ds.glmerSLMA.R

#' @title Fits Generalized Linear Mixed-Effect Models via Study-Level Meta-Analysis
#' @description \code{ds.glmerSLMA} fits a Generalized Linear Mixed-Effects Model
#' (GLME) on data from one or multiple sources with pooling via SLMA (study-level meta-analysis).
#' @details \code{ds.glmerSLMA} fits a generalized linear mixed-effects model (GLME) 
#' - e.g. a logistic or Poisson regression model including both fixed and random effects -
#'  on data from single or multiple sources. 
#'  
#'  This function is similar to \code{glmer} function from \code{lme4} package in native R.
#'  
#'  When there are multiple data sources, the GLME is fitted to convergence 
#'  in each data source independently. The estimates and standard errors returned
#'  to the client-side which enable cross-study pooling  using Study-Level Meta-Analysis (SLMA).
#'  The SLMA used by default \code{metafor} package  
#'  but as the SLMA occurs on the client-side (a standard R environment), the user can choose 
#'  any approach to meta-analysis. Additional information about fitting GLMEs 
#'  using \code{glmer} function can be obtained using R help for \code{glmer} and the \code{lme4} package. 
#'  
#' In \code{formula} most shortcut notation allowed by \code{glmer()} function is
#' also allowed by \code{ds.glmerSLMA}. 
#' Many GLMEs can be fitted very simply using a formula like:
#' \deqn{y~a+b+(1|c)} 
#' which simply means fit an GLME  with \code{y} as the outcome variable (e.g. 
#' a binary case-control using a logistic regression model or a count or a survival
#' time using a Poisson regression model), \code{a} and \code{b}
#' as fixed effects, and \code{c} as a random effect or grouping factor. 
#' 
#' It is also possible to fit models with random slopes by specifying a model such as 
#' \deqn{y~a+b+(1+b|c)} 
#' where the effect of \code{b} can vary randomly between groups defined by \code{c}.
#' Implicit nesting can be specified with formulas such as: \eqn{y~a+b+(1|c/d)}
#' or \eqn{y~a+b+(1|c)+(1|c:d)}. 
#' 
#' 
#' The \code{dataName} argument avoids you having to specify the name of the
#' data frame in front of each covariate in the formula. 
#' For example, if the data frame is called \code{DataFrame} you avoid having to write: 
#' \eqn{DataFrame$y~DataFrame$a+DataFrame$b+(1|DataFrame$c)}.
#' 
#' The \code{checks} argument verifies that the variables in the model are all defined (exist) 
#' on the server-site at every study
#' and that they have the correct characteristics required to fit the model. 
#' It is suggested to make \code{checks} argument TRUE if an unexplained
#' problem in the model fit is encountered because the running process takes several minutes.
#' 
#' 
#' In the \code{family} argument can be specified two types of models to fit:
#'  \itemize{
#'    \item{\code{"binomial"}}{: logistic regression models}
#'    \item{\code{"poisson"}}{: poisson regression models}
#' }
#' 
#' Note if you are fitting a gaussian model (a standard linear mixed
#' model) you should use \code{ds.lmerSLMA} and not \code{ds.glmerSLMA}. 
#' For more information you can see R help for \code{lmer} and \code{glmer}. 
#' 
#' In \code{control_type} at present only one such parameter can be modified,
#' namely the tolerance of the convergence criterion to the gradient of the log-likelihood 
#' at the maximum likelihood achieved. We have enabled this because our practical experience
#' suggests that in situations where the model looks to have converged with sensible parameter
#' values but formal convergence is not being declared if we allow the model to be more
#' tolerant to a non-zero gradient the same parameter values are obtained but formal
#' convergence is declared. The default value for the \code{check.conv.grad} is \code{0.001} (note that
#' the default value of this argument in \code{ds.lmerSLMA} is  \code{0.002}). 
#' 
#' In \code{control_value} at present (see \code{control_type})
#' the only parameter this can be is the convergence tolerance \code{check.conv.grad}. In
#' general, models will be identified as having converged more readily if the value set
#' for \code{check.conv.grad} is increased from its default value (\code{0.001}).  Please note
#' that the risk of doing this is that the model is also more likely to be declared
#' as having converged at a local maximum that is not the global maximum likelihood.
#' This will not generally be a problem if the likelihood surface is well behaved but if
#' you have a problem with convergence you might usefully compare all the parameter
#' estimates and standard errors obtained using the default tolerance (\code{0.001}) even though
#' that has not formally converged with those obtained after convergence using the higher
#' tolerance. 
#' 
#' Server function called: \code{glmerSLMADS2} 
#' 
#' @param formula an object of class formula describing the model to be fitted. 
#' For more information see \strong{Details}. 
#' @param offset  a character string specifying the name of a variable to be used as
#' an offset.
#' @param weights a character string specifying the name of a variable containing
#' prior regression weights for the fitting process.
#' @param combine.with.metafor logical. If TRUE the
#' estimates and standard errors for each regression coefficient are pooled across
#' studies using random-effects meta-analysis under maximum likelihood (ML),
#' restricted maximum likelihood (REML) or fixed-effects meta-analysis (FE). Default TRUE. 
#' @param dataName a character string specifying the name of a data frame
#' that contains all of the variables in the GLME formula. For more information see \strong{Details}.
#' @param checks logical. If TRUE \code{ds.glmerSLMA} checks the structural integrity 
#' of the model. Default FALSE. For more information see \strong{Details}.  
#' @param datasources a list of \code{\link{DSConnection-class}} objects obtained after login. 
#' If the \code{datasources} argument is not specified
#' the default set of connections will be used: see \code{\link{datashield.connections_default}}.
#' @param family a character string specifying the distribution of the observed
#' value of the outcome variable around the predictions generated by the linear predictor.
#' This can be set as \code{"binomial"} or \code{"poisson"}. 
#' For more information see \strong{Details}. 
#' @param control_type an optional character string vector specifying the nature of a parameter
#' (or parameters) to be modified in the \code{convergence control options} which can be viewed or
#' modified via the \code{glmerControl} function of the package \code{lme4}. 
#' For more information see \strong{Details}.  
#' @param control_value numeric representing the new value which you want to allocate the
#' control parameter corresponding to the \code{control-type}. 
#' For more information see \strong{Details}.
#' @param nAGQ an integer value indicating the number of points per axis for evaluating the adaptive 
#' Gauss-Hermite approximation to the log-likelihood. Defaults 1, corresponding to the Laplace approximation.
#' For more information see  R \code{glmer} function help. 
#' @param verbose an integer value. If \eqn{verbose > 0} the output is generated during the optimization of
#' the parameter estimates. If \eqn{verbose > 1} the output is generated during the individual penalized 
#' iteratively reweighted least squares (PIRLS) steps. Default \code{verbose} 
#'  value is 0 which means no additional output. 
#' @param start_theta a numeric vector of length equal to the number of random effects. Specify to retain
#' more control over the optimisation. See \code{glmer()} for more details.
#' @param start_fixef a numeric vector of length equal to the number of fixed effects (NB including the intercept). 
#' Specify to retain more control over the optimisation. See \code{glmer()} for more details.
#' @param notify.of.progress specifies if console output should be produced to indicate
#' progress. Default  FALSE.
#' @param assign a logical, indicates whether the function will call a second server-side function
#' (an assign) in order to save the regression outcomes (i.e. a glmerMod object) on each server.
#' Default FALSE.
#' @param newobj a character string specifying the name of the object to which the glmerMod object
#' representing the model fit on the serverside in each study is to be written. This argument is 
#' used only when the argument \code{assign} is set to TRUE.
#' If no <newobj> argument is specified, the output object defaults to "new.glmer.obj". 
#' @return Many of the elements of the output list returned by \code{ds.glmerSLMA} are 
#' equivalent to those returned by the \code{glmer()} function in native R. However,
#' potentially disclosive elements
#' such as individual-level residuals and linear predictor values are blocked. 
#' In this case, only non-disclosive elements are returned from each study separately.
#' 
#' The list of elements returned by \code{ds.glmerSLMA} is mentioned below: 
#' 
#' @return \code{coefficients}: a matrix with 5 columns:
#'    \itemize{
#'    \item{First}{: the names of all of the regression parameters (coefficients) in the model} 
#'    \item{second}{: the estimated values} 
#'    \item{third}{: corresponding standard errors of the estimated values} 
#'    \item{fourth}{: the ratio of estimate/standard error} 
#'    \item{fifth}{: the p-value treating that as a standardised normal deviate} 
#' }
#' @return \code{CorrMatrix}: the correlation matrix of parameter estimates.
#' @return \code{VarCovMatrix}: the variance-covariance matrix of parameter estimates.
#' @return \code{weights}: the vector (if any) holding regression weights.
#' @return \code{offset}: the vector (if any) holding an offset.
#' @return \code{cov.scaled}: equivalent to \code{VarCovMatrix}.
#' @return \code{Nmissing}: the number of missing observations in the given study.
#' @return \code{Nvalid}: the number of valid (non-missing) observations in the given study.
#' @return \code{Ntotal}: the total number of observations 
#'                        in the given study (\code{Nvalid} + \code{Nmissing}).
#' @return \code{data}: equivalent to input parameter \code{dataName} (above).
#' @return \code{call}: summary of key elements of the call to fit the model.
#' @return Once the study-specific output has been returned, the function returns the
#' number of elements relating to the pooling of estimates across studies via
#' study-level meta-analysis. These are as follows:
#' @return \code{input.beta.matrix.for.SLMA}: a matrix containing the vector of coefficient
#' estimates from each study.
#' @return \code{input.se.matrix.for.SLMA}: a matrix containing the vector of standard error
#' estimates for coefficients from each study.
#' @return \code{SLMA.pooled.estimates}: a matrix containing pooled estimates for each
#' regression coefficient across all studies with pooling under SLMA via
#' random-effects meta-analysis under maximum likelihood (ML), restricted maximum
#' likelihood (REML) or via fixed-effects meta-analysis (FE).
#' @return \code{convergence.error.message}: reports for each study whether the model converged.
#' If it did not some information about the reason for this is reported.
#' @examples 
#' \dontrun{
#' 
#'  ## Version 6, for version 5 see Wiki
#'   # Connecting to the Opal servers
#'   
#'   require('DSI')
#'   require('DSOpal')
#'   require('dsBaseClient')
#'   
#'   builder <- DSI::newDSLoginBuilder()
#'   builder$append(server = "study1", 
#'                  url = "http://192.168.56.100:8080/", 
#'                  user = "administrator", password = "datashield_test&", 
#'                  table = "CNSIM.CNSIM1", driver = "OpalDriver")
#'   builder$append(server = "study2", 
#'                  url = "http://192.168.56.100:8080/", 
#'                  user = "administrator", password = "datashield_test&", 
#'                  table = "CNSIM.CNSIM2", driver = "OpalDriver")
#'   builder$append(server = "study3",
#'                  url = "http://192.168.56.100:8080/", 
#'                  user = "administrator", password = "datashield_test&", 
#'                  table = "CNSIM.CNSIM3", driver = "OpalDriver")
#'   logindata <- builder$build()
#'   
#'   # Log onto the remote Opal training servers
#'   connections <- DSI::datashield.login(logins = logindata, assign = TRUE, symbol = "D") 
#'   
#'   # Select all rows without missing values
#'   
#'   ds.completeCases(x1 = "D", newobj = "D.comp", datasources = connections)
#'   
#'   # Fit a Poisson regression model
#'   
#'   ds.glmerSLMA(formula = "LAB_TSC ~ LAB_HDL + (1 | GENDER)",
#'                offset = NULL,
#'                dataName = "D.comp",
#'                datasources = connections,
#'                family = "poisson")
#'                
#'   # Clear the Datashield R sessions and logout
#'   datashield.logout(connections)
#'   
#'   builder <- DSI::newDSLoginBuilder()
#'   builder$append(server = "study1", 
#'                  url = "http://192.168.56.100:8080/", 
#'                  user = "administrator", password = "datashield_test&", 
#'                  table = "CLUSTER.CLUSTER_SLO1", driver = "OpalDriver")
#'   builder$append(server = "study2", 
#'                  url = "http://192.168.56.100:8080/", 
#'                  user = "administrator", password = "datashield_test&", 
#'                  table = "CLUSTER.CLUSTER_SLO2", driver = "OpalDriver")
#'   builder$append(server = "study3",
#'                  url = "http://192.168.56.100:8080/", 
#'                  user = "administrator", password = "datashield_test&", 
#'                  table = "CLUSTER.CLUSTER_SLO3", driver = "OpalDriver")
#'   logindata <- builder$build()
#'   
#'    # Log onto the remote Opal training servers
#'    connections <- DSI::datashield.login(logins = logindata, assign = TRUE, symbol = "D")
#'                 
#'                 
#'      # Fit a Logistic regression model
#'   
#'   ds.glmerSLMA(formula = "Male ~  incid_rate +diabetes + (1 | age)",
#'                dataName = "D",
#'                datasources = connections[2],#only the second server is used (study2)
#'                family = "binomial")
#'   
#'   
#'   # Clear the Datashield R sessions and logout
#'   datashield.logout(connections) 
#'   }
#'   
#' 
#' 
#' @author DataSHIELD Development Team
#' @export
#' 
ds.glmerSLMA <- function(formula=NULL, offset=NULL, weights=NULL, combine.with.metafor=TRUE, dataName=NULL,
                       checks=FALSE, datasources=NULL, family=NULL, 
                       control_type = NULL, control_value = NULL, nAGQ = 1L, verbose = 0,
                       start_theta = NULL, start_fixef = NULL, notify.of.progress=FALSE, 
                       assign=FALSE, newobj=NULL){
  
  # look for DS connections
  if(is.null(datasources)){
    datasources <- datashield.connections_find()
  }

  # ensure datasources is a list of DSConnection-class
  if(!(is.list(datasources) && all(unlist(lapply(datasources, function(d) {methods::is(d,"DSConnection")}))))){
    stop("The 'datasources' were expected to be a list of DSConnection-class objects", call.=FALSE)
  }

  # verify that 'formula' was set
  if(is.null(formula)){
    stop(" Please provide a valid regression formula!", call.=FALSE)
  }
  
  # check if user gave offset or weights directly in formula, if so the argument 'offset' or 'weights'
  # to provide name of offset or weights variable
  if(sum(as.numeric(grepl('offset', formula, ignore.case=TRUE)))>0 ||
     sum(as.numeric(grepl('weights', formula, ignore.case=TRUE)))>0)
  {
    cat("\n\n WARNING: you may have specified an offset or regression weights")
    cat("\n as part of the model formula. In ds.glm (unlike the usual glm in R)")
    cat("\n you must specify an offset or weights separately from the formula")
    cat("\n using the offset or weights argument.\n\n")
  }
  
  formula <- stats::as.formula(formula)
  
  # check that 'family' was set
  if(is.null(family)){
    stop(" Please provide a valid 'family' argument!", call.=FALSE)
  }
  
  # if the argument 'dataName' is set, check that the data frame is defined (i.e. exists) on the server site
  if(!(is.null(dataName))){
    defined <- isDefined(datasources, dataName)
  }
  
  # beginning of optional checks - the process stops if any of these checks fails #
  if(checks){
    message(" -- Verifying the variables in the model")
    # call the function that checks the variables in the formula are defined (exist) on the server site and are not missing at complete
    
    glmChecks(formula, dataName, offset, weights, datasources)
  }else{
    #message("WARNING:'checks' is set to FALSE; variables in the model are not checked and error messages may not be intelligible!")
  }
  
  #formula as text, then split at pipes to avoid triggering parser
  formula <- Reduce(paste, deparse(formula))
  formula <- gsub("|", "xxx", formula, fixed = TRUE)
  formula <- gsub("(", "yyy", formula, fixed = TRUE)
  formula <- gsub(")", "zzz", formula, fixed = TRUE)
  formula <- gsub("/", "ppp", formula, fixed = TRUE)
  formula <- gsub(":", "qqq", formula, fixed = TRUE)
  formula <- gsub(" ", "", formula, fixed = TRUE)
  formula <- stats::as.formula(formula)
  #formula <- strsplit(x = formurand()la, split="|", fixed=TRUE)[[1]]
  
  # sort out the start values into transmissable format
  
  if(!is.null(start_theta)){
    theta = paste0(as.character(start_theta), collapse=",")
  }else{
    theta = NULL
  }
  if(!is.null(start_fixef)){
    fixef = paste0(as.character(start_fixef), collapse=",")
  }else{
    fixef = NULL
  }
  
  
  #Sort out control_type and control_value
  
  if(!is.null(control_type) && is.null(control_value))
  {
    errorMessage.cv<-"ERROR: if control_type is non-null, you must specify a valid control_value eg control_value<-1.0e-7"
    #	print(errorMessage.cv)
    return(list(errorMessage=errorMessage.cv))
  }
  
  if(!is.null(control_value))
  {
    if(is.character(control_value))
    {
      control_value.transmit<-control_value
    }else{
      control_value.transmit<-as.character(control_value)
    }
  }else{
    control_value.transmit<-NULL
  }
  
  #check nAGQ is not null which would block the call  
  if(is.null(nAGQ))
  {
    nAGQ<-1L
  }
  
  #NOW CALL SECOND COMPONENT OF glmDS TO GENERATE SCORE VECTORS AND INFORMATION MATRICES
  
  
  calltext <- call('glmerSLMADS2', formula, offset, weights, dataName, family, 
                   control_type, control_value.transmit, nAGQ, verbose, theta, fixef)
  
  if(assign==TRUE){
    
    if(is.null(newobj)){
      newobj <- "new.glmer.obj"
    }
    
    
    if (notify.of.progress) {
        cat("\n\nSAVING SERVERSIDE glmerMod OBJECT AS: <",newobj,">\n\n")
    }

    calltext.2 <- call('glmerSLMADS.assign', formula, offset, weights, dataName, family, 
                       control_type, control_value.transmit, nAGQ, verbose, theta, fixef)
    
    DSI::datashield.assign(datasources, newobj, calltext.2)
    
  }
  
  study.summary <- datashield.aggregate(datasources, calltext)
  
  
  
  numstudies<-length(datasources)
  
  numstudies<-length(datasources)
  
  study.include.in.analysis<-NULL
  study.with.errors<-NULL
  all.studies.valid<-1
  no.studies.valid<-1
  
  for(j in 1:numstudies)
  {
    ss1<-study.summary[[j]]
    if(ss1$disclosure.risk==0)
    {
      study.include.in.analysis<-c(study.include.in.analysis,j)
      no.studies.valid<-0
      
    }else{
      study.with.errors<-c(study.with.errors,j)
      all.studies.valid<-0
    }
    
  }
  
  if (notify.of.progress)
  {
    if(!all.studies.valid)
    {
      for(sse in study.with.errors)
      {
        cat("\n","Error report from second serverside function for study",sse,"\n")
        cat("############################################################","\n")
        cat(unlist(study.summary[[sse]][[1]]),"\n")
        cat(unlist(study.summary[[sse]][[2]]),"\n\n")
        
        num.messages<-length(study.summary[[sse]])-2
        for(m in 1:num.messages)
        {
          if(!is.null(unlist(study.summary[[sse]][[2+m]])))
          {
            cat(unlist(study.summary[[sse]][[2+m]]),"\n\n")
          }
        }
      }
    }
    
    if(all.studies.valid)
    {
      cat("\nAll studies passed disclosure tests\n")
      cat("Please check for convergence warnings in the study summaries\n\n\n")
    }
  }
  
  
  
  #MAKE SURE THAT IF SOME STUDIES HAVE MORE PARAMETERS IN THE
  #FITTED glm (eg BECAUSE OF ALIASING) THE FINAL RETURN MATRICES
  #HAVE ENOUGH ROWS TO FIT THE MAXIMUM LENGTH
  
  
  numcoefficients.max<-0
  
  for(g in study.include.in.analysis){
    if(length(study.summary[[g]]$coefficients[,1])>numcoefficients.max){
      numcoefficients.max<-length(study.summary[[g]]$coefficients[,1])
    }
  }
  
  numcoefficients<-numcoefficients.max
  
  betamatrix<-matrix(NA,nrow<-numcoefficients,ncol=numstudies)
  sematrix<-matrix(NA,nrow<-numcoefficients,ncol=numstudies)
  
  
  for(k in study.include.in.analysis){
    betamatrix[,k]<-study.summary[[k]]$coefficients[,1]
    sematrix[,k]<-study.summary[[k]]$coefficients[,2]
  }
  
  ################################################
  #ANNOTATE OUTPUT MATRICES WITH STUDY INDICATORS#
  ################################################
  
  study.names.list<-NULL
  betas.study.names.list<-NULL
  ses.study.names.list<-NULL
  
  
  
  for(v in 1:numstudies){
    
    study.names.list<-c(study.names.list,paste0("study",as.character(v)))
    betas.study.names.list<-c(betas.study.names.list,paste0("betas study ",as.character(v)))
    ses.study.names.list<-c(ses.study.names.list,paste0("ses study ",as.character(v)))
  }
  
  dimnames(betamatrix)<-list(dimnames(study.summary[[1]]$coefficients)[[1]], betas.study.names.list)
  dimnames(sematrix)<-list(dimnames(study.summary[[1]]$coefficients)[[1]], ses.study.names.list)
  
  output.summary.text<-paste0("list(")
  
  for(u in 1:numstudies){
    output.summary.text<-paste0(output.summary.text,"study",as.character(u),"=study.summary[[",as.character(u),"]],"," ")
  }
  
  output.summary.text.save<-output.summary.text
  output.summary.text<-paste0(output.summary.text,"input.beta.matrix.for.SLMA=as.matrix(betamatrix),input.se.matrix.for.SLMA=as.matrix(sematrix))")
  
  
  output.summary<-eval(parse(text=output.summary.text))
  #######################END OF ANNOTATION CODE
  
  SLMA.pooled.ests.matrix<-matrix(NA,nrow<-numcoefficients,ncol=6)
  
  
  if(!combine.with.metafor){
    return(output.summary)
  }
  
  if(no.studies.valid)
  {
    return(output.summary)
  }
  
  #NOW ONLY WORKING WITH SITUATIONS WITH AT LEAST ONE VALID STUDY
  
  #IF combine.with.metafor == TRUE, FIRST CHECK THAT THE MODELS IN EACH STUDY MATCH
  #IF THERE ARE DIFFERENT NUMBERS OF PARAMETERS THE ANALYST WILL
  #HAVE TO USE THE RETURNED MATRICES FOR betas AND ses TO DETERMINE WHETHER
  #COMBINATION ACROSS STUDIES IS POSSIBLE AND IF SO, WHICH PARAMETERS GO WITH WHICH
  #ALSO DETERMINE WHICH STUDIES HAVE VALID DATA
  
  beta.matrix.for.SLMA<-as.matrix(betamatrix)
  se.matrix.for.SLMA<-as.matrix(sematrix)
  
  #SELECT VALID COLUMNS ONLY (THERE WILL ALWAYS BE AT LEAST ONE)
  
  usecols<-NULL
  
  for(ut in 1:(dim(beta.matrix.for.SLMA)[2]))
  {
    if(!is.na(beta.matrix.for.SLMA[1,ut])&&!is.null(beta.matrix.for.SLMA[1,ut]))
    {
      usecols<-c(usecols,ut)
    }
  }
  
  
  betamatrix.all<-beta.matrix.for.SLMA
  sematrix.all<-se.matrix.for.SLMA
  
  betamatrix.valid<-beta.matrix.for.SLMA[,usecols]
  sematrix.valid<-se.matrix.for.SLMA[,usecols]
  
  #CHECK FOR MATCHED PARAMETERS
  
  num.valid.studies<-as.numeric(dim(as.matrix(betamatrix.valid))[2])
  coefficient.vectors.match<-TRUE
  
  
  
  if(num.valid.studies>1){
    for(j in 1:(num.valid.studies-1))
    {
      if(length(betamatrix.valid[,j])!=length(betamatrix.valid[,(j+1)]))coefficient.vectors.match<-FALSE
    }
  }else{
    coefficient.vectors.match<-TRUE
  }
  
  
  
  
  if(!coefficient.vectors.match){
    cat("\n\nModels in different sources vary in structure\nplease match coefficients for meta-analysis individually\n")
    cat("nYou can use the DataSHIELD generated estimates and standard errors as the basis for a meta-analysis\nbut carry out the final pooling step independently of DataSHIELD using whatever meta-analysis package you wish\n\n")
    return(list(output.summary=output.summary))
  }
  
  
  
  #IF combine.with.metafor == TRUE AND MODEL STRUCTURES MATCH ACROSS ALL STUDIES
  #CREATE STUDY LEVEL META-ANALYSIS (SLMA) ESTIMATES FOR ALL PARAMETERS
  #USING metafor() AND THREE APPROACHES TO SLMA: SLMA UNDER MAXIMUM LIKELIHOOD (SMLA-ML)
  #SLMA UNDER RESTRICTED MAXIMUM LIKELIHOOD (SMLA-REML) AND USING FIXED EFFECTS (SLMA-FE)
  
  dimnames(SLMA.pooled.ests.matrix)<-list(dimnames(betamatrix.valid)[[1]],
                                          c("pooled.ML","se.ML","pooled.REML","se.REML","pooled.FE","se.FE"))
  
  
  
  
  
  for(p in 1:numcoefficients){
    rma.ML<-metafor::rma(yi=as.matrix(betamatrix.valid)[p,], sei=as.matrix(sematrix.valid)[p,], method="ML")
    rma.REML<-metafor::rma(yi=as.matrix(betamatrix.valid)[p,], sei=as.matrix(sematrix.valid)[p,], method="REML")
    rma.FE<-metafor::rma(yi=as.matrix(betamatrix.valid)[p,], sei=as.matrix(sematrix.valid)[p,], method="FE")
    
    SLMA.pooled.ests.matrix[p,1]<-rma.ML$beta
    SLMA.pooled.ests.matrix[p,2]<-rma.ML$se
    
    SLMA.pooled.ests.matrix[p,3]<-rma.REML$beta
    SLMA.pooled.ests.matrix[p,4]<-rma.REML$se
    
    SLMA.pooled.ests.matrix[p,5]<-rma.FE$beta
    SLMA.pooled.ests.matrix[p,6]<-rma.FE$se
    
  }
  
  test.error.message<-FALSE
  full.error.message<-rep("",numstudies)
  
  
  for(q in 1:numstudies)
  {
    if(!is.null(output.summary[[q]]$optinfo$conv$lme4$messages))
    {
      test.error.message<-TRUE
    }
  }  
  
  for(q in 1:numstudies)
  {
    if(is.null(output.summary[[q]]$optinfo$conv$lme4$messages))
    {
      full.error.message[q]<-paste0("Study",q,": no convergence error reported")
    }
    
    
    if(!is.null(output.summary[[q]]$optinfo$conv$lme4$messages))
    {
      full.error.message[q]<-paste0("Study",q,": ",output.summary[[q]]$optinfo$conv$lme4$messages)
    }
    
  }
  
  if (notify.of.progress)
  {
    cat("Convergence information\n")
    for(r in 1:numstudies)
    {
      cat(full.error.message[r],"\n")
    }
  }	
  
  return(list(output.summary=output.summary, num.valid.studies=num.valid.studies,betamatrix.all=betamatrix.all,sematrix.all=sematrix.all, betamatrix.valid=betamatrix.valid,sematrix.valid=sematrix.valid,
              SLMA.pooled.ests.matrix=SLMA.pooled.ests.matrix,Convergence.error.message=full.error.message))
  
}

# ds.glmerSLMA