flexCWM (version 1.1)

glmcwm: Fit for the Generalized Linear Mixed CWM

Description

Maximum likelihood fitting of the Generalized Linear Mixed Cluster-Weighted Model by using the EM algorithm.

Usage

glmcwm (Y, Xcont=NULL, Xcate=NULL, m=NULL, familyY="Gaussian", k=2, 
  mY=1, method="Nelder-Mead", initialization="random.soft", start.z=NULL, 
  iter.max=1000, threshold=1.0e-04,loglikplot, seed=NULL)

Arguments

Y

numerical vector for the response variable.

Xcont

matrix for the continuous covariates.

Xcate

matrix for the categorical covariates.

m

number of levels for each categorical variable in Xcate (starting by 1).

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.

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
• Xcont,Xcate
  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", "AICc", "AICu", "AIC3", "AWE", "BIC", "CAIC", "ICL"
  Information criteria
• 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 <- glmcwm(Y=Y,Xcont=X,k=1:4,seed=1)