| Type: | Package |
| Title: | Computing the Singular BIC for Multiple Models |
| Version: | 0.2.0 |
| Date: | 2016-09-20 |
| Description: | Computes the sBIC for various singular model collections including: binomial mixtures, factor analysis models, Gaussian mixtures, latent forests, latent class analyses, and reduced rank regressions. |
| License: | GPL (≥ 3) |
| URL: | https://github.com/Lucaweihs/sBIC |
| BugReports: | https://github.com/Lucaweihs/sBIC/issues |
| Imports: | poLCA, R.oo (≥ 1.20.0), R.methodsS3, mclust, igraph (≥ 1.0.1), Rcpp (≥ 0.12.3), combinat, flexmix, hash |
| LinkingTo: | Rcpp |
| Suggests: | testthat, mvtnorm, knitr, MASS |
| VignetteBuilder: | knitr |
| RoxygenNote: | 5.0.1 |
| Collate: | 'ModelPoset.R' 'MixtureModels.R' 'BinomialMixtures.R' 'FactorAnalyses.R' 'GaussianMixtures.R' 'LCAs.R' 'LatentForests-Helpers.R' 'LatentForests.R' 'RcppExports.R' 'ReducedRankRegressions.R' 'sBIC-Function.R' 'sbic.R' |
| NeedsCompilation: | yes |
| Packaged: | 2016-09-30 23:20:04 UTC; lucaweihs |
| Author: | Luca Weihs [aut, cre], Martyn Plummer [ctb] |
| Maintainer: | Luca Weihs <lucaw@uw.edu> |
| Repository: | CRAN |
| Date/Publication: | 2016-10-01 14:31:14 |
sBIC package documentation.
Description
Computes the sBIC for various model collections including:
Binomial mixtures
Factor analyses
Gaussian mixtures
Latent forests
Latent class analyses
Reduced rank regressions
The primary functionality of this package can be accessed through the sBIC function.
Construct a poset of binomial mixture models.
Description
Creates an object representing a collection of binomial mixture models. There is one model for each fixed number of components from 1 to some specified maximum. In particular each model is identified by a single number specifiying the number of components in the model. Models are naturally ordered by inclusion so that, for example, a model with 2 components comes before a model with 3 or more components.
Usage
BinomialMixtures(maxNumComponents = 1, phi = "default")
Arguments
maxNumComponents |
the maximum number of components allowed in a model, will create a hierarchy of all models with less than or equal to this number. |
phi |
parameter controlling the strength of the sBIC penalty. |
Value
An object representing the collection.
Construct a poset of factor analysis models.
Description
Creates an object representing a collection of factor analysis models. There is one model for each fixed number of factors from 0 to some specified maximum number of factors. Each model is identified by a single number, in particular the model with n factors is associated with the model numbered (n + 1), this is because we allow a model with 0 factors and would like all models to be numbered with strictly positive integers for consistency. Models are naturally ordered by inclusion so that, for example, a model with 2 factors comes before a model with 3 or more factors.
Usage
FactorAnalyses(numCovariates = 1, maxNumFactors = 0)
Arguments
numCovariates |
the number of covariates in all of the models. |
maxNumFactors |
the maximum number of factors allowed in a model, will create a hierarchy of all models with less than or equal to this number. |
Value
An object representing the collection.
Construct a poset of gaussian mixture models.
Description
Creates an object representing a collection of gaussian mixture models. There is one model for each fixed number of components from 1 to some specified maximum. In particular each model is identified by a single number specifiying the number of components in the model. Models are naturally ordered by inclusion so that, for example, a model with 2 components comes before a model with 3 or more components.
Usage
GaussianMixtures(maxNumComponents = 1, dim = 1,
phi = "default", restarts = 50)
Arguments
maxNumComponents |
the maximum number of gaussian components to consider in a mixture. |
dim |
the ambient dimension in which the gaussian mixtures reside. Default is 1, corresponding to gaussian mixtures on the real line. |
phi |
parameter controlling the strength of the sBIC penalty. |
restarts |
the number of random restarts to perform when computing the MLE. |
Value
An object representing the collection.
Construct a poset of latent class analysis models.
Description
Creates an object representing a collection of latent class analysis models. There is one model for each fixed number of latent classes from 1 to some specified maximum. In particular each model is identified by a single number specifiying the number of latent classes in the model. Models are naturally ordered by inclusion so that, for example, a model with 2 latent classes comes before a model with 3 or more latent classes.
Usage
LCAs(maxNumClasses = 1, numVariables = 2,
numStatesForVariables = 2, phi = "default")
Arguments
maxNumClasses |
the number of classes in the largest LCA model to considered. |
numVariables |
the number of observed variables. |
numStatesForVariables |
the number of states for each observed variable, at the moment these must all be equal. |
phi |
parameter controlling the strength of the sBIC penalty. |
Value
An object representing the collection.
Construct a poset of gaussian latent forest models.
Description
For a fixed binary forest where all leaves represent observed variables this
function creates an object representing all gaussian latent forest models
that are submodels of the given model. All models are enumerated from 1 to
the total number of subforests, see the method getSupport.LatentForests
for details on how to determine which model a particular model number
corresponds to. Models are naturally ordered by inclusion so that, for
example, the forest that has no edges is less than all other models.
Usage
LatentForests(numLeaves = 0, E = matrix(numeric(0), ncol = 2))
Arguments
numLeaves |
the number of observed variables (these are the leaves of the model) |
E |
a 2xm matrix of edges corresponding to the edges of the 'super forest' f for which we compute all subforests. f should have nodes 1:numLeaves as leaves of the forest with no internal nodes as leaves. |
Value
An object representing the collection.
Linear collections of mixture models.
Description
An abstract class representing a collection of mixture models that are linearly ordered by the number of components in the mixture. This class should not be instantiated, just extended.
Usage
MixtureModels(phi = "default")
Arguments
phi |
parameter controlling the strength of the sBIC penalty. |
Value
An object representing the collection.
See Also
GaussianMixtures, BinomialMixtures, LCAs
Construct a poset of reduced rank regression models.
Description
Creates an object representing a collection of reduced rank regression models. There is one model for each fixed rank from 1 to some specified maximum. In particular each model is identified by a single number specifiying the rank of the regression matrix in the model. Models are naturally ordered by inclusion so that, for example, a model with 2 rank 2 comes before before a model with rank 3 or greater.
Usage
ReducedRankRegressions(numResponses, numCovariates, maxRank)
Arguments
numResponses |
the number of response variables. |
numCovariates |
the number of covariates. |
maxRank |
the largest rank model to be included in the collection. |
Value
An object representing the collection.
EM-algorithm for latent forests.
Description
Uses the EM-algorithm (with multiple random restarts) to compute an approximate maximum likelihood estimate for a given latent forest model.
Usage
emMain(this, model, starts, maxIter, tol)
## S3 method for class 'LatentForests'
emMain(this, model, starts=5, maxIter=1000, tol=1e-4)
Arguments
this |
the LatentForests object. |
model |
the model for which to compute the approximate MLE. |
starts |
the number of random restarts. |
maxIter |
the maximum number of iterations to complete in the algorithm. |
tol |
the tolerance to use a convergence criterion. |
One EM-iteration.
Description
A private method that performs a single iteration of the EM-algorithm, this is a helper function for emMain method.
Usage
emSteps(this, support, S)
## S3 method for class 'LatentForests'
emSteps(this, support, S)
Arguments
this |
the LatentForests object. |
support |
the support of the model. |
S |
the current covariance matrix. |
Generate all non-isomorphic binary trees.
Description
Generates all non-isomorphic binary trees with a given number of leaves where leaves are considered labeled and inner nodes are unlabeled. Takes as argument the number of leaves for which to produce the binary trees and returns a list of (n-1)x2 matrices where each row corresponds to a edge in the tree. These edge matrices will be in 'directed order,' i.e. will be so that if they are considered to be directed edges then the resulting graph will have exactly one source.
Usage
generateAllBinaryTrees(numLeaves)
Arguments
numLeaves |
the number of leaves |
Edges representing the largest model.
Description
When creating the LatentForests object a set of edges representing the largest model is required. This function returns those edges as a matrix. This matrix will have edges in the same order but may have flipped which node comes first in any particular edge. That is if edge (1,4) was the 5th edge then it will remain the 5th edge but may now be of the form (4,1).
Usage
getAllEdges(this, model)
## S3 method for class 'LatentForests'
getAllEdges(this, model)
Arguments
this |
the LatentForests object. |
model |
the model number. |
Create a covariance matrix.
Description
Creates a covariance matrix for the latent forest model where edge correlations are given. Here edge correlations are given as a vector and correspond (in order) to the edges returned by this$getAllEdges().
Usage
getCovMat(this, edgeCorrelations)
## S3 method for class 'LatentForests'
getCovMat(this, edgeCorrelations)
Arguments
this |
the LatentForests object. |
edgeCorrelations |
the edge correlations in a numeric vector. |
Return the set data.
Description
If data has been set for the object using the setData() function then will return that data, otherwise will throw an error.
Usage
getData(this)
## S3 method for class 'BinomialMixtures'
getData(this)
## S3 method for class 'FactorAnalyses'
getData(this)
## S3 method for class 'GaussianMixtures'
getData(this)
## S3 method for class 'LCAs'
getData(this)
## S3 method for class 'LatentForests'
getData(this)
## S3 method for class 'ReducedRankRegressions'
getData(this)
Arguments
this |
the object from which to get the data. |
Model dimension.
Description
Computes the dimension of a model in the model poset.
Usage
getDimension(this, model)
## S3 method for class 'BinomialMixtures'
getDimension(this, model)
## S3 method for class 'FactorAnalyses'
getDimension(this, model)
## S3 method for class 'GaussianMixtures'
getDimension(this, model)
## S3 method for class 'LCAs'
getDimension(this, model)
## S3 method for class 'LatentForests'
getDimension(this, model)
## S3 method for class 'ReducedRankRegressions'
getDimension(this, model)
Arguments
this |
the object representing the model poset. |
model |
the model for which the dimension should be computed. |
Get model with the given support.
Description
Returns the model number corresponding to a given 0-1 vector representing the support of the model. This support should corresponds to the edges returned by this$getAllEdges()
Usage
getModelWithSupport(this, support)
## S3 method for class 'LatentForests'
getModelWithSupport(this, support)
Arguments
this |
the LatentForests object. |
support |
the 0-1 vector representing the support. |
Number of factors for a model.
Description
Given a model number returns the number of factors in that model
Usage
getNumFactorsForModel(this, model)
## S3 method for class 'FactorAnalyses'
getNumFactorsForModel(this, model)
Arguments
this |
the FactorAnalyses object. |
model |
the model number. |
Get number of leaves.
Description
Gets the number of leaves in the latent forest models.
Usage
getNumLeaves(this)
## S3 method for class 'LatentForests'
getNumLeaves(this)
Arguments
this |
the LatentForests object. |
Number of models.
Description
Returns the number of models in the collection.
Usage
getNumModels(this)
## S3 method for class 'BinomialMixtures'
getNumModels(this)
## S3 method for class 'FactorAnalyses'
getNumModels(this)
## S3 method for class 'GaussianMixtures'
getNumModels(this)
## S3 method for class 'LCAs'
getNumModels(this)
## S3 method for class 'LatentForests'
getNumModels(this)
## S3 method for class 'ReducedRankRegressions'
getNumModels(this)
Arguments
this |
the model poset object. |
Number of samples in the set data.
Description
If data has been set using the setData method then returns the number of samples in the data. Otherwise throws an error.
Usage
getNumSamples(this)
## S3 method for class 'BinomialMixtures'
getNumSamples(this)
## S3 method for class 'FactorAnalyses'
getNumSamples(this)
## S3 method for class 'GaussianMixtures'
getNumSamples(this)
## S3 method for class 'LCAs'
getNumSamples(this)
## S3 method for class 'LatentForests'
getNumSamples(this)
## S3 method for class 'ReducedRankRegressions'
getNumSamples(this)
Arguments
this |
the object from which to get the number of samples. |
Maximum number of vertices.
Description
A private method for LatentForests that computes the number of vertices a tree with this$getNumLeaves() number of leaves has.
Usage
getNumVertices(this)
## S3 method for class 'LatentForests'
getNumVertices(this)
Arguments
this |
the LatentForests object. |
Get the phi parameter.
Description
Gets the phi parameter controlling the strength of the sBIC penalty.
Usage
getPhi(this, phi)
## S3 method for class 'MixtureModels'
getPhi(this, phi)
Arguments
this |
the MixtureModels object. |
phi |
the new phi value. |
The prior on the models.
Description
Returns the unnormalized prior on the collection.
Usage
getPrior(this)
## S3 method for class 'BinomialMixtures'
getPrior(this)
## S3 method for class 'FactorAnalyses'
getPrior(this)
## S3 method for class 'GaussianMixtures'
getPrior(this)
## S3 method for class 'LCAs'
getPrior(this)
## S3 method for class 'LatentForests'
getPrior(this)
## S3 method for class 'ReducedRankRegressions'
getPrior(this)
Arguments
this |
the model poset object. |
Sampling covariance matrix.
Description
Returns the sampling covariance matrix for the data set with setData().
Usage
getSamplingCovMat(this)
## S3 method for class 'LatentForests'
getSamplingCovMat(this)
Arguments
this |
the LatentForests object. |
Get support for a given model.
Description
Given a model number returns the support of the model. Let E by the matrix of edges returned by this$getAllEdges(), the support is represented by a 0-1 vector v where the ith entry of v is 1 if the ith edge in E is in the model and is 0 otherwise.
Usage
getSupport(this, model)
## S3 method for class 'LatentForests'
getSupport(this, model)
Arguments
this |
the LatentForests object. |
model |
the model number. |
Topological ordering of models.
Description
Returns a topological ordering of models in the collection.
Usage
getTopOrder(this)
## S3 method for class 'BinomialMixtures'
getTopOrder(this)
## S3 method for class 'FactorAnalyses'
getTopOrder(this)
## S3 method for class 'GaussianMixtures'
getTopOrder(this)
## S3 method for class 'LCAs'
getTopOrder(this)
## S3 method for class 'LatentForests'
getTopOrder(this)
## S3 method for class 'ReducedRankRegressions'
getTopOrder(this)
Arguments
this |
the model poset object. |
Learning coefficient
Description
Computes the learning coefficient for a model with respect to one of the model's submodels.
Usage
learnCoef(this, superModel, subModel)
## S3 method for class 'MixtureModels'
learnCoef(this, superModel, subModel)
## S3 method for class 'FactorAnalyses'
learnCoef(this, superModel, subModel)
## S3 method for class 'LatentForests'
learnCoef(this, superModel, subModel)
## S3 method for class 'ReducedRankRegressions'
learnCoef(this, superModel, subModel)
Arguments
this |
the object representing the model poset. |
superModel |
the larger model of the two input models. |
subModel |
the submodel of the larger model. |
Multivariate gaussian log-likelihood.
Description
A private method that returns the log-likelihood of the data set with setData() under a multivariate gaussian model with a given covariance matrix and assumed 0 means.
Usage
logLike(this, covMat)
## S3 method for class 'LatentForests'
logLike(this, covMat)
Arguments
this |
the LatentForests object. |
covMat |
a covariance matrix. |
Maximum likelihood for data.
Description
Computes the maximum likelihood of a model in the model poset for the data set using the setData command.
Usage
logLikeMle(this, model, ...)
## S3 method for class 'BinomialMixtures'
logLikeMle(this, model, ...)
## S3 method for class 'FactorAnalyses'
logLikeMle(this, model, starts = 1, ...)
## S3 method for class 'GaussianMixtures'
logLikeMle(this, model, ...)
## S3 method for class 'LCAs'
logLikeMle(this, model, ...)
## S3 method for class 'LatentForests'
logLikeMle(this, model, ...)
## S3 method for class 'ReducedRankRegressions'
logLikeMle(this, model, ...)
Arguments
this |
the object representing the model poset. |
model |
the model for which the maximum likelihood should be computed. |
... |
further parameters to be passed to methods |
starts |
The number of starting values to be tried |
Help compute the MLE.
Description
A private method that acts as a helper function for the logLikeMLE method in the ReducedRankRegressions class.
Usage
logLikeMleHelper(this, model)
## S3 method for class 'ReducedRankRegressions'
logLikeMleHelper(this, model)
Arguments
this |
the ReducedRankRegressions object. |
model |
the model number. |
Maximum likelihood estimator.
Description
Computes the maximum likelihood estimator of the model parameters (for a given model in the collection) given the data set with setData.
Usage
mle(this, model)
## S3 method for class 'BinomialMixtures'
mle(this, model)
## S3 method for class 'FactorAnalyses'
mle(this, model)
## S3 method for class 'GaussianMixtures'
mle(this, model)
## S3 method for class 'LCAs'
mle(this, model)
## S3 method for class 'LatentForests'
mle(this, model)
Arguments
this |
the object representing the model poset. |
model |
the model for which the maximum likelihood should be computed. |
Parents of a model.
Description
Returns the immediate parents of a given model, i.e. those models M that are (in the poset ordering) less than the given model but for which there exists no other model M' such that M < M' < (given model).
Usage
parents(this, model)
## S3 method for class 'MixtureModels'
parents(this, model)
## S3 method for class 'FactorAnalyses'
parents(this, model)
## S3 method for class 'LatentForests'
parents(this, model)
## S3 method for class 'ReducedRankRegressions'
parents(this, model)
Arguments
this |
the object representing the model poset. |
model |
the model for which the parents should be found. |
Compute the sBIC.
Description
Computes the sBIC for a given collection of models.
Usage
sBIC(X, mod)
Arguments
X |
the data for which the maximum likelihood estimates will be computed
for the given collection of models. To see how this data should be
formatted check the documentation for |
mod |
an object representing a poset of models of the same type, e.g. a collection of binomial mixture models. The currently implemented models include:
|
Value
A named list containing the components
logLike - the computed MLE log-likelihoods for each model.
sBIC - the sBIC score for each model.
BIC - the usual BIC score for each model.
modelPoset - the input model poset mod.
Set data for a model poset.
Description
Sets the data to be used by a poset of models when computing MLEs.
Usage
setData(this, data)
Arguments
this |
the model poset object. |
data |
the data to be set. |
Set data for the binomial mixture models.
Description
Sets the data to be used by the binomial mixture models when computing MLEs.
Usage
## S3 method for class 'BinomialMixtures'
setData(this, data)
Arguments
this |
the BinomialMixtures object. |
data |
the data to be set, should be a numeric vector of non-negative integers. |
Set data for the factor analysis models.
Description
Sets the data to be used by the factor analysis models when computing MLEs.
Usage
## S3 method for class 'FactorAnalyses'
setData(this, data)
Arguments
this |
the FactorAnalyses object. |
data |
the data to be set, should matrix of observed responses. |
Set data for the gaussian mixture models.
Description
Sets the data to be used by the gaussian mixture models when computing MLEs.
Usage
## S3 method for class 'GaussianMixtures'
setData(this, data)
Arguments
this |
the GaussianMixtures object. |
data |
the data to be set, a matrix where each row corresponds to a single multivariate observation. If the corresponding GaussianMixtures object has ambient dimension 1, then data may be a numeric vector of observations. |
Set data for the LCA models.
Description
Sets the data to be used by the LCA models when computing MLEs.
Usage
## S3 method for class 'LCAs'
setData(this, data)
Arguments
this |
the LCAs object. |
data |
the data to be set, should be an integer valued matrix where each row represents a single sample from the observed variables. |
Set data for the latent forest models.
Description
Sets the data to be used by the latent forest models models for computing MLEs.
Usage
## S3 method for class 'LatentForests'
setData(this, data)
Arguments
this |
the LatentForests object. |
data |
the data to be set, should matrix of observed values where each row corresponds to a single sample. |
Set data for the reduced rank regression models.
Description
Sets the data to be used by the reduced rank regression models when computing MLEs.
Usage
## S3 method for class 'ReducedRankRegressions'
setData(this, data)
Arguments
this |
the ReducedRankRegressions object. |
data |
the data to be set, should be a named list with two components:
|
Set phi parameter.
Description
Set the phi parameter in a mixture model object to a different value.
Usage
setPhi(this, phi)
## S3 method for class 'MixtureModels'
setPhi(this, phi)
Arguments
this |
the MixtureModels object. |
phi |
the new phi value. |