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#
# Copyright 2007-2021 by the individuals mentioned in the source code history
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
#------------------------------------------------------------------------------
# Author: Michael D. Hunter
# Date: 2016-01-30
# Filename: MxRobustSE.R
# Purpose: Write a function for robust standard errors
#------------------------------------------------------------------------------
##' imxRowGradients
##'
##' This is an internal function exported for those people who know
##' what they are doing.
##'
##' This function computes the gradient for each row of data.
##' The returned object is a matrix with the same number of rows as the data,
##' and the same number of columns as there are free parameters.
##'
##' @param model An OpenMx model object that has been run
##' @param robustSE Logical; are the row gradients being requested to calculate robust standard errors?
##' @param dependencyModels Vector of character strings naming
##' submodels that do not contain data, but contain objects
##' to which data-containing models make reference.
imxRowGradients <- function(model, robustSE=FALSE, dependencyModels=character(0)){
if(is.null(model@output)){
stop("The 'model' argument has no output. Give me a model that has been run.")
}
#If 'model' contains submodels and uses the multigroup fitfunction, then we can be pretty sure what we're supposed to do to get
#row gradients:
if(length(model@submodels)){
if(is(model@fitfunction,"MxFitFunctionMultigroup")){
grads <- NULL
paramLabels <- names(omxGetParameters(model))
numParam <- length(paramLabels)
contributingModelNames <- model@fitfunction$groups
custom.compute <- mxComputeSequence(list(mxComputeNumericDeriv(checkGradient=FALSE, hessian=FALSE), mxComputeReportDeriv()))
for(i in 1:length(model@submodels)){
#Ignore submodels that don't contribute to the multigroup fitfunction:
if(length(grep(pattern=model@submodels[[i]]$name,x=contributingModelNames))){
currModel <- model@submodels[[i]]
if(is.null(currModel@data)){
if(robustSE){
#This is a warning, not an error, because there are edge cases where the robust SEs could still be valid:
warning(paste("submodel '",currModel@name,"' contributes to the multigroup fitfunction but contains no data; robust standard errors may be incorrect",sep=""))
}
next
}
if(currModel@data$type!="raw"){
if(robustSE){
stop(paste("submodel '",currModel@name,"' contributes to the multigroup fitfunction but does not contain raw data, which is required for robust standard errors",sep=""))
}
next
}
if(robustSE && is(currModel@fitfunction, "MxFitFunctionWLS")){
stop(paste("submodel '",currModel@name,"' contributes to the multigroup fitfunction but uses WLS fit; robust standard errors require ML fit",sep=""))
}
if(length(currModel@submodels)){ #<--Possible TODO: handle this case with function recursion
if(robustSE){
warning(paste("submodel '",currModel@name,
"' contains submodels of its own; support for submodels of submodels not implemented, so robust standard errors may be incorrect",sep=""))
}
else{
warning(paste("submodel '",currModel@name,
"' contains submodels of its own; support for submodels of submodels not implemented",sep=""))
}
}
if(length(dependencyModels)){
currModel <- mxModel(currModel,model@submodels[dependencyModels])
}
#By itself, a GREML model can't get robust SEs; you'd end up calculating the variance of the row derivatives for a sample of n=1 row.
#But, if it's a submodel contributing to a multigroup fit (admittedly a corner case), then it's just another data row
#(though I am not sure if the theory underlying the sandwich estimator still applies for restricted maximum likelihood):
if(is(currModel@expectation, "MxExpectationGREML")){
#There is assumed to be only one "row" with GREML expectation, even if the raw dataset isn't (yet) structured that way:
currGrads <- matrix(0,nrow=1,ncol=numParam,dimnames=list(NULL,paramLabels))
grun <- mxRun(mxModel(currModel, custom.compute))
currGrads[1,names(grun$output$gradient)] <- grun$output$gradient
grads <- rbind(grads,currGrads)
}
else{
currData <- currModel@data$observed
currGrads <- matrix(0,nrow=nrow(currData),ncol=numParam,dimnames=list(NULL,paramLabels))
for(j in 1:nrow(currData)){
grun <- mxRun(mxModel(currModel, custom.compute, mxData(currData[j,,drop=FALSE],"raw")), silent=as.logical((j-1)%%100))
currGrads[j,names(grun$output$gradient)] <- grun$output$gradient
}
grads <- rbind(grads,currGrads)
}
}
}
}
else{stop("to obtain gradients for data rows in submodels, please use an MxFitFunctionMultigroup in 'model'")}
}
else{ #i.e., if no submodels
if(is.null(model@data)){
stop("The 'model' argument must have data, or if multigroup, use an MxFitFunctionMultigroup")
}
if(model$data$type!='raw'){
stop("The 'model' argument must have raw (not summary) data.")
}
nrows <- nrow(model$data$observed)
data <- model@data@observed
custom.compute <- mxComputeSequence(list(mxComputeNumericDeriv(checkGradient=FALSE, hessian=FALSE), mxComputeReportDeriv()))
grads <- matrix(NA, nrows, length(coef(model)))
gmodel <- model
for(i in 1:nrows){
gmodel <- mxModel(gmodel, custom.compute, mxData(data[i,,drop=FALSE], 'raw'))
grun <- mxRun(gmodel, silent = as.logical((i-1)%%100), suppressWarnings = FALSE)
grads[i,] <- grun$output$gradient #get gradient
}
}
return(grads)
}
##' imxRobustSE
##'
##' This is an internal function exported for those people who know
##' what they are doing.
##'
##' This function computes robust standard errors via a sandwich estimator.
##' The "bread" of the sandwich is the numerically computed inverse Hessian
##' of the likelihood function. This is what is typically used for standard
##' errors throughout OpenMx. The "meat" of the sandwich is proportional to
##' the covariance matrix of the numerically computed row derivatives of the
##' likelihood function (i.e. row gradients).
##'
##' When \code{details=FALSE}, only the standard errors are returned.
##'
##' When \code{details=TRUE},
##' a list with five named elements is returned. Element \code{SE} is the
##' vector of standard errors that is also returned when \code{details=FALSE}.
##' Element \code{cov} is the full robust covariance matrix of the parameter
##' estimates; the square root of the diagonal of \code{cov} gives the
##' standard errors. Element \code{bread} is the aforementioned
##' "bread"--the naive (non-robust) covariance matrix of the parameter
##' estimates. Element \code{meat} is the aforementioned "meat," proportional
##' to the covariance matrix of the row gradients. Element \code{TIC}
##' is the model's Takeuchi Information Criterion, which is a generalization
##' of AIC calculated from the "bread," the "meat," and the loglikelihood
##' at the maximum-likelihood solution.
##'
##' This function does not work correctly with multigroup models in which the
##' groups themselves contain subgroups. This function also does not correctly handle
##' multilevel data.
##'
##' @param model An OpenMx model object that has been run.
##' @param details Logical. whether to return the full parameter
##' covariance matrix.
##' @param dependencyModels Passed to \code{imxRowGradients()}.
imxRobustSE <- function(model, details=FALSE, dependencyModels=character(0)){
if(is(model@expectation, "MxExpectationGREML")){
stop("robust standard errors cannot be calculated for a single-group model that uses GREML expectation")
}
if(!length(model@output$vcov)){
stop("imxRobustSE() requires model to have a nonempty 'vcov' output slot (has the model been run?)")
}
if(imxHasWLS(model)){
stop("'model' uses a WLS fitfunction; robust standard errors are automatically calculated for WLS models when they are run with the default compute plan")
}
if(!is(model@fitfunction, "MxFitFunctionML") && !is(model@fitfunction, "MxFitFunctionMultigroup")){
warning(paste("imxRobustSE() requires a maximum-likelihood fit, but 'model' uses ",class(model@fitfunction),"; robust standard errors will only be correct if the fitfunction units are -2lnL",sep=""))
}
parnames <- dimnames(model@output$vcov)
# if(!is.na(model@output$infoDefinite) && model@output$infoDefinite){
# #solve() will fail if Hessian is computationally singular;
# #chol2inv() will only fail if Hessian is exactly singular.
# bread <- chol2inv(chol(model@output$hessian/2))
# }
# #An indefinite Hessian usually means some SEs will be NaN:
# else{bread <- solve(model@output$hessian/2)}
bread <- vcov(model)
dimnames(bread) <- parnames
#The row gradients are the slowest part, so only do them now that we know the bread is good:
grads <- imxRowGradients(model, robustSE=TRUE, dependencyModels)/-2
meat <- nrow(grads)*var(grads)
rm(grads) #<--Could be huge in Big Data contexts...
dimnames(meat) <- parnames
ret <- OpenMx::"%&%"(bread, meat)
dimnames(ret) <- parnames
TIC <- NA
if(length(model@output$Minus2LogLikelihood)){TIC <- model@output$Minus2LogLikelihood + 2*sum(diag(meat%*%bread))}
if(details){
return(list(SE=sqrt(diag(ret)), cov=ret, bread=bread, meat=meat, TIC=TIC))
} else {
return(sqrt(diag(ret)))
}
}
#robse <- imxRobustSE(thresholdModelrun)
#cbind(robse, prevSE)
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