AIC.moc {moc}R Documentation

Information Criterion for MOC models

Description

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 on object of class logLik containing the log-Likelihood,degrees of freedom and number of observations.

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

entropy.default the default method compute entropy and standardized entropy of a set of probablilities.

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

The entropy of a set of k probabilities (π_1,...,π_k) is computed as - sum( wt * post * log(post) ), it reaches its minimum of 0 when one of the π_i=1 (minimum uncertainty) and its maximum of log(k) when all the probabilities are equal π_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 sum and the 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).

Usage


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

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

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

Arguments

object,... Objects of class moc.
k can be any real number or the string "BIC".

Details

The computed value 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, entropy = - sum( wt * post * log(post) ) 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).

Value

A data frame with the relevant information for one or more objects is returned .

Note

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.

Author(s)

Bernard Boulerice <Bernard.Boulerice@umontreal.ca>

References

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

See Also

moc


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