flexCWM (version 1.0)

gcwm: Flexible Cluster-Weighted Modeling

Description

Run the Generalized Linear Gaussian Cluster-Weighted Model

Usage

gcwm (Y, X, familyY="Gaussian", k=2, ic=c("BIC", "AIC", "ICL"), mY=1, 
  method="Nelder-Mead", initialization="random.soft", start.z=NULL, 
  iter.max=1000, threshold=1.0e-04, loglikplot=FALSE, seed=NULL)

Arguments

Y

numerical vector for the response variable.

X

matrix for the covariates.

familyY

the exponential distribution used for Y|x in each cluster; it can be:

• "Gaussian"
• "Poisson"
• "Binomial"
• "Gamma"

Default value is "Gaussian".

k

a vector containing the numbers of clusters to be tried. The one with the lowest information criterion is selected. Default value is 2.

ic

the information criteria by which the best model is selected when lencgth(k)>1. Possible values are

• "BIC"
• "AIC"
• "ICL"

mY

When familyY="Binomial", it sets the sample size. Default value is 1 (Bernoulli distribution).

method

optimization method used in the M-step of the EM algorithm (see optim). Default value is "Nelder-Mead".

initialization

initialization strategy for the EM-algorithm. It can be:

• "random.soft"
• "random.hard"
• "manual"

Default value is "random.soft".

start.z

matrix of soft or hard classification: it is used only if initialization="manual".

iter.max

maximum number of iterations in the EM-algorithm. Default value is 200.

threshold

threshold for Aitken acceleration procedure. Default value is 1.0e-04.

loglikplot

if TRUE, the log-likelihood values against the iterations are plotted. Default value FALSE.

seed

the seed for the random number generator, when random initializations are used; if NULL, current seed is not changed. Default value is NULL.

Value

• This function returns a list of values related to the model selected. It contains:
• Y
  response variable
• X
  covariates
• familyY
  exponential distribution used for Y|x in each cluster
• p
  number of covariates
• k
  number of groups
• n
  sample size
• npar
  number of parameters
• mY
  sample size, used when familyY="Binomial"
• prior
  weights for the mixture components
• muX
  covariates means
• VarX
  covariates variances
• PX
  marginal distribution of X for each cluster
• beta
  regression coefficients
• muY
  mean of Y
• dispY
  dispersion parameter of Y
• VarFunY
  variance function of Y
• VarY
  variance of Y
• nuY
  when familyY="Gamma", the gamma distribution is parameterized according to muY and nuY (see McCullagh, P. and Nelder, J. 1989)
• PY
  conditional distribution of Y|x for each cluster
• iter.stop
  number of iterations performed in EM algorithm
• z
  matrix of posterior probabilities
• group
  classification vector
• loglik
  final log-likelihood value
• AIC
• BIC
• ICL
• call
  an object of class call

References

Ingrassia, S., Minotti, S. C., and Vittadini, G. (2012). Local statistical modeling via the cluster-weighted approach with elliptical distributions. Journal of Classification, 29(3), 363-401. Ingrassia, S., Minotti, S. C., Punzo, A., and Vittadini, G. (2012). Generalized linear Gaussian cluster-weighted modeling. arXiv.org e-print 1211.1171, available at: http://arxiv.org/abs/1211.1171. McCullagh, P. and Nelder, J. (1989). Generalized Linear Models. Chapman & Hall, Boca Raton, 2nd edition

See Also

flexCWM-package, tourism

Examples

data(tourism)
Y <- tourism$overnights
X <- tourism$attendance
res <- gcwm(Y=Y,X=X,k=1:4,seed=1)
plot(cbind(Y,X),col=res$best$group)