Package mixAK

This package contains a mixture of statistical methods including the MCMC methods to analyze normal mixtures. Methods from the following areas can be found here

• Density estimation via normal mixtures and MCMC
• Multivariate generalized linear mixed models with a normal mixture in the distribution of random effects
• Univariate distributions
• Multivariate distributions
• Miscellaneous random number generation
• Matrix linear algebra
• Basic statistics
• Utilities
• Datasets

This overview provides a sorted list of the functions of the package and links to few more involved examples.

1. Density estimation via normal mixtures and MCMC

• NMixMCMC
  
  • There exists a print method for objects of class NMixMCMC.
• NMixChainsDerived
  
• NMixPlugDA
  
• NMixPredDensJoint2
  
  • This is a generic function with default method and a method for objects of class NMixMCMC and GLMM_MCMC implemented.
  • There is also a plot method for objects of class NMixPredDensJoint2.
• NMixPredCondDensJoint2
  
  • This is a generic function with default method and a method for objects of class NMixMCMC and GLMM_MCMC implemented.
  • There is also a plot method for objects of class NMixPredCondDensJoint2.
• NMixPlugDensJoint2
  
  • This is a generic function with default method and a method for objects of class NMixMCMC and GLMM_MCMC implemented.
  • There is also a plot method for objects of class NMixPlugDensJoint2.
• NMixPlugCondDensJoint2
  
  • This is a generic function with default method and a method for objects of class NMixMCMC and GLMM_MCMC implemented.
  • There is also a plot method for objects of class NMixPlugCondDensJoint2.
• NMixPredDensMarg
  
  • This is a generic function with default method and a method for objects of class NMixMCMC and GLMM_MCMC implemented.
  • There is also a plot method for objects of class NMixPredDensMarg.
• NMixPredCDFMarg
  
  • This is a generic function with default method and a method for objects of class NMixMCMC and GLMM_MCMC implemented.
  • There is also a plot method for objects of class NMixPredCDFMarg.
• NMixPredCondDensMarg
  
  • This is a generic function with default method and a method for objects of class NMixMCMC and GLMM_MCMC implemented.
  • There is also a plot method for objects of class NMixPredCondDensMarg.
• NMixPlugDensMarg
  
  • This is a generic function with default method and a method for objects of class NMixMCMC and GLMM_MCMC implemented.
  • There is also a plot method for objects of class NMixPlugDensMarg.
• NMixPlugCondDensMarg
  
  • This is a generic function with default method and a method for objects of class NMixMCMC and GLMM_MCMC implemented.
  • There is also a plot method for objects of class NMixPlugCondDensMarg.
• Y2T
  
  • This is a generic function with default method to transform a fitted distribution of Y = trans(T) into a distribution of T = itrans(Y).
  • There are methods for objects of class NMixPredDensMarg, NMixPlugDensMarg, NMixPredCDFMarg, NMixPredDensJoint2, NMixPlugDensJoint2, NMixPredCondDensMarg, NMixPlugCondDensMarg, NMixPredCondDensJoint2, NMixPlugCondDensJoint2.

Supplementary material for this part is available:

• Komárek, A. (2009). A new R package for Bayesian estimation of multivariate normal mixtures allowing for selection of the number of components and interval-censored data. Computational Statistics and Data Analysis, 53(12). 3932-3947, doi: 10.1016/j.csda.2009.05.006.
  Paper describing the methods implemented in the package.
• Komarek-NMix-supplement.pdf
  Supplement to the paper which includes some technical details.
• Galaxy.pdf, Galaxy.R, Galaxy.Rnw
  Example of 1 dimensional analysis using the RJ-MCMC.
• Faithful.pdf, Faithful.R, Faithful.Rnw
  Example of 2 dimensional analysis.
• Tandmob.pdf, Tandmob.R, Tandmob.Rnw
  Example of 6 dimensional analysis with the interval-censored data.

2. Multivariate generalized linear mixed models with a normal mixture in the distribution of random effects

• GLMM_MCMC
  
  • There exists a print method for objects of class GLMM_MCMC.
• GLMM_longitDA
  

3. Univariate distributions

• rTNorm
  Random number generation from a truncated normal distribution.

4. Multivariate distributions

• dMVN, rMVN, rcMVN
  (Log-)density and random number genaration for a multivariate normal distribution.
• rTMVN
  Random number genaration from a truncated multivariate normal distribution.
• dMVNmixture, dMVNmixture2, rMVNmixture, rMVNmixture2
  (Log-)density and random number genaration for a mixture of (multivariate) normal distributions.
• dWishart, rWishart
  (Log-)density and random number genaration for a Wishart distribution.
• rDirichlet
  Random number genaration from a Dirichlet distribution.

5. Miscellaneous random number generation

• rRotationMatrix
  Random rotation matrix.
• rSamplePair
  Sample a random pair.

6. Matrix linear algebra

• MatMPpinv
  Moore-Penrose pseudoinverse of a squared matrix.
• MatSqrt
  Square root of a matrix.

7. Basic statistics

• BLA
  Best linear approximation with respect to the mean squared error (theoretical least squares).

8. Utilities

• SP2Rect
  Conversion of a symmetric matrix stored in a packed format (lower triangle only) into a matrix.
• autolayout
  

9. Datasets

• Acidity
  Acidity index measured in a sample of 155 lakes in North-Central Wisconsin.
• Enzyme
  Enzymatic activity in the blood, for an enzyme involved in the metabolism of carcinogenic substances, among a group of 245 unrelated individuals.
• Faithful
  Waiting time between eruptions and the duration of the eruption for the Old Faithful geyser in Yellowstone National Park, Wyoming, USA, version used in Härdle (1991).
• Galaxy
  Velocities of 82 distant galaxies, diverging from our own galaxy.
• Tandmob
  Dental (Signal Tandmobiel) data for 4430 6-12 year old children.
• TandmobEmer
  Data derived from Tandmob.