diff --git a/dev/index.html b/dev/index.html index 3698bdaf..2d026918 100644 --- a/dev/index.html +++ b/dev/index.html @@ -1,3 +1,3 @@ Home · QuasiCopula
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QuasiCopula.jl

Authors: Sarah Ji, Kenneth Lange, Hua Zhou, Janet Sinsheimer, Benjamin Chu

A Flexible Quasi-Copula Distribution for Statistical Modeling

Package Features

Installation

Download and install Julia. Within Julia, copy and paste the following: 

using Pkg
-pkg"add https://github.com/OpenMendel/QuasiCopula.jl.git"

This package supports Julia v1.6+.

Manual Outline

+pkg"add https://github.com/OpenMendel/QuasiCopula.jl.git"

This package supports Julia v1.6+.

Manual Outline

diff --git a/dev/man/AR_Examples/index.html b/dev/man/AR_Examples/index.html index a59b8e34..56c80ffd 100644 --- a/dev/man/AR_Examples/index.html +++ b/dev/man/AR_Examples/index.html @@ -102,4 +102,4 @@ -1.49822 -1.14855 -0.489077 0.401748 0.871632 1.12837 - 0.461106 0.608666 + 0.461106 0.608666 diff --git a/dev/man/CS_Examples/index.html b/dev/man/CS_Examples/index.html index 99cc5c11..cbfcaf95 100644 --- a/dev/man/CS_Examples/index.html +++ b/dev/man/CS_Examples/index.html @@ -97,4 +97,4 @@ -0.0339459 -0.0155735 1.81842 2.03892 0.46641 1.53359 - -0.743613 1.08437 + -0.743613 1.08437 diff --git a/dev/man/VC_Examples/index.html b/dev/man/VC_Examples/index.html index 5413a5ac..f526d828 100644 --- a/dev/man/VC_Examples/index.html +++ b/dev/man/VC_Examples/index.html @@ -118,4 +118,4 @@ 3.09211 3.44262 -0.111956 -0.0381218 -9.59795e5 9.89505e5 - -3.52785e5 3.63607e5 + -3.52785e5 3.63607e5 diff --git a/dev/man/api/index.html b/dev/man/api/index.html index 72ebdd55..848afc4e 100644 --- a/dev/man/api/index.html +++ b/dev/man/api/index.html @@ -1,2 +1,2 @@ -API · QuasiCopula
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API

Documentation for QuasiCopua.jl's functions.

Index

Functions

QuasiCopula.fit! — Function
fit!(gcm::GLMCopulaARModel, solver=Ipopt.IpoptSolver)

Fit an GLMCopulaARModel object by MLE using a nonlinear programming solver. This is for Poisson and Bernoulli base distributions with no additional base distribution parameters than the mean. Start point should be provided in gcm.β, gcm.ρ, gcm.σ2.

Arguments

  • gcm: A GLMCopulaARModel model object.
  • solver: Specified solver to use. By default we use IPOPT with 100 quas-newton iterations with convergence tolerance 10^-6. (default solver = Ipopt.IpoptSolver(print_level=3, max_iter = 100, tol = 10^-6, limited_memory_max_history = 20, hessian_approximation = "limited-memory"))
source
fit!(gcm::GLMCopulaCSModel, solver=Ipopt.IpoptSolver)

Fit an GLMCopulaCSModel object by MLE using a nonlinear programming solver. This is for Poisson and Bernoulli base distributions with no additional base distribution parameters than the mean. Start point should be provided in gcm.β, gcm.ρ, gcm.σ2.

Arguments

  • gcm: A GLMCopulaCSModel model object.
  • solver: Specified solver to use. By default we use IPOPT with 100 quas-newton iterations with convergence tolerance 10^-6. (default solver = Ipopt.IpoptSolver(print_level=3, max_iter = 100, tol = 10^-6, limited_memory_max_history = 20, hessian_approximation = "limited-memory"))
source
fit!(gcm::Union{GaussianCopulaARModel, GaussianCopulaCSModel}, solver=Ipopt.IpoptSolver)

Fit a GaussianCopulaARModel or GaussianCopulaCSModel object by MLE using a nonlinear programming solver. Start point should be provided in gcm.β, gcm.τ, gcm.ρ, gcm.σ2.

Arguments

  • gcm: A GaussianCopulaARModel or GaussianCopulaCSModel model object.
  • solver: Specified solver to use. By default we use IPOPT with 100 quas-newton iterations with convergence tolerance 10^-6. (default solver = Ipopt.IpoptSolver(print_level=3, max_iter = 100, tol = 10^-6, limited_memory_max_history = 20, hessian_approximation = "limited-memory"))
source
fit!(gcm::Union{GLMCopulaVCModel, Poisson_Bernoulli_VCModel}, solver=Ipopt.IpoptSolver(print_level=5))

Fit a GLMCopulaVCModel or Poisson_Bernoulli_VCModel model object by MLE using a nonlinear programming solver. This is for Poisson and Bernoulli base distributions or a mixture of the two with no additional base distribution parameters than the mean. Start point should be provided in gcm.β, gcm.θ.

Arguments

  • gcm: A GLMCopulaVCModel model object.
  • solver: Specified solver to use. By default we use IPOPT with 100 quas-newton iterations with convergence tolerance 10^-6. (default solver = Ipopt.IpoptSolver(print_level=3, max_iter = 100, tol = 10^-6, limited_memory_max_history = 20, hessian_approximation = "limited-memory"))
source
fit!(gcm::NBCopulaVCModel, solver=Ipopt.IpoptSolver)

Fit an NBCopulaVCModel object by block MLE using a nonlinear programming solver. Start point should be provided in gcm.β, gcm.θ, gcm.r. In our block updates, we fit 15 iterations of gcm.β, gcm.θ using IPOPT, followed by 10 iterations of Newton on nuisance parameter gcm.r. Convergence is declared when difference of successive loglikelihood is less than tol.

Arguments

  • gcm: A NBCopulaVCModel model object.
  • solver: Specified solver to use. By default we use IPOPT with 100 quas-newton iterations with convergence tolerance 10^-6. (default solver = Ipopt.IpoptSolver(print_level = 0, max_iter = 15, limited_memory_max_history = 20, warm_start_init_point = "yes", mu_strategy = "adaptive", hessian_approximation = "limited-memory"))

Optional Arguments

  • tol: Convergence tolerance for the max block iter updates (default tol = 1e-6).
  • maxBlockIter: Number of maximum block iterations to update gcm.β, gcm.θ and gcm.r (default maxBlockIter = 10).
source
fit!(gcm::NBCopulaARModel, solver=Ipopt.IpoptSolver)

Fit an NBCopulaARModel object by block MLE using a nonlinear programming solver. Start point should be provided in gcm.β, gcm.ρ, gcm.σ2, gcm.r. In our block updates, we fit 15 iterations of gcm.β, gcm.ρ, gcm.σ2 using IPOPT, followed by 10 iterations of Newton on nuisance parameter gcm.r. Convergence is declared when difference of successive loglikelihood is less than tol.

Arguments

  • gcm: A NBCopulaARModel model object.
  • solver: Specified solver to use. By default we use IPOPT with 100 quas-newton iterations with convergence tolerance 10^-6. (default solver = Ipopt.IpoptSolver(print_level = 0, max_iter = 15, limited_memory_max_history = 20, warm_start_init_point = "yes", mu_strategy = "adaptive", hessian_approximation = "limited-memory"))

Optional Arguments

  • tol: Convergence tolerance for the max block iter updates (default tol = 1e-6).
  • maxBlockIter: Number of maximum block iterations to update gcm.β, gcm.θ and gcm.r (default maxBlockIter = 10).
source
fit!(gcm::NBCopulaCSModel, solver=Ipopt.IpoptSolver)

Fit an NBCopulaCSModel object by block MLE using a nonlinear programming solver. Start point should be provided in gcm.β, gcm.ρ, gcm.σ2, gcm.r. In our block updates, we fit 15 iterations of gcm.β, gcm.ρ, gcm.σ2 using IPOPT, followed by 10 iterations of Newton on nuisance parameter gcm.r. Convergence is declared when difference of successive loglikelihood is less than tol.

Arguments

  • gcm: A NBCopulaCSModel model object.
  • solver: Specified solver to use. By default we use IPOPT with 100 quas-newton iterations with convergence tolerance 10^-6. (default solver = Ipopt.IpoptSolver(print_level = 0, max_iter = 15, limited_memory_max_history = 20, warm_start_init_point = "yes", mu_strategy = "adaptive", hessian_approximation = "limited-memory"))

Optional Arguments

  • tol: Convergence tolerance for the max block iter updates (default tol = 1e-6).
  • maxBlockIter: Number of maximum block iterations to update gcm.β, gcm.θ and gcm.r (default maxBlockIter = 10).
source
fit_quasi!(gcm::GaussianCopulaVCModel, solver=Ipopt.IpoptSolver)

Fit an GaussianCopulaVCModel object by MLE using a nonlinear programming solver. Start point should be provided in gcm.β, gcm.θ, gcm.τ this is for Normal base.

Arguments

  • gcm: A GaussianCopulaVCModel model object.
  • solver: Specified solver to use. By default we use IPOPT with 100 quas-newton iterations with convergence tolerance 10^-6. (default solver = Ipopt.IpoptSolver(print_level=3, max_iter = 100, tol = 10^-6, limited_memory_max_history = 20, warm_start_init_point="yes", hessian_approximation = "limited-memory"))
source
QuasiCopula.logl — Function
logl(gcm)

Get the loglikelihood at the given parameters in gcm, at the optimal solution.

Arguments

  • gcm: One of GaussianCopulaVCModel, GaussianCopulaARModel, GaussianCopulaCSModel, GLMCopulaVCModel, GLMCopulaARModel, GLMCopulaCSModel, NBCopulaVCModel, NBCopulaARModel, NBCopulaCSModel or Poisson_Bernoulli_VCModel model objects.
source
QuasiCopula.get_CI — Function
get_CI(gcm)

Get the confidence interval of all parameters, at the optimal solution.

Arguments

  • gcm: One of GaussianCopulaVCModel, GaussianCopulaARModel, GaussianCopulaCSModel, GLMCopulaVCModel, GLMCopulaARModel, GLMCopulaCSModel, NBCopulaVCModel, NBCopulaARModel, NBCopulaCSModel or Poisson_Bernoulli_VCModel model objects.
source

Models

QuasiCopula.AR_model — Function
AR_model(df, y, grouping, d, link; penalized = penalized)

Form the autoregressive (AR(1)) model for intercept only regression with the specified base distribution (d) and link function (link).

Arguments

  • df: A named DataFrame
  • y: Ouctcome variable name of interest, specified as a Symbol. This variable name must be present in df.
  • grouping: Grouping or Clustering variable name of interest, specified as a Symbol. This variable name must be present in df.
  • d: Base Distribution of outcome from Distributions.jl.
  • link: Canonical Link function of the base distribution specified in d, from GLM.jl.

Optional Arguments

  • penalized: Boolean to specify whether or not to add an L2 Ridge penalty on the variance parameter for the AR(1) structured covariance. One can put true (e.g. penalized = true) to add this penalty for numerical stability (default penalized = false).
source
AR_model(df, y, grouping, covariates, d, link; penalized = penalized)

Form the autoregressive (AR(1)) model for regression with the specified base distribution (d) and link function (link).

Arguments

  • df: A named DataFrame
  • y: Ouctcome variable name of interest, specified as a Symbol. This variable name must be present in df.
  • grouping: Grouping or Clustering variable name of interest, specified as a Symbol. This variable name must be present in df.
  • covariates: Covariate names of interest as a vector of Symbols. Each variable name must be present in df.
  • d: Base Distribution of outcome from Distributions.jl.
  • link: Canonical Link function of the base distribution specified in d, from GLM.jl.

Optional Arguments

  • penalized: Boolean to specify whether or not to add an L2 Ridge penalty on the variance parameter for the AR(1) structured covariance. One can put true (e.g. penalized = true) to add this penalty for numerical stability (default penalized = false).
source
QuasiCopula.CS_model — Function
CS_model(df, y, grouping, d, link)

Form the compound symmetric (CS) model for intercept only regression with the specified base distribution (d) and link function (link).

Arguments

  • df: A named DataFrame
  • y: Ouctcome variable name of interest, specified as a Symbol. This variable name must be present in df.
  • grouping: Grouping or Clustering variable name of interest, specified as a Symbol. This variable name must be present in df.
  • d: Base Distribution of outcome from Distributions.jl.
  • link: Canonical Link function of the base distribution specified in d, from GLM.jl.

Optional Arguments

  • penalized: Boolean to specify whether or not to add an L2 Ridge penalty on the variance parameter for the CS structured covariance. One can turn this option on by specifying penalized = true to add this penalty for numerical stability. (default penalized = false).
source
CS_model(df, y, grouping, covariates, d, link; penalized = penalized)

Form the compound symmetric (CS) model for regression with the specified base distribution (d) and link function (link).

Arguments

  • df: A named DataFrame
  • y: Ouctcome variable name of interest, specified as a Symbol. This variable name must be present in df.
  • grouping: Grouping or Clustering variable name of interest, specified as a Symbol. This variable name must be present in df.
  • covariates: Covariate names of interest as a vector of Symbols. Each variable name must be present in df.
  • d: Base Distribution of outcome from Distributions.jl.
  • link: Canonical Link function of the base distribution specified in d, from GLM.jl.

Optional Arguments

  • penalized: Boolean to specify whether or not to add an L2 Ridge penalty on the variance parameter for the CS structured covariance. One can turn this option on by specifying penalized = true to add this penalty for numerical stability. (default penalized = false).
source
QuasiCopula.VC_model — Function
VC_model(df, y, grouping, d, link)

Form the variance component model (VCM) for intercept only regression with a random intercept covariance matrix and the specified base distribution (d) and link function (link).

Arguments

  • df: A named DataFrame
  • y: Ouctcome variable name of interest, specified as a Symbol. This variable name must be present in df.
  • grouping: Grouping or Clustering variable name of interest, specified as a Symbol. This variable name must be present in df.
  • d: Base Distribution of outcome from Distributions.jl.
  • link: Canonical Link function of the base distribution specified in d, from GLM.jl.

Optional Arguments

  • penalized: Boolean to specify whether or not to add an L2 Ridge penalty on the variance components vector. One can put true (e.g. penalized = true) to add this penalty for numerical stability (default penalized = false).
source
VC_model(df, y, grouping, covariates, d, link)

Form the variance component model (VCM) for regression with a random intercept covariance matrix and the specified base distribution (d) and link function (link).

Arguments

  • df: A named DataFrame
  • y: Ouctcome variable name of interest, specified as a Symbol. This variable name must be present in df.
  • grouping: Grouping or Clustering variable name of interest, specified as a Symbol. This variable name must be present in df.
  • covariates: Covariate names of interest as a vector of Symbols. Each variable name must be present in df.
  • d: Base Distribution of outcome from Distributions.jl.
  • link: Canonical Link function of the base distribution specified in d, from GLM.jl.

Optional Arguments

  • penalized: Boolean to specify whether or not to add an L2 Ridge penalty on the variance components vector. One can put true (e.g. penalized = true) to add this penalty for numerical stability (default penalized = false).
source
VC_model(df, y, grouping, covariates, V, d, link)

Form the variance component model (VCM) for intercept only regression with the specified base distribution (d) and link function (link).

Arguments

  • df: A named DataFrame
  • y: Ouctcome variable name of interest, specified as a Symbol. This variable name must be present in df.
  • grouping: Grouping or Clustering variable name of interest, specified as a Symbol. This variable name must be present in df.
  • V: Vector of Vector of Positive Semi-Definite (PSD) Covariance Matrices. V is of length n, where n is the number of groups/clusters. Each element of V is also a Vector, but of length m. Here m is the number of variance components. Each element of V is a Vector of di x di PSD covariance matrices under the VCM framework, where d_i is the cluster size of the ith cluster, which may vary for each cluster of observations i in [1, n]. Each of these dimensions must match that specified in df.
  • d: Base Distribution of outcome from Distributions.jl.
  • link: Canonical Link function of the base distribution specified in d, from GLM.jl.

Optional Arguments

  • penalized: Boolean to specify whether or not to add an L2 Ridge penalty on the variance components vector. One can put true (e.g. penalized = true) to add this penalty for numerical stability (default penalized = false).
source
VC_model(df, y, grouping, covariates, V, d, link)

Form the variance component model (VCM) for regression with the specified base distribution (d) and link function (link).

Arguments

  • df: A named DataFrame
  • y: Ouctcome variable name of interest, specified as a Symbol. This variable name must be present in df.
  • grouping: Grouping or Clustering variable name of interest, specified as a Symbol. This variable name must be present in df.
  • covariates: Covariate names of interest as a vector of Symbols. Each variable name must be present in df.
  • V: Vector of Vector of Positive Semi-Definite (PSD) Covariance Matrices. V is of length n, where n is the number of groups/clusters. Each element of V is also a Vector, but of length m. Here m is the number of variance components. Each element of V is a Vector of di x di PSD covariance matrices under the VCM framework, where d_i is the cluster size of the ith cluster, which may vary for each cluster of observations i in [1, n]. Each of these dimensions must match that specified in df.
  • d: Base Distribution of outcome from Distributions.jl.
  • link: Canonical Link function of the base distribution specified in d, from GLM.jl.

Optional Arguments

  • penalized: Boolean to specify whether or not to add an L2 Ridge penalty on the variance components vector. One can put true (e.g. penalized = true) to add this penalty for numerical stability (default penalized = false).
source
+API · QuasiCopula
Edit on GitHub

API

Documentation for QuasiCopua.jl's functions.

Index

Functions

QuasiCopula.fit! — Function
fit!(gcm::GLMCopulaARModel, solver=Ipopt.IpoptSolver)

Fit an GLMCopulaARModel object by MLE using a nonlinear programming solver. This is for Poisson and Bernoulli base distributions with no additional base distribution parameters than the mean. Start point should be provided in gcm.β, gcm.ρ, gcm.σ2.

Arguments

  • gcm: A GLMCopulaARModel model object.
  • solver: Specified solver to use. By default we use IPOPT with 100 quas-newton iterations with convergence tolerance 10^-6. (default solver = Ipopt.IpoptSolver(print_level=3, max_iter = 100, tol = 10^-6, limited_memory_max_history = 20, hessian_approximation = "limited-memory"))
source
fit!(gcm::GLMCopulaCSModel, solver=Ipopt.IpoptSolver)

Fit an GLMCopulaCSModel object by MLE using a nonlinear programming solver. This is for Poisson and Bernoulli base distributions with no additional base distribution parameters than the mean. Start point should be provided in gcm.β, gcm.ρ, gcm.σ2.

Arguments

  • gcm: A GLMCopulaCSModel model object.
  • solver: Specified solver to use. By default we use IPOPT with 100 quas-newton iterations with convergence tolerance 10^-6. (default solver = Ipopt.IpoptSolver(print_level=3, max_iter = 100, tol = 10^-6, limited_memory_max_history = 20, hessian_approximation = "limited-memory"))
source
fit!(gcm::Union{GaussianCopulaARModel, GaussianCopulaCSModel}, solver=Ipopt.IpoptSolver)

Fit a GaussianCopulaARModel or GaussianCopulaCSModel object by MLE using a nonlinear programming solver. Start point should be provided in gcm.β, gcm.τ, gcm.ρ, gcm.σ2.

Arguments

  • gcm: A GaussianCopulaARModel or GaussianCopulaCSModel model object.
  • solver: Specified solver to use. By default we use IPOPT with 100 quas-newton iterations with convergence tolerance 10^-6. (default solver = Ipopt.IpoptSolver(print_level=3, max_iter = 100, tol = 10^-6, limited_memory_max_history = 20, hessian_approximation = "limited-memory"))
source
fit!(gcm::Union{GLMCopulaVCModel, Poisson_Bernoulli_VCModel}, solver=Ipopt.IpoptSolver(print_level=5))

Fit a GLMCopulaVCModel or Poisson_Bernoulli_VCModel model object by MLE using a nonlinear programming solver. This is for Poisson and Bernoulli base distributions or a mixture of the two with no additional base distribution parameters than the mean. Start point should be provided in gcm.β, gcm.θ.

Arguments

  • gcm: A GLMCopulaVCModel model object.
  • solver: Specified solver to use. By default we use IPOPT with 100 quas-newton iterations with convergence tolerance 10^-6. (default solver = Ipopt.IpoptSolver(print_level=3, max_iter = 100, tol = 10^-6, limited_memory_max_history = 20, hessian_approximation = "limited-memory"))
source
fit!(gcm::NBCopulaVCModel, solver=Ipopt.IpoptSolver)

Fit an NBCopulaVCModel object by block MLE using a nonlinear programming solver. Start point should be provided in gcm.β, gcm.θ, gcm.r. In our block updates, we fit 15 iterations of gcm.β, gcm.θ using IPOPT, followed by 10 iterations of Newton on nuisance parameter gcm.r. Convergence is declared when difference of successive loglikelihood is less than tol.

Arguments

  • gcm: A NBCopulaVCModel model object.
  • solver: Specified solver to use. By default we use IPOPT with 100 quas-newton iterations with convergence tolerance 10^-6. (default solver = Ipopt.IpoptSolver(print_level = 0, max_iter = 15, limited_memory_max_history = 20, warm_start_init_point = "yes", mu_strategy = "adaptive", hessian_approximation = "limited-memory"))

Optional Arguments

  • tol: Convergence tolerance for the max block iter updates (default tol = 1e-6).
  • maxBlockIter: Number of maximum block iterations to update gcm.β, gcm.θ and gcm.r (default maxBlockIter = 10).
source
fit!(gcm::NBCopulaARModel, solver=Ipopt.IpoptSolver)

Fit an NBCopulaARModel object by block MLE using a nonlinear programming solver. Start point should be provided in gcm.β, gcm.ρ, gcm.σ2, gcm.r. In our block updates, we fit 15 iterations of gcm.β, gcm.ρ, gcm.σ2 using IPOPT, followed by 10 iterations of Newton on nuisance parameter gcm.r. Convergence is declared when difference of successive loglikelihood is less than tol.

Arguments

  • gcm: A NBCopulaARModel model object.
  • solver: Specified solver to use. By default we use IPOPT with 100 quas-newton iterations with convergence tolerance 10^-6. (default solver = Ipopt.IpoptSolver(print_level = 0, max_iter = 15, limited_memory_max_history = 20, warm_start_init_point = "yes", mu_strategy = "adaptive", hessian_approximation = "limited-memory"))

Optional Arguments

  • tol: Convergence tolerance for the max block iter updates (default tol = 1e-6).
  • maxBlockIter: Number of maximum block iterations to update gcm.β, gcm.θ and gcm.r (default maxBlockIter = 10).
source
fit!(gcm::NBCopulaCSModel, solver=Ipopt.IpoptSolver)

Fit an NBCopulaCSModel object by block MLE using a nonlinear programming solver. Start point should be provided in gcm.β, gcm.ρ, gcm.σ2, gcm.r. In our block updates, we fit 15 iterations of gcm.β, gcm.ρ, gcm.σ2 using IPOPT, followed by 10 iterations of Newton on nuisance parameter gcm.r. Convergence is declared when difference of successive loglikelihood is less than tol.

Arguments

  • gcm: A NBCopulaCSModel model object.
  • solver: Specified solver to use. By default we use IPOPT with 100 quas-newton iterations with convergence tolerance 10^-6. (default solver = Ipopt.IpoptSolver(print_level = 0, max_iter = 15, limited_memory_max_history = 20, warm_start_init_point = "yes", mu_strategy = "adaptive", hessian_approximation = "limited-memory"))

Optional Arguments

  • tol: Convergence tolerance for the max block iter updates (default tol = 1e-6).
  • maxBlockIter: Number of maximum block iterations to update gcm.β, gcm.θ and gcm.r (default maxBlockIter = 10).
source
fit_quasi!(gcm::GaussianCopulaVCModel, solver=Ipopt.IpoptSolver)

Fit an GaussianCopulaVCModel object by MLE using a nonlinear programming solver. Start point should be provided in gcm.β, gcm.θ, gcm.τ this is for Normal base.

Arguments

  • gcm: A GaussianCopulaVCModel model object.
  • solver: Specified solver to use. By default we use IPOPT with 100 quas-newton iterations with convergence tolerance 10^-6. (default solver = Ipopt.IpoptSolver(print_level=3, max_iter = 100, tol = 10^-6, limited_memory_max_history = 20, warm_start_init_point="yes", hessian_approximation = "limited-memory"))
source
QuasiCopula.logl — Function
logl(gcm)

Get the loglikelihood at the given parameters in gcm, at the optimal solution.

Arguments

  • gcm: One of GaussianCopulaVCModel, GaussianCopulaARModel, GaussianCopulaCSModel, GLMCopulaVCModel, GLMCopulaARModel, GLMCopulaCSModel, NBCopulaVCModel, NBCopulaARModel, NBCopulaCSModel or Poisson_Bernoulli_VCModel model objects.
source
QuasiCopula.get_CI — Function
get_CI(gcm)

Get the confidence interval of all parameters, at the optimal solution.

Arguments

  • gcm: One of GaussianCopulaVCModel, GaussianCopulaARModel, GaussianCopulaCSModel, GLMCopulaVCModel, GLMCopulaARModel, GLMCopulaCSModel, NBCopulaVCModel, NBCopulaARModel, NBCopulaCSModel or Poisson_Bernoulli_VCModel model objects.
source

Models

QuasiCopula.AR_model — Function
AR_model(df, y, grouping, d, link; penalized = penalized)

Form the autoregressive (AR(1)) model for intercept only regression with the specified base distribution (d) and link function (link).

Arguments

  • df: A named DataFrame
  • y: Ouctcome variable name of interest, specified as a Symbol. This variable name must be present in df.
  • grouping: Grouping or Clustering variable name of interest, specified as a Symbol. This variable name must be present in df.
  • d: Base Distribution of outcome from Distributions.jl.
  • link: Canonical Link function of the base distribution specified in d, from GLM.jl.

Optional Arguments

  • penalized: Boolean to specify whether or not to add an L2 Ridge penalty on the variance parameter for the AR(1) structured covariance. One can put true (e.g. penalized = true) to add this penalty for numerical stability (default penalized = false).
source
AR_model(df, y, grouping, covariates, d, link; penalized = penalized)

Form the autoregressive (AR(1)) model for regression with the specified base distribution (d) and link function (link).

Arguments

  • df: A named DataFrame
  • y: Ouctcome variable name of interest, specified as a Symbol. This variable name must be present in df.
  • grouping: Grouping or Clustering variable name of interest, specified as a Symbol. This variable name must be present in df.
  • covariates: Covariate names of interest as a vector of Symbols. Each variable name must be present in df.
  • d: Base Distribution of outcome from Distributions.jl.
  • link: Canonical Link function of the base distribution specified in d, from GLM.jl.

Optional Arguments

  • penalized: Boolean to specify whether or not to add an L2 Ridge penalty on the variance parameter for the AR(1) structured covariance. One can put true (e.g. penalized = true) to add this penalty for numerical stability (default penalized = false).
source
QuasiCopula.CS_model — Function
CS_model(df, y, grouping, d, link)

Form the compound symmetric (CS) model for intercept only regression with the specified base distribution (d) and link function (link).

Arguments

  • df: A named DataFrame
  • y: Ouctcome variable name of interest, specified as a Symbol. This variable name must be present in df.
  • grouping: Grouping or Clustering variable name of interest, specified as a Symbol. This variable name must be present in df.
  • d: Base Distribution of outcome from Distributions.jl.
  • link: Canonical Link function of the base distribution specified in d, from GLM.jl.

Optional Arguments

  • penalized: Boolean to specify whether or not to add an L2 Ridge penalty on the variance parameter for the CS structured covariance. One can turn this option on by specifying penalized = true to add this penalty for numerical stability. (default penalized = false).
source
CS_model(df, y, grouping, covariates, d, link; penalized = penalized)

Form the compound symmetric (CS) model for regression with the specified base distribution (d) and link function (link).

Arguments

  • df: A named DataFrame
  • y: Ouctcome variable name of interest, specified as a Symbol. This variable name must be present in df.
  • grouping: Grouping or Clustering variable name of interest, specified as a Symbol. This variable name must be present in df.
  • covariates: Covariate names of interest as a vector of Symbols. Each variable name must be present in df.
  • d: Base Distribution of outcome from Distributions.jl.
  • link: Canonical Link function of the base distribution specified in d, from GLM.jl.

Optional Arguments

  • penalized: Boolean to specify whether or not to add an L2 Ridge penalty on the variance parameter for the CS structured covariance. One can turn this option on by specifying penalized = true to add this penalty for numerical stability. (default penalized = false).
source
QuasiCopula.VC_model — Function
VC_model(df, y, grouping, d, link)

Form the variance component model (VCM) for intercept only regression with a random intercept covariance matrix and the specified base distribution (d) and link function (link).

Arguments

  • df: A named DataFrame
  • y: Ouctcome variable name of interest, specified as a Symbol. This variable name must be present in df.
  • grouping: Grouping or Clustering variable name of interest, specified as a Symbol. This variable name must be present in df.
  • d: Base Distribution of outcome from Distributions.jl.
  • link: Canonical Link function of the base distribution specified in d, from GLM.jl.

Optional Arguments

  • penalized: Boolean to specify whether or not to add an L2 Ridge penalty on the variance components vector. One can put true (e.g. penalized = true) to add this penalty for numerical stability (default penalized = false).
source
VC_model(df, y, grouping, covariates, d, link)

Form the variance component model (VCM) for regression with a random intercept covariance matrix and the specified base distribution (d) and link function (link).

Arguments

  • df: A named DataFrame
  • y: Ouctcome variable name of interest, specified as a Symbol. This variable name must be present in df.
  • grouping: Grouping or Clustering variable name of interest, specified as a Symbol. This variable name must be present in df.
  • covariates: Covariate names of interest as a vector of Symbols. Each variable name must be present in df.
  • d: Base Distribution of outcome from Distributions.jl.
  • link: Canonical Link function of the base distribution specified in d, from GLM.jl.

Optional Arguments

  • penalized: Boolean to specify whether or not to add an L2 Ridge penalty on the variance components vector. One can put true (e.g. penalized = true) to add this penalty for numerical stability (default penalized = false).
source
VC_model(df, y, grouping, covariates, V, d, link)

Form the variance component model (VCM) for intercept only regression with the specified base distribution (d) and link function (link).

Arguments

  • df: A named DataFrame
  • y: Ouctcome variable name of interest, specified as a Symbol. This variable name must be present in df.
  • grouping: Grouping or Clustering variable name of interest, specified as a Symbol. This variable name must be present in df.
  • V: Vector of Vector of Positive Semi-Definite (PSD) Covariance Matrices. V is of length n, where n is the number of groups/clusters. Each element of V is also a Vector, but of length m. Here m is the number of variance components. Each element of V is a Vector of di x di PSD covariance matrices under the VCM framework, where d_i is the cluster size of the ith cluster, which may vary for each cluster of observations i in [1, n]. Each of these dimensions must match that specified in df.
  • d: Base Distribution of outcome from Distributions.jl.
  • link: Canonical Link function of the base distribution specified in d, from GLM.jl.

Optional Arguments

  • penalized: Boolean to specify whether or not to add an L2 Ridge penalty on the variance components vector. One can put true (e.g. penalized = true) to add this penalty for numerical stability (default penalized = false).
source
VC_model(df, y, grouping, covariates, V, d, link)

Form the variance component model (VCM) for regression with the specified base distribution (d) and link function (link).

Arguments

  • df: A named DataFrame
  • y: Ouctcome variable name of interest, specified as a Symbol. This variable name must be present in df.
  • grouping: Grouping or Clustering variable name of interest, specified as a Symbol. This variable name must be present in df.
  • covariates: Covariate names of interest as a vector of Symbols. Each variable name must be present in df.
  • V: Vector of Vector of Positive Semi-Definite (PSD) Covariance Matrices. V is of length n, where n is the number of groups/clusters. Each element of V is also a Vector, but of length m. Here m is the number of variance components. Each element of V is a Vector of di x di PSD covariance matrices under the VCM framework, where d_i is the cluster size of the ith cluster, which may vary for each cluster of observations i in [1, n]. Each of these dimensions must match that specified in df.
  • d: Base Distribution of outcome from Distributions.jl.
  • link: Canonical Link function of the base distribution specified in d, from GLM.jl.

Optional Arguments

  • penalized: Boolean to specify whether or not to add an L2 Ridge penalty on the variance components vector. One can put true (e.g. penalized = true) to add this penalty for numerical stability (default penalized = false).
source
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