# mmeln: mmeln : mixture of multivariate normal In giguerch/mmeln: Estimation of Multinormal Mixture Distribution

## Description

constructor for objects of class mmeln: mixture of multivariate normal

## Usage

 ```1 2``` ```mmeln(Y,G=2,p=dim(Y)[2],form.loc=NULL,X=NULL, form.mel=NULL,Z=NULL,cov="IND",equalcov=FALSE,param=NULL) ```

## Arguments

 `Y` A matrix containing the data used for estimation. This matrix may contains NA but it needs at least one observation per row.It's assumed that the missing mechanism is not related to the data under study (MAR: Missing At Random). `G` The number of groups in the mixture `p` Doesn't need to be specified. It's the dimension of the multivariate data (number of column in Y) `form.loc,X` Location design of the model. By default, the mean model is used where we estimate p mean in each group. Only one of these two parameters must be specified depending if the model is specified through a formula (See R documentation) or a design matrix. If you want to specify a different design for each group you must pass the arguments as a list. See examples below for further details. If a formula is used it must use variable of length p representing the design across time, for example : ~temps where temps=factor(1:4). If a design matrix is used, it must be of dimension p*k where k<=p `form.mel,Z` Mixture design of the model. Only one of these two parameters must be specified. The design is constant across groups. This is equivalent to multinomial regression `cov` Covariance type (for now only the CS structure is implemented). Enter either the type of covariance as a string or as numeric corresponding to the position in the following choices : 1)UN (general unstructured covariance),2 CS (Compound Symmetry with constant variance) ,3) UCS (Compound Symmetry with unconstant variance) ,4) AR1 (Auto-regressive of order 1 with constant variance), 5) UAR1 (Auto-regressive of order 1 with unconstant variance),6) IND: (diagonal structure with constant variance), 7) UIND (diagonal structure with unconstant variance) `equalcov` Logical value T/F indicating if the variance is equal across groups. Default to FALSE. `param` list of list of parameters. Usually not specified. The parameters should be estimated through the estim.mmeln function. param will look like this list(mu=list(mu1,mu2,...,mug) ,tau=c(tau1,...,tauk),sigma=list(sigma1,sigma2,...,sigmag)) where mui is the vector of location parameter in the group i and sigmai is the vector of location parameter in the group i for which the length must equal the number of column in the design matrix. Also sigmai is the vector of covariance parameters in the group i. Each covariance is parameterized in a vector containing first the distinct value of standard deviation and then the distinct value of correlation from top to bottom and left to right.

## Details

This object describes the way the mixture is design and permits a lot of different modelisation of the data. Many specific methods are associated with this class of objects: print, anova, logLik, post. Once a solution is find through the estim.mmeln function, the object is promoted to an object of class mmelnSOL but inherits of all the attributes and function of the mmeln class but gains is own print method. The attributes in a mmeln object should be accessed via adequate function inside the mmeln library except if handle by an advanced user.

## Value

Retourne un objet de type "mmeln" ayant les arguments suivants :

 `obj\$Y` The data matrix `obj\$Yl` A list of length N containing the data in each row without the NA value. `obj\$Yv` A list of length N indicating the column where there is valid data `obj\$G` The number of groups `obj\$p` Number of column in Y `obj\$pi` A vector where pi[i] is the number of observation in row i `obj\$N` Number of row in Y `obj\$M` Number of total observations sum_i=1^N(pi) `obj\$Xg` The list of location design matrices `obj\$pl` The number of location parameters `obj\$Z` Mixture design matrix `obj\$pm` The number of mixture parameters `obj\$cov` Covariance type `obj\$equalcov` logical value indicating if covariance is equal across group `obj\$pc` The number of covariance parameters

## Author(s)

Charles-Ãdouard GiguÃ¨re

## References

McLachlan, G. & Peel, D. (2000), Finite mixture models,Wiley

Bernard D. Flury (1997), A first course in multivariate statistics, Springer

Pinheiro JosÃ© C. & Bates Douglas M. (2000), Mixed-Effects Models in S and S-PLUS, Springer

M.S. Srivastava (2002), Methods of Multivariate Statistics, WILEY

 ```1 2 3 4 5 6``` ```data(exY) ### estimation of the parameters of the mixture temps <- 0:2 mmeln1 <- mmeln(Y, G = 3, form.loc = list(~temps, ~temps + I(temps^2), ~temps + I(temps^2)), form.mel = ~SEXE, cov = "CS") ```