Description Usage Arguments Details Value Author(s) References See Also Examples
Maximum likelihood fitting of the cluster-weighted model by the EM algorithm.
1 2 3 4 5 | cwm(formulaY = NULL, familyY = gaussian, data, Xnorm = NULL, Xbin = NULL,
Xpois = NULL, Xmult = NULL, modelXnorm = NULL, Xbtrials = NULL, k = 1:3,
initialization = c("random.soft", "random.hard", "kmeans", "mclust", "manual"),
start.z = NULL, seed = NULL, maxR = 1, iter.max = 1000, threshold = 1.0e-04,
eps = 1e-100, parallel = FALSE, pwarning = FALSE)
|
formulaY |
an optional object of class " |
familyY |
a description of the error distribution and link function to be used for the conditional distribution of Y in each mixture component. This can be a character string naming a
Default value is |
data |
an optional |
Xnorm, Xbin, Xpois, Xmult |
an optional matrix containing variables to be used for marginalization having normal, binomial, Poisson and multinomial distributions. |
modelXnorm |
an optional vector of character strings indicating the parsimonious models to be fitted for variables in |
Xbtrials |
an optional vector containing the number of trials for each column in |
k |
an optional vector containing the numbers of mixture components to be tried. Default value is |
initialization |
an optional character string. It sets the initialization strategy for the EM-algorithm. It can be:
Default value is |
start.z |
matrix of soft or hard classification: it is used only if |
seed |
an optional scalar. It sets the seed for the random number generator, when random initializations are used; if |
maxR |
number of initializations to be tried. Default value is 1. |
iter.max |
an optional scalar. It sets the maximum number of iterations in the EM-algorithm. Default value is 200. |
threshold |
an optional scalar. It sets the threshold for the Aitken acceleration procedure. Default value is 1.0e-04. |
eps |
an optional scalar. It sets the smallest value for eigenvalues of covariance matrices for |
parallel |
When |
pwarning |
When |
When familyY = binomial
, the response variable must be a matrix with two columns, where the first column is the number of "successes" and the second column is the number of "failures".
When several models have been estimated, methods summary
and print
consider the best model according to the information criterion in criterion
, among the estimated models having a number of components among those in k
an error distribution among those in familyY
and a parsimonious model among those in modelXnorm
.
This function returns a class cwm
object, which is a list of values related to the model selected. It contains:
call |
an object of class |
formulaY |
an object of class |
familyY |
the distribution used for the conditional distribution of Y in each mixture component. |
data |
a |
concomitant |
a list containing |
|
number of trials used for |
models |
a list; each element is related to one of the models fitted. Each element is a list and contains: |
posterior
posterior probabilities
iter
number of iterations performed in EM algorithm
k
number of (fitted) mixture components.
size
estimated size of the groups.
cluster
classification vector
loglik
final log-likelihood value
df
overall number of estimated parameters
prior
weights for the mixture components
IC
list containing values of the information criteria
converged
logical; TRUE
if EM algorithm converged
GLModels
a list; each element is related to a mixture component and contains:
model
a "glm
" class object.
sigma
estimated local scale parameters of the conditional distribution of Y, when familyY
is gaussian
or student.t
t_df
estimated degrees of freedom of the t distribution, when familyY
is student.t
nuY
estimated shape parameter, when familyY
is Gamma
. The gamma distribution is parameterized according to McCullagh & Nelder (1989, p. 30)
concomitant
a list with estimated concomitant variables parameters for each mixture component
normal.d, multinomial.d, poisson.d, binomial.d
marginal distribution of concomitant variables
normal.mu
mixture component means for Xnorm
normal.Sigma
mixture component covariance matrices for Xnorm
normal.model
models fitted for Xnorm
multinomial.probs
multinomial distribution probabilities for Xmult
poisson.lambda
lambda parameters for Xpois
binomial.p
binomial probabilities for Xbin
Mazza A., Punzo A., Ingrassia S.
Mazza, A., Ingrassia, S., and Punzo, A. (2018). flexCWM: A Flexible Framework for Cluster-Weighted Models. Journal of Statistical Software, 86(2), 1-30.
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., and Punzo, A. (2014). Model-based clustering via linear cluster-weighted models. Computational Statistics and Data Analysis, 71, 159-182.
Ingrassia, S., Punzo, A., and Vittadini, G. (2015). The Generalized Linear Mixed Cluster-Weighted Model. Journal of Classification, 32(forthcoming)
McCullagh, P. and Nelder, J. (1989). Generalized Linear Models. Chapman & Hall, Boca Raton, 2nd edition
Punzo, A. (2014). Flexible Mixture Modeling with the Polynomial Gaussian Cluster-Weighted Model. Statistical Modelling, 14(3), 257-291.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | ## an exemple with artificial data
data("ExCWM")
attach(ExCWM)
str(ExCWM)
# mixtures of binomial distributions
resXbin <- cwm(Xbin = Xbin, k = 1:2, initialization = "kmeans")
getParXbin(resXbin)
# Mixtures of Poisson distributions
resXpois <- cwm(Xpois = Xpois, k = 1:2, initialization = "kmeans")
getParXpois(resXpois)
# parsimonious mixtures of multivariate normal distributions
resXnorm <- cwm(Xnorm = cbind(Xnorm1,Xnorm2), k = 1:2, initialization = "kmeans")
getParXnorm(resXnorm)
## an exemple with real data
data("students")
attach(students)
str(students)
# CWM
fit2 <- cwm(WEIGHT ~ HEIGHT + HEIGHT.F , Xnorm = cbind(HEIGHT, HEIGHT.F),
k = 2, initialization = "kmeans", modelXnorm = "EEE")
summary(fit2, concomitant = TRUE)
plot(fit2)
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