AIC.moc {moc} | R Documentation |
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).
## S3 method for class 'moc': AIC(object,...,k=2) ## S3 method for class 'moc': logLik(object,...) ## S3 method for class 'moc': entropy(object,...)
object,... |
Objects of class moc . |
k |
can be any real number or the string "BIC". |
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).
A data frame with the relevant information for one or more objects is returned .
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@umontreal.ca>
McLachlan, G. and Peel, D. (2000) Finite mixture models,Wiley-Interscience, New York.