Automatic Fitting of Mixtures of Conjugate Distributions to a Sample

Fitting a series of mixtures of conjugate distributions to a sample, using Expectation-Maximization (EM). The number of mixture components is specified by the vector Nc. First a Nc[1] component mixture is fitted, then a Nc[2] component mixture, and so on. The mixture providing the best AIC value is then selected.

Usage

automixfit(sample, Nc = seq(1, 4), k = 6, thresh = -Inf, verbose = FALSE, ...)

Arguments

sample: Sample to be fitted by a mixture distribution.
Nc: Vector of mixture components to try out (default seq(1,4)).
k: Penalty parameter for AIC calculation (default 6)
thresh: The procedure stops if the difference of subsequent AIC values is smaller than this threshold (default -Inf). Setting the threshold to 0 stops automixfit once the AIC becomes worse.
verbose: Enable verbose logging.
...: Further arguments passed to mixfit, including type.

Value

As result the best fitting mixture model is returned, i.e. the model with lowest AIC. All other models are saved in the attribute models.

Details

The type argument specifies the distribution of the mixture components, and can be a normal, beta or gamma distribution.

The penalty parameter k is 2 for the standard AIC definition. Collet (2003) suggested to use values in the range from 2 to 6, where larger values of k penalize more complex models. To favor mixtures with fewer components a value of 6 is used as default.

References

Collet D. Modeling Survival Data in Medical Research. 2003; Chapman and Hall/CRC.

Examples

# random sample of size 1000 from a mixture of 2 beta components
bm <- mixbeta(beta1=c(0.4, 20, 90), beta2=c(0.6, 35, 65))
bmSamp <- rmix(bm, 1000)

# fit with EM mixture models with up to 10 components and stop if
# AIC increases
bmFit <- automixfit(bmSamp, Nc=1:10, thresh=0, type="beta")
bmFit
#> EM for Beta Mixture Model
#> Log-Likelihood = 1099.367
#> 
#> Univariate beta mixture
#> Mixture Components:
#>   comp1     comp2    
#> w  0.586131  0.413869
#> a 33.422658 18.251968
#> b 61.784396 82.825370

# advanced usage: find out about all discarded models
bmFitAll <- attr(bmFit, "models")

sapply(bmFitAll, AIC, k=6)
#>         2         3         1 
#> -2168.735 -2150.802 -1871.069