See Details for a description of the individual functions.
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## S3 method for class 'mixmod' logLik(object, ...) ## S3 method for class 'mixmod' qval(x, map=FALSE, ...) ## S3 method for class 'mixmod' qfun(x, map=FALSE, ...) ## S3 method for class 'mdmixmod' qfun(x, map=FALSE, ...) ## S3 method for class 'mixmod' aic(x, ...) ## S3 method for class 'mixmod' bic(x, ...) ## S3 method for class 'mixmod' entropy(x, map=FALSE, ...) ## S3 method for class 'mixmod' iclbic(x, map=FALSE, ...) ## S3 method for class 'mdmixmod' siclbic(x, map=FALSE, ...)
an object of class
logLik calculates L(theta|X), the log-likelihood of the estimated parameters theta with respect to the observed data X, while
qval calculates the “Q-value”, the expectation with respect to the hidden data of the log-likelihood with respect to the complete data: Q(theta) = E[L(theta|X,Y)] for
mixmod and Q(theta) = E[L(theta|X,Y,Y0)] for
qfun returns the hidden and observed portions of the Q-value separately, as elements of a vector.
siclbic calculate various information criteria for model selection with mixture models of class
mdmixmod. These criteria are Akaike's information criterion (AIC, Akaike, 1974), the Bayes information criterion (BIC, Schwarz, 1978), the classification entropy (Biernacki et al., 2000), the integrated complete likelihood BIC (ICL-BIC, Biernacki et al., 2000), and the simplified ICL-BIC (SICL-BIC) for objects of class
mdmixmod, respectively. They are defined as follows:
|AIC||=||2 L(theta|X) - 2 |Theta||
|BIC||=||2 L(theta|X) - |Theta| log(N)|
|entropy||=||2 L(theta|X) - 2 Q(theta)|
|ICL-BIC||=||2 Q(theta) - |Theta| log(N)|
|SICL-BIC||=|| 2 E[L(theta|X,Y0)] - |Theta| log(N) (
where |Theta| is the size of the parameter space and N is the size of the data. Generally, the model which provides the highest value of any information criterion should be selected. Current testing indicates that ICL-BIC is preferred for
mixmod and BIC for
A numeric vector for
qfun, a numeric scalar for the other functions.
Some authors define AIC, BIC, and ICL-BIC as the negative of the quantities given in Details.
Akaike, H. (1974) A new look at the statistical model identification, IEEE Transactions on Automatic Control 19(6), 716–723.
Biernacki, C. and Celeux, G. and Govaert, G. (2000) Assessing a mixture model for clustering with the integrated completed likelihood, IEEE Transactions on Pattern Analysis and Machine Intelligence 22(7), 719–725.
McLachlan, G.J. and Thriyambakam, K. (2008) The EM Algorithm and Extensions, John Wiley & Sons.
Schwarz, G. (1978) Estimating the dimension of a model, The Annals of Statistics 6(2), 461–464.
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