior and posterior mixture probabilities of moc models.

## S3 method for class 'moc'
AIC(object, ..., k = 2)

## S3 method for class 'moc'
logLik(object, ...)

loglike.moc(object, parm = object$coef, evaluate = FALSE)

## S3 method for class 'moc'
entropy(object, ...)

`object, ...`	Objects of class `moc`.
`k`	Can be any real number or the string "BIC".
`parm`	Parameters values at which the \log(Likelihood) is evaluated.
`evaluate`	Boolean indicating whether re-evaluation of the model is desired. If `TRUE` `parm` will be used as new starting values.

The computed value in AIC.moc is -2*\log(Likelihood) + k*npar. Specific treatment is carried for BIC (k = \log(nsubject*nvar)), AIC (k = 2) and \log(Likelihood) (k = 0). Setting k = "BIC", will produce a table with BIC, mixture posterior entropy = - \Sum_i_k( wt[i] * post[i,k] * \log(post[i,k]) ) which is an indicator of mixture separation, df and ICL-BIC = BIC + 2 * entropy which is an entropy corrected BIC, see McLachlan, G. and Peel, D. (2000) and Biernacki, C. et al. (2000).

AIC.moc returns a data frame with the relevant information for one or more moc objects.

The likelihood methods works on a single moc object: logLik.moc returns an object of class logLik with attributes df, nobs and moc.name while loglike.moc returns a matrix containing \log(Likelihood) and corresponding estimated parameters with attributes moc.name and parameters.

entropy.moc returns a data.frame with number of groups, total and mean standardized prior and posterior entropy of multiple moc objects. The percentage of reduction from prior to posterior entropy within a model is also supplied.

Be aware that degrees of freedom (df) for mixture models are usually useless (if not meaningless) and likelihood-ratio of apparently nested models often doesn't converge to a Chi-Square with corresponding df.

Bernard Boulerice <bernard.boulerice.bb@gmail.com>

McLachlan, G. and Peel, D. (2000) Finite mixture models, Wiley-Interscience, New York.

Biernacki, C., Celeux, G., Govaert, G. (2000) Assessing a Mixture Model with the Integrated Completed Likelihood, IEEE Transaction on Pattern Analysis and Machine Learning, 22, pp. 719–725.

moc, confint.moc, profiles.postCI, entropyplot.moc, npmle.gradient