select: Finite Mixture Model Selection by Information Criterion
In mixR: Finite Mixture Modeling for Raw and Binned Data

Description Usage Arguments Details Value See Also Examples

This function selects the best model from a candidate of mixture models based on the information criterion BIC.

select(
  x,
  ncomp,
  family = c("normal", "weibull", "gamma", "lnorm"),
  mstep.method = c("bisection", "newton"),
  init.method = c("kmeans", "hclust"),
  tol = 1e-06,
  max_iter = 500
)

`x`	a numeric vector for raw data or a three-column matrix for the binned data
`ncomp`	a vector of positive integers specifying the number of components of the candidate mixture models
`family`	a character string specifying the family of the mixture model. It can only be one element from `normal`, `weibull`, `gamma` or `lnorm`.
`mstep.method`	a character string specifying the method used in M-step of the EM algorithm when fitting weibull or gamma mixture models. It can be either `bisection` or `newton`. The default is `bisection`.
`init.method`	a character string specifying the method used for providing initial values for the parameters for EM algorithm. It can be one of `kmeans` or `hclust`. The default is `kmeans`
`tol`	the tolerance for the stopping rule of EM algorithm. It is the value to stop EM algorithm when the two consecutive iterations produces loglikelihood with difference less than `tol`. The default value is 1e-6.
`max_iter`	the maximum number of iterations for the EM algorithm (default 500).

By specifying different number of components, the function select fits a series of mixture models for a given family, and a mixture model with minimum value of BIC is regarded as the best.

The function returns an object of class selectEM which contains the following items.

`ncomp`	the specified number of components of the candidate mixture models
`equal.var`	a logical vector indicating whether the variances of each component in each mixture model are constrained to be the same (only for `normal` family)
`bic`	the value of BIC for each mixture model
`best`	an indicator of the best model
`family`	the family of the mixture model

plot.selectEM, bs.test, mixfit

## selecting the optimal normal mixture model by BIC
set.seed(105)
x <- rmixnormal(1000, c(0.3, 0.4, 0.3), c(-4, 0, 4), c(1, 1, 1))
hist(x, breaks = 40)
ret <- select(x, ncomp = 2:5)
## [1] "The final model: normal mixture (equal variance) with 3 components"

## (not run) selecting the optimal Weibull mixture model by BIC
## set.seed(106)
## x <- rmixweibull(1000, c(0.3, 0.4, 0.3), c(2, 5, 8), c(0.7, 0.6, 1))
## ret <- select(x, ncomp = 2:5, family = "weibull")
## [1] "The final model: weibull mixture with 3 components"

## (not run) selecting the optimal Gamma mixture model by BIC
## set.seed(107)
## x <- rmixgamma(1000, c(0.3, 0.7), c(2, 5), c(0.7, 1))
## ret <- select(x, ncomp = 2:5, family = "gamma")
## [1] "The final model: gamma mixture with 2 components"


## (not run) selecting the optimal lognormal mixture model by BIC
## set.seed(108)
## x <- rmixlnorm(1000, c(0.2, 0.3, 0.2, 0.3), c(4, 7, 9, 12), c(1, 0.5, 0.7, 1))
## ret <- select(x, ncomp = 2:6, family = "lnorm")
## [1] "The final model: lnorm mixture with 4 components"