FD.estimation: Flexible Dirichlet Estimation
In FlexDir: Tools to Work with the Flexible Dirichlet Distribution

Description Usage Arguments Details Value References See Also Examples

Estimates the vector of parameters of a Flexible Dirichlet distribution through an EM-based maximum likelihood approach.

1 2	FD.estimation(data, normalize = F, iter.initial.SEM = 50, iter.final.EM = 100, verbose = T)

`data`	a matrix or a dataframe containing only the variables in the model. Rows must sum to one, or `normalize` must be set `TRUE`.
`normalize`	if `TRUE`, each row of `data` will be divided by its own total to become a point of the simplex. Values in `data` must be positive.
`iter.initial.SEM`	number of iterations for the initial SEM step. Default to 50.
`iter.final.EM`	number of iterations for the final EM step. Default to 100.
`verbose`	if `TRUE`, the progression of the elaboration and the results will be printed on screen.

The procedure is made up of four stages:

Clustering: The algorithm applies many different clustering rules to the dataset, in order to exploit the specific cluster patterns that the parameter structure of the model involves.
Labelling: Once the initial partitions are obtained, group labeling needs to be established because any clustering algorithm assigns the group labels randomly, but the FD cluster structure entails a precise labelling scheme.
Initial SEM: A Stochastic E-M algorithm is applied at every initial partition and every possible label permutation identified.
Final E-M: The previous step must be seen as a multiple initialization strategy. At this point only the best one is selected and a final E-M algorithm is used to find the point that maximizes the likelihood of the parameter vector.

an object of class FDfitted. It's a list composed by:

alpha: Estimated values of the parameter vector Alpha
p: Estimated values of the parameter vector P
tau: Estimated value of the parameter Tau
logL: LogLikelihood
data: Normalized dataset

Ongaro, A. and Migliorati, S. (2013) A generalization of the Dirichlet distribution. Journal of Multivariate Analysis, 114, 412–426.

Migliorati, S., Ongaro, A. and Monti, G. S. (2016) A structured Dirichlet mixture model for compositional data: inferential and applicative issues. Statistics and Computing, doi:10.1007/s11222-016-9665-y.

FD.generate, FD.stddev, FD.aicbic, FD.barycenters, FD.ternaryplot, FD.rightplot, FD.marginalplot

data <- FD.generate(n=20,a=c(12,7,15),p=c(0.3,0.4,0.3),t=8)
data
results <- FD.estimation(data, normalize=TRUE,iter.initial.SEM = 5,iter.final.EM = 10)
results
summary(results)