Public Documentation

Documentation for MixedModels.jl's public interface.

MixedModels

# MixedModels.GeneralizedLinearMixedModel — Type.

GeneralizedLinearMixedModel

Generalized linear mixed-effects model representation

Members:

  • LMM: a LinearMixedModel - used for the random effects only.
  • dist: a UnivariateDistribution - typically Bernoulli(), Binomial(), Gamma() or Poisson().
  • link: a suitable GLM.Link object
  • β: the fixed-effects vector
  • θ: covariance parameter vector
  • b: similar to u, equivalent to broadcast!(*, b, LMM.Λ, u)
  • u: a vector of matrices of random effects
  • u₀: similar to u. Used in the PIRLS algorithm if step-halving is necessary.
  • X:
  • y: the response vector
  • μ: the mean vector
  • η: the linear predictor
  • devresid: vector of squared deviance residuals
  • offset: offset₀ + X * β
  • offset₀: prior offset; T[] is allowed
  • wrkresid: vector of working residuals
  • wrkwt: vector of working weights
  • wt: vector of prior case weights, a value of T[] indicates equal weights.

# MixedModels.LinearMixedModel — Type.

LinearMixedModel

Linear mixed-effects model representation

Members

  • formula: the formula for the model
  • mf: the model frame, mostly used to get the terms component for labelling fixed effects
  • wttrms: a length nt vector of weighted model matrices. The last two elements are X and y.
  • trms: a vector of unweighted model matrices. If isempty(sqrtwts) the same object as wttrms
  • Λ: a length nt - 2 vector of lower triangular matrices
  • sqrtwts: the Diagonal matrix of the square roots of the case weights. Allowed to be size 0
  • A: an nt × nt symmetric matrix of matrices representing hcat(Z,X,y)'hcat(Z,X,y)
  • R: a nt × nt matrix of matrices - the upper Cholesky factor of Λ'AΛ+I
  • opt: an OptSummary object

# MixedModels.OptSummary — Type.

OptSummary

Summary of an NLopt optimization

Members

  • initial: a copy of the initial parameter values in the optimization
  • final: a copy of the final parameter values from the optimization
  • fmin: the final value of the objective
  • feval: the number of function evaluations
  • optimizer: the name of the optimizer used, as a Symbol

# MixedModels.ReMat — Type.

ReMat

A representation of the model matrix for a random-effects term

# MixedModels.ScalarReMat — Type.

ScalarReMat

The representation of the model matrix for a scalar random-effects term

Members

  • f: the grouping factor as a PooledDataVector
  • z: the raw random-effects model matrix as a Vector
  • fnm: the name of the grouping factor as a Symbol
  • cnms: a Vector of column names

# MixedModels.VarCorr — Type.

VarCorr

An encapsulation of information on the fitted random-effects variance-covariance matrices.

Members

  • Λ: the vector of lower triangular matrices from the MixedModel
  • fnms: a Vector{ASCIIString} of grouping factor names
  • cnms: a Vector{Vector{ASCIIString}} of column names
  • s: the estimate of σ, the standard deviation of the per-observation noise

The main purpose of defining this type is to isolate the logic in the show method.

# MixedModels.VectorReMat — Type.

VectorReMat

The representation of the model matrix for a vector-valued random-effects term

Members

  • f: the grouping factor as a PooledDataVector
  • z: the transposed raw random-effects model matrix
  • fnm: the name of the grouping factor as a Symbol
  • cnms: a Vector of column names (row names after transposition) of z

# Base.LinAlg.cond — Method.

cond(m::MixedModel)

Returns the vector of the condition numbers of the blocks of m.Λ

# Base.std — Method.

std{T}(m::MixedModel{T})

The estimated standard deviations of the variance components as a Vector{Vector{T}}.

# MixedModels.LaplaceDeviance — Method.

LaplaceDeviance{T,D}(m::GeneralizedLinearMixedModel{T,D})

Return the Laplace approximation to the deviance of m.

If the distribution D does not have a scale parameter the Laplace approximation is defined as the squared length of the conditional modes, u, plus the determinant of Λ'Z'ZΛ + 1, plus the sum of the squared deviance residuals.

# MixedModels.bootstrap! — Method.

bootstrap!{T}(r::Matrix{T}, m::LinearMixedModel{T}, f!::Function;
    β=fixef(m), σ=sdest(m), θ=getθ(m))

Overwrite columns of r with the results of applying the mutating extractor f! to parametric bootstrap replications of model m.

The signature of f! should be f!{T}(v::AbstractVector{T}, m::LinearMixedModel{T})

Named Arguments

β::Vector{T}, σ::T, and θ::Vector{T} are the values of the parameters in m for simulation of the responses.

# MixedModels.cfactor! — Method.

cfactor!(A::AbstractMatrix)

A slightly modified version of chol! from Base

Uses inject! (as opposed to copy!), downdate! (as opposed to syrk! or gemm!) and recursive calls to cfactor!.

Note: The cfactor! method for dense matrices calls LAPACK.potrf! directly to avoid errors being thrown when A is computationally singular

# MixedModels.fixef — Method.

fixef(m::MixedModel)

Returns the fixed-effects parameter vector estimate.

# MixedModels.getθ — Method.

getθ(A::LowerTriangular{T, Matrix{T}})

Return a vector of the elements of the lower triangle of A (column-major ordering)

# MixedModels.glmm — Method.

glmm(f::Formula, fr::ModelFrame, d::Distribution[, l::GLM.Link])

Return a GeneralizedLinearMixedModel object.

The value is ready to be fit! but has not yet been fit.

# MixedModels.lmm — Method.

lmm(f::DataFrames.Formula, fr::DataFrames.DataFrame; weights = [])

Create a LinearMixedModel from f, which contains both fixed-effects terms and random effects, and fr.

The return value is ready to be fit! but has not yet been fit.

# MixedModels.lmm — Method.

lmm(m::MixedModel)

Extract the LinearMixedModel from a MixedModel.

If m is a LinearMixedModel return m. If m is a GeneralizedLinearMixedModel return m.LMM.

# MixedModels.lowerbd — Method.

lowerbd{T}(A::LowerTriangular{T,Matrix{T}})

Return the vector of lower bounds on the parameters, θ.

These are the elements in the lower triangle in column-major ordering. Diagonals have a lower bound of 0. Off-diagonals have a lower-bound of -Inf.

# MixedModels.lowerbd — Method.

lowerbd(m::LinearMixedModel)

Return the vector of lower bounds on the covariance parameter vector θ

# MixedModels.objective — Method.

objective(m::LinearMixedModel)

Return negative twice the log-likelihood of model m

# MixedModels.pirls! — Method.

pirls!(m::GeneralizedLinearMixedModel)

Use Penalized Iteratively Reweighted Least Squares (PIRLS) to determine the conditional modes of the random effects.

# MixedModels.pwrss — Method.

pwrss(m::LinearMixedModel)

The penalized residual sum-of-squares.

# MixedModels.ranef — Function.

ranef{T}(m::MixedModel{T}, uscale=false)

Returns, as a Vector{Matrix{T}}, the conditional modes of the random effects in model m.

If uscale is true the random effects are on the spherical (i.e. u) scale, otherwise on the original scale.

# MixedModels.refit! — Method.

refit!{T}(m::LinearMixedModel{T}[, y::Vector{T}])

Refit the model m after installing response y.

If y is omitted the current response vector is used.

# MixedModels.remat — Method.

 remat(e::Expr, df::DataFrames.DataFrame)

A factory for ReMat objects.

e should be of the form :(e1 | e2) where e1 is a valid rhs of a Formula and pool(e2) can be evaluated within df. The result is a ScalarReMat or a VectorReMat, as appropriate.

# MixedModels.sdest — Method.

sdest(m::LinearMixedModel)

Return the estimate of σ, the standard deviation of the per-observation noise.

# MixedModels.setθ! — Method.

setθ!{T}(m::LinearMixedModel{T}, v::Vector{T})

Install v as the θ parameters in m. Changes m.Λ only.

# MixedModels.simulate! — Method.

simulate!(m::LinearMixedModel; β=fixef(m), σ=sdest(m), θ=getΘ(m))

Overwrite the response (i.e. m.trms[end]) with a simulated response vector from model m.

# MixedModels.varest — Method.

varest(m::LinearMixedModel)

Returns the estimate of σ², the variance of the conditional distribution of Y given B.

# StatsBase.fit! — Function.

fit!(m::LinearMixedModel[, verbose::Bool=false[, optimizer::Symbol=:LN_BOBYQA]])

Optimize the objective of a LinearMixedModel.

A value for optimizer should be the name of an NLopt derivative-free optimizer allowing for box constraints.

# StatsBase.fit! — Function.

fit!(m::GeneralizedLinearMixedModel[, verbose = false, optimizer=:LN_BOBYQA]])

Optimize the objective function for m

# StatsBase.vcov — Method.

 vcov(m::MixedModel)

Returns the estimated covariance matrix of the fixed-effects estimator.