multinomialOrder: Estimate the Number of Components in a Multinomial Mixture...

In tmanole/GroupSortFuse: Estimating the Number of Components in Finite Mixture Models

Description

Estimate the order of a finite mixture of multinomial models with fixed and known number of trials.

Usage

multinomialOrder(y, lambdas, K = NULL, ...)

Arguments

y	n by D matrix consisting of the data, where n is the sample size and D is the number of categories. The rows of y must sum to a constant value, taken to be the number of trials.
lambdas	Vector of tuning parameter values.
K	Upper bound on the true number of components. If K is NULL, at least one of the control parameters theta and pii must be non-NULL, and K is inferred from their number of columns.
...	Additional control parameters. See the Details section.

Details

The following is a list of additional control parameters.

• theta D by K matrix of starting values where each column is the vector of multinomial probabilities for one mixture component. The columns of theta should therefore sum to 1. If theta=NULL, the starting values are chosen using the MCMC algorithm described by Grenier (2016).

• pii Vector of size K whose elements must sum to 1, consisting of the starting values for the mixing proportions. If NULL, it will be set to a discrete uniform distribution with K support points.

• penalty Choice of penalty, which may be "SCAD", "MCP", "SCAD-LLA", "MCP-LLA" or "ADAPTIVE-LASSO". Default is "SCAD".

• mcmcIter Number of iterations for the starting value algorithm described by Grenier (2016).

• uBound Upper bound on the tuning parameter of the proximal gradient algorithm.

• C Tuning parameter for penalizing the mixing proportions.

• a Tuning parameter for the SCAD or MCP penalty. Default is 3.7.

• convMem Convergence criterion for the modified EM algorithm.

• convPgd Convergence criterion for the proximal gradient descent algorithm.

• maxMem Maximum number of iterations of the Modified EM algorithm.

• maxPgd Maximum number of iterations of the proximal gradient descent algorithm.

• verbose If TRUE, print updates while the function is running.

Value

An object with S3 classes gsf and multinomialGsf, consisting of a list with the estimates produced for every tuning parameter in lambdas.

References

Manole, T., Khalili, A. 2019. "Estimating the Number of Components in Finite Mixture Models via the Group-Sort-Fuse Procedure".

Grenier, I. (2016) Bayesian Model Selection for Deep Exponential Families. M.Sc. dissertation, McGill University Libraries.

Examples

 require(MM)
 data(pollen)
 set.seed(1)
 out <- multinomialOrder(pollen, K=12, lambdas=seq(0.1, 1.6, 0.2))
 tuning <- bicTuning(pollen, out)
 plot(out, eta=TRUE, gg=FALSE, opt=tuning$result$lambda)

tmanole/GroupSortFuse documentation built on Jan. 12, 2022, 10:37 p.m.