R/allvc.R

In npmlreg: Nonparametric Maximum Likelihood Estimation for Random Effect Models

"allvc" <-
function(formula,
                    random=~1,
                    family = gaussian(),
                    data,
                    k = 4,
                    random.distribution="np",
                    tol = 0.5,
                    offset,
                    weights,
                    pluginz,
                    na.action,
                    EMmaxit=500,
                    EMdev.change=0.001,
                    lambda=0,
                    damp=TRUE,
                    damp.power=1,
                    spike.protect=0,
                    sdev,
                    shape,
                    plot.opt=3,
                    verbose=TRUE,
                    ...)
{
  # R function allvc in package npmlreg.  NPML/GQ for variance component models.
  # Type  ?npmlreg for licence, copyright, and version information.

  call <- match.call()
  if (is.character(family))
      family <- get(family, mode = "function", envir = parent.frame())
  if (is.function(family))
    family <- family()
  if (is.null(family$family)) {
    print(family)
    stop("`family' not recognized")
  }
  
  data  <-as.data.frame(data)
  ddim  <-dim(data)
  mf    <- match.call(expand.dots = FALSE)
  
  #  Test for inadmissibly removed intercept term
  if (k>1 && random.distribution=='np' && max(length(grep('- 1', deparse(formula(mf)))),length(grep('-1', deparse(formula(mf))))) >0 ){
      stop(" term '-1'  in model formula not supported for k>1 & random.distribution='np'. ")
  }
   
  # Test for incorrect offset specification in formula object
  testoffset<-try(is.null(attr(terms(formula(mf)),"offset")),silent=TRUE)
  if (!(class(testoffset)=="try-error" || testoffset)){
      stop("Please specify offset as separate argument outside the model formula.")
  }
  
  # Extract variables from call and set up initial (fixed effect) model
  m    <- match(c("formula", "data", "subset", "weights", "na.action", 
               "etastart", "mustart", "offset"), names(mf), 0)

  
  mf   <- mf[c(1, m)]
  mf$drop.unused.levels <- TRUE
  mf[[1]] <- as.name("model.frame")
  mf <- try(eval(mf,  parent.frame()), silent=TRUE)
  if (class(mf)=="try-error"){
      if (!missing(offset) && length(offset) != ddim[1]) {
      stop("Number of offsets is ", length(offset), ", should equal ", ddim[1], " (number of observations)")
      }
      if (!missing(weights) && length(weights) != ddim[1]){
      stop("Number of weights is ", length(weights), ", should equal ", ddim[1], " (number of observations)")
      }
      stop(geterrmessage())
  }
  offset  <- model.offset(mf) 
  weights <- model.weights(mf)
  X  <- Y <- XZ <- NULL
  Y  <- model.response(mf, "any") # response # for 0.42 changed from "numeric to "any"
  Ym <- is.matrix(Y)
  N  <- NROW(Y)  # corresponds to ddim[1] if there are no missing values
  
  # Set up weights and offset  for initial glm
  if (is.null(offset)){offset <- rep(0,N) }
  if (is.null(weights)){weights <- rep(1,N)}   
  data$offset <- numeric(1); data$pweights<-numeric(1)  
  data  <- if (is.matrix(Y)) data[dimnames(Y)[[1]],] else  data[names(Y),] # omit missing values   
  data$offset <- offset;  data$pweights <- weights
 
  # Extract variable names from random part 
  rform    <- random
  mform    <- strsplit(as.character(random)[2],'\\|')[[1]]
  mform    <- gsub(' ', '',mform)
  if (length(mform)==1){stop("Please use function alldist for overdispersion models")} 
  mform1   <- mform[1]
  mform2   <- mform[2]
  if(!(mform2 %in% names(data))){stop("The specified clustering variable is not contained in the data frame.")}  
  if (random.distribution=='gq' && mform1!="1"){stop("Random coefficient models are only supported for random.distribution='np'.")}


  # initial fit and simple glm for k=1
  fit    <- glm(formula, family=family, weights=pweights, offset=offset, data=data,...)
  names0 <- dimnames(data)[[1]] 
  w0     <- fit$prior.weights  # store prior weights for output
  off0   <- fit$offset; names(off0)<-names0   # store offset for output
  Y      <- fit$y  
  l0     <- length(fit$coef)  
  tol0   <- tol # for main title of graphical output 
  
  # For binomial models, check weights: case weights, or number of trials?
  if(family$family=="binomial"){
      data$pweights<- data$pweights^Ym
      YP<- binomial.expand(Y,1,w0/data$pweights); 
      Y<- YP[[1]]; PY<-YP[[2]];r<-YP[[3]]; n<-YP[[4]]
  } 
    
  # Initial estimates of  standard deviation and/or shape parameter  (response distr.)     
  sdev.miss  <- missing(sdev)
  shape.miss <- missing(shape)
  if (family$family=="gaussian"){
        sdev  <-  ifelse(sdev.miss, sqrt(summary(fit)$dispersion), sdev)
        shape <- 0
  } else if (family$family =="Gamma"||family$family =="inverse.gaussian") {
         # Estimate sdev from residuals on linear predictor scale, see Einbeck & Hinde (2006):
        sdev  <- ifelse(sdev.miss, sqrt(switch(family$link,
                        "log"= sum(data$pweights*(log(Y)-log(fitted(fit)))^2)/(sum(data$pweights)),
                        "inverse"= sum(data$pweights*(1/Y-1/(fitted(fit)))^2)/(sum(data$pweights)),
                        "identity"= sum(data$pweights*(Y-fitted(fit))^2)/(sum(data$pweights)),
                         "1/mu^2"=   sum(data$pweights*(1/(Y^2)-1/(fitted(fit))^2)^2)/(sum(data$pweights)),                                          
                        )), sdev) 
        shape <- ifelse(shape.miss,1/summary(fit)$dispersion, shape)
  } else {
        sdev  <- 1
        shape <- 0
  } 
   
  # Initial disparity (-2logL)    
  ML.dev0 <- -2*sum(data$pweights*switch(family$family,
             "gaussian"= dnorm(fit$y, fitted(fit), sdev, log=TRUE),
             "poisson" = dpois(fit$y, fitted(fit), log=TRUE),
             "binomial"= dbinom(Y[,1],Y[,1]+Y[,2], fitted(fit), log=TRUE),
             "Gamma"   = dgamma(fit$y, shape=shape, scale=fitted(fit)/shape, log=TRUE),
              "inverse.gaussian"= dinvgauss(fit$y,fitted(fit), shape=shape, log=TRUE),                
            ))

  # Return (glm) output and terminate if k=1
  if (k == 1){
      if (random.distribution=="np"){
        names(fit$coefficients) <- ifelse(names(fit$coefficients)=="(Intercept)", "MASS1", names(fit$coefficients))
      }
      post.prob <-  matrix(1,N,1,dimnames=list(names0,"") )
    
     # print(fit)  
      fit <- c( fit[c(1,2,3,8,9)],
              disparity = ML.dev0,
              deviance = fit$dev,
              fit[c(12,16,17,18)],
              call = call,  
              formula = formula,
              random = "none",
              data = list(subset(data,select=1:ddim[2])),
              model = list(model.matrix(fit)),
              weights = list(w0),
              offset = list(off0),
              mass.points = list(fit$coef[1]),
              masses = list(c("MASS1"=1)),
              sdev = list(list(sdev=sdev, sdevk=sdev)),
              shape = list(list(shape=shape,shapek=shape)),
              rsdev= 0,
              post.prob = list(post.prob),
              post.int =  list(fit$coef[1]),
              ebp = list(family$linkfun(fit$fitted)),
              EMiter = 0,
              EMconverged = "none",
              lastglm = list(fit),
              Misc = list(list(lambda=lambda, tol=tol0))
              )
      if (random.distribution =="np"){
              class(fit) <- 'glmmNPML'
      } else {
             class(fit) <- 'glmmGQ'
      }     
      return(fit)
  } else if (!(k %in% 1:600)){
      stop("This choice of k is not supported.")
  }
  
  # Omit integration point if GH weights are too small  
  tmp      <- gqz(k, minweight = 1e-50)  # from version 0.39-1; changed to 1e-50 in v0.42
  k0       <- k   # from 0.42: save for glmmGQ output
  k        <- min(k, dim(tmp)[1]);
  
  # Expand the data
  if(family$family=="binomial"){
      YP   <- binomial.expand(Y,k,rep(1,N)); Y<- YP[[1]]; PY<-YP[[2]];r<-YP[[3]]; n<-YP[[4]]
  }  else  {
      Y    <- rep(Y,k)
  }
  X        <- expand.vc(X,k)# expand design matrix
  datak    <- expand.vc(data,k)
  kindex   <- rep(1:k,rep(N,k))# index for the mixtures
  #tmp      <- gqz(k,minweight=1e-55)  # omitted from version 0.39-1
  z0       <- -tmp$location
  z        <- rep(-tmp$location,rep(N,k))
  p        <- tmp$weight
  group    <- factor(levels(factor(datak[,mform2])))# 20/04/06 
  offset   <- datak$offset    # expand offset
  pweights <- datak$pweights  # expand weights
  

  # Generate the random design matrix and append to fixed matrix
  if (random.distribution=='np'){  # Nonparametric random effect
      X <- model.matrix(formula,datak)[,-1,drop=FALSE]
      datak$MASS <- gl(k,N)
      if (mform1=='1'){ 
          random <- formula(~MASS-1) 
      } else {
          # Nonparametric random coefficient
          random <- formula(paste('~ MASS + ', paste(mform1, 'MASS',sep=":",collapse='+'), '-1',sep=''))
      }
  } else {
      #print(mform)
      # Gaussian random effects
      X <- model.matrix(formula,datak)
      #if (mform1=='1')
      random <- formula('~ z - 1')
      #else
      #random <- formula(paste('~',paste(mform1,'z - 1',sep=':'),sep='')) ##R.E.D. 13/2/06 # this case seems to be excluded anyway. 05/11/07 JE
   }
  Z <- model.matrix(random,datak)
  
  if (dim(X)[1]!= dim(Z)[1]){ 
    if (dim(X)[1]== dim(Z)[1]/k && dim(X)[2] <=1) { X<- expand(X,k)} 
    # corrects possible problems if the data were not provided as a proper data frame, but e.g. as a time series 31/08/18
    else {
      cat("The missing value routine cannot cope with this model. Please specify the random term also as fixed term and try again. " )
    }
  }

  XZ <- cbind(X,Z)
  
  # Set up indices for hierarchical model
  nr        <- nlevels(group)
  ijindex   <- rep(1:N,k)
  groupij   <- factor(data[,mform2]) # 20/04/06
  groupijk  <- rep(groupij,k)
  Intercept <- names(fit$effects)[1]=='(Intercept)'
  nf        <- length(names(fit$effects))

  # Extend linear predictor
  if (missing(pluginz)){
      sz <- tol* sdev*z
  } else {
      if (length(pluginz)!=k){
        stop("pluginz needs to be a vector of length k.")  # 30/09/09
      } else {
        sz <- rep(pluginz-fit$coef[[1]],rep(N,k))
      }
  }  
  Eta <- fit$linear.predictor + sz
        # The extra term stops unrelated regressions
  
  
  # Initial EM trajectory values 
  if (random.distribution=="np"){
      tol <- max(min(tol,1),1-damp)
      if(length(fit$coef)==1){
          followmass <- matrix(Eta[(1:k)*N],1,k)-offset[(1:k)*N]
          } else {
          followmass <- matrix(fit$coef[1]+sz[(1:k)*N],1,k)
          }
  }  else {
      followmass <- NULL; tol <- 1
  }

  # Expanded fitted values
  Mu <- family$linkinv(Eta)
  if (sum(is.na(Mu))>0){
     if (family$link=="1/mu^2"){                                                                      
        warning("The squared reciprocal link will often fail. Try family=...(link=log) instead.")
     }
     stop("Unable to transform extended linear predictor to response scale.")
   }  

  

  # Calculate loglikelihood for fixed model
  f <- switch(family$family,
              "gaussian"=dnorm(Y,Mu,tol*sdev,log=TRUE),
              "poisson" =dpois(Y,Mu,log=TRUE),
              "binomial"=dbinom(r,n,Mu,log=TRUE),
               "Gamma"=dgamma(Y,shape=shape/tol^2,scale=Mu*tol^2/shape ,log=TRUE),
               "inverse.gaussian"= dinvgauss(Y, Mu, shape= shape/tol^2, log=TRUE),
               )
  
  # Calculate the weights from initial model
  groupk <- interaction(groupijk,factor(kindex))
  mik    <- matrix(tapply(f*pweights,groupk,sum),nrow=nr,ncol=k)  #16-03-06
  tmp    <- weightslogl.calc.w(p,mik,rep(1,nr))   #16-03-06
  w      <- tmp$w[match(groupij,group),]    #17-03-06

  # Initialize for EM loop
  ML.dev    <- ML.dev0
  iter      <- ml <- 1
  converged <- FALSE
  sdevk<-rep(sdev,k);  shapek<-rep(shape,k)    #19-03-06
   
  ##########Start of EM ##########
  while (iter <= EMmaxit && (!converged || (iter<=9 && random.distribution=='np' && damp && (family$family=="gaussian" && sdev.miss || (family$family=="Gamma"|| family$family=="inverse.gaussian") && shape.miss)  ))){   
      if (verbose){cat(iter,'..')}

      # M-Step: Weighted GLM
      fit <- try(glm.fit(x=XZ, y=Y, weights = as.vector(w)*pweights, family = family, offset=offset,...))                                
      if (class(fit)=="try-error"){
                stop("Singularity or Likelihood-Spike at iteration #", iter,  ". 
                Check model specification, enable spike protection or smooth among components.")
      }
      
      # EM Trajectories      
      if (random.distribution=="np"){ 
          masspoint<- fit$coef[l0:(l0+k-1)]
          followmass<-rbind(followmass, masspoint)
      }
      
      # Fitted response from current model
      Mu <- fitted(fit)
      
      # Unequal component dispersion parameters  
      if (family$family=="gaussian"){
          if (sdev.miss){ sdev<- sqrt(sum((as.vector(w)*pweights)*(Y-Mu)^2)/sum(as.vector(w)*pweights))}
          sdevk<-rep(sdev,k) 
          if (lambda!=0){
              for (l in 1:k){
                wk<-matrix(1,k,N); wk[1:k,]<-dkern(1:k,l,k,lambda);wk<-t(wk)
                sdevk[l] <-  sqrt(sum(wk* as.vector(w)*pweights *(Y-Mu)^2)/sum(wk*as.vector(w)*pweights))
              }
              sk<-rep(sdevk,rep(N,k))
          } else {
              sk<-sdev
          }
      }  else {
          sdevk <-rep(NA,k)
      }
      if (family$family=="Gamma"){
           if (shape.miss) { shape<-(sum(as.vector(w)*pweights))*1/sum(as.vector(w)*pweights*((Y-fitted(fit))/fitted(fit))^2)}
           shapek<-rep(shape,k) 
           if (lambda!=0){
                for (l in 1:k){
                  wk<-matrix(1,k,N); wk[1:k,]<-dkern(1:k,l,k,lambda);wk<-t(wk)
                  shapek[l] <- sum(wk*as.vector(w)*pweights)/ sum(wk* as.vector(w)*pweights*((Y-Mu)/Mu)^2)
                  }
                shk<-rep(shapek,rep(N,k))
           } else {
                shk<-shape
           }
       } else if (family$family=="inverse.gaussian"){
           if (shape.miss) { shape<-(sum(as.vector(w)*pweights))*1/sum(as.vector(w)*pweights*(Y-fitted(fit))^2/(fitted(fit))^3)}
           shapek<-rep(shape,k) 
           if (lambda!=0){
                for (l in 1:k){
                  wk<-matrix(1,k,N); wk[1:k,]<-dkern(1:k,l,k,lambda);wk<-t(wk)
                  shapek[l] <- sum(wk*as.vector(w)*pweights)/ sum(wk* as.vector(w)*pweights*(Y-Mu)^2/Mu^3)
                }
                shk<-rep(shapek,rep(N,k))
           } else {
                shk<-shape
           }
      } else {
           shapek<-rep(NA,k)
      }

      
      
      # Calculate loglikelihood for expanded model for this iteration
      f <- switch(family$family,
              "gaussian"=dnorm(Y,Mu,(1-(1-tol)^(damp.power*iter+1))*sk,log=TRUE),
              "poisson" =dpois(Y,Mu,log=TRUE),
              "binomial"=dbinom(r,n,Mu,log=TRUE),
               "Gamma"=dgamma(Y,shape=shk/(1-(1-tol)^(damp.power*iter+1))^2,scale=Mu*(1-(1-tol)^(damp.power*iter+1))^2/shk,log=TRUE),
               "inverse.gaussian"=dinvgauss(Y, Mu, shape= shk/(1-(1-tol)^(damp.power*iter+1))^2, log=TRUE),           
           )
      
      # E-Step: Update weights     
      mik  <- matrix(tapply(f*pweights,groupk,sum),nrow=nr,ncol=k) #16-3-06
      tmp  <- weightslogl.calc.w(p,mik, rep(1,nr))   #16-03-06
      w    <- tmp$w[match(groupij,group),]
      
      # Calculate the component proportions from the weights
      if (random.distribution=='np'){ 
          p <- as.vector(apply(tmp$w,2,mean)) # differs from alldist - no weights needed on upper level! 
      }
      
      # Update disparity and check for convergence
      ML.dev[iter+1] <- ifelse(is.na(tmp$ML.dev), Inf, tmp$ML.dev)
      if (ML.dev[iter+1]>ML.dev0) {ml<-ml+1}
      converged <- abs(ML.dev[iter+1] - ML.dev[iter])< EMdev.change
      iter <- iter + 1
  
      # Check for likelihood spikes
      if (random.distribution != 'gq' && spike.protect!=0){
          if (family$family=='gaussian' && abs(min(sdevk/masspoint)) <0.000001*spike.protect){break}  # Avoid Likelihhod Spikes
          if ( (family$family=='Gamma'||family$family=='inverse.gaussian') && abs(max(shapek/masspoint))> 10^6*spike.protect){break}
      }  
  
   }########################### End of EM loop #############

  # Print on screen information on EM convergence  
  if (verbose){cat("\n")
      if (converged){
        cat("EM algorithm met convergence criteria at iteration # ", iter-1,"\n")
      } else{
        cat("EM algorithm failed to meet convergence criteria at iteration # ", iter-1,"\n")
      }
  }
  
  # Compute model deviance
  Deviance <- switch(family$family,
              "gaussian"= sdev^2*ML.dev[iter]-sdev^2* sum(data$pweights[1:N] * log(2*pi*sdev^2)),
              "poisson" =ML.dev[iter] +2*sum(data$pweights[1:N]*(-Y[1:N]+Y[1:N]*log(Y[1:N]+(Y[1:N]==0))-lfactorial(Y[1:N]))),
              "binomial"=ML.dev[iter] +2*sum(data$pweights[1:N]*(lfactorial(n)-lfactorial(r)-lfactorial(n-r) - n*log(n) + r*log(r+(r==0))+(n-r)*log(n-r+((n-r)==0)))[1:N]),
              "Gamma"=1/shape*ML.dev[iter]+2/shape*(sum(data$pweights[1:N])*shape*(log(shape)-1)-sum(data$pweights[1:N])*lgamma(shape)-sum(data$pweights[1:N]*log(Y[1:N]))),
                 "inverse.gaussian"=   1/shape*( ML.dev[iter]+ sum(data$pweights[1:N])*log(shape/(2*pi)) - 3*sum(data$pweights[1:N]*log(Y[1:N])) ),      
              )
  
  # Compute  posterior prob. etc.                          
  mass.points   <- masses <- NULL
  np            <- length(fit$coef)
  ebp           <- apply(w*matrix(fit$linear.predictor,N,k,byrow=FALSE),1,sum)  # Emp. Bayes Pred. (Aitkin, 96)
  ebp.fitted    <- family$linkinv(ebp)
  ebp.residuals <- Y[1:N]- ebp.fitted
  names(ebp)    <- names(ebp.fitted) <- names(ebp.residuals) <- names0
  if (mform1 %in% substring(names(fit$coef),1, nchar(mform1))){length(fit$coefficients) <- np <- np-1}# if one variable is random *and* fixed 
  # if (is.na(fit$coefficients[np])){length(fit$coefficients) <- np <- np-1}# replaced by the line above from 0.42 on
  m <- seq(1,np)[substr(attr(fit$coefficients, 'names'),1,4)=='MASS']
  if (random.distribution=="np"){ 
      mass.points   <- fit$coefficients[m] # from 0.42
  } else {  
      a <- ifelse(names(fit$coef[1])== "(Intercept)", fit$coef[1], 0) 
      mass.points <- a + fit$coef["z"]*z0           # from 0.42, np replaced by "z"
  }
  post.prob     <- matrix(w, nrow=N, byrow=FALSE, dimnames=list(names0, 1:k) )
  post.int      <- as.vector(post.prob %*% mass.points[1:k]); names(post.int)<-names0
    
  # Write tol values as plot title if alldist is called from tolfind:
  if ((plot.opt==1 || plot.opt==2) && par("mfrow")[1]>2) { # Write tol values as plot title if alldist is called from tolfind:
           plot.main <- substitute("tol"== tol0, list(tol0=tol0))
      } else {
           plot.main <- c("")
  }
   
  # Set up graphics device and plot disparity trend 
  if (plot.opt==3 && random.distribution=="np"){
      par(mfrow=c(2,1), cex=0.5, cex.axis=1.5, cex.lab=1.5)
  }
  if (plot.opt==1|| plot.opt==3){
      if  ((family$family=="gaussian" && sdev.miss|| (family$family=="Gamma"||family$family=="inverse.gaussian") && shape.miss) && damp && random.distribution=='np' && iter>=max(8,ml+1)){
          # Linear interpolation for initial cycles
          ML.dev[2: max(7,ml)]<-ML.dev0+ 1:max(6,ml-1)/ max(7,ml)*(ML.dev[max(8,ml+1)]-ML.dev0) 
      }  
      plot(0:(iter-1),ML.dev, col=1,type="l",xlab='EM iterations',ylab='-2logL', main= plot.main )
      if (verbose){ cat("Disparity trend plotted.\n")}
  }

  # Prepare output for glmmNPML objects
  if (random.distribution=="np") {
      masses        <- as.vector(apply(tmp$w,2,mean))                # differs from alldist - no weights needed on upper level! 
      names(masses) <- paste('MASS',1:k,sep='')                    
      
      # Estimate random effect standard deviation # from 0.42
      rsdev         <- sqrt(sum(masses * (mass.points[1:length(masses)]- sum(masses*mass.points[1:length(masses)]) )^2))
      
      # Compute fixed part residuals
      if (family$family=="binomial"){
          R0 <- family$linkfun(PY[1:N])
      } else  {
          R0 <- family$linkfun(Y[1:N])
      }
      if(dim(X)[2]>0){
        R <-R0 - X[1:N,]%*%matrix(fit$coef[1:dim(X)[2]])-offset[1:N]
      } else {
        R <- R0 - offset[1:N]
      }
      R <- as.vector(R);  names(R) <- names0   
         
      # EM trajectory plot
      if ( mform1=='1' && all(is.finite(R))){ 
           ylim <- c(min(R), max(R))  #29/06/2006
      } else  { 
          ylim <- c(min(followmass[,]),max(followmass[,]))
      }
      if(any(is.na(ylim)) &  plot.opt >1 ){
              cat("Singularity: EM Trajectory plot not available.", "\n");
              plot.opt<-min(plot.opt,1)
      }
      if (plot.opt==2|| plot.opt==3){
            plot(0:(iter-1),followmass[,1],col=1,type='l',ylim=ylim,ylab='mass points',xlab='EM iterations', main= plot.main )
            for (i in 1:k){ lines(0:(iter-1), followmass[,i],col=i)
                 if (mform1=='1'){ points(rep(iter-1,length(R)),R)}}
            if (verbose){cat("EM Trajectories plotted.\n")}
      }

      
      # glmmNPML output 
      fit <- c( fit[1],
                residuals = list(ebp.residuals),
                fitted.values = list(ebp.fitted),
                fit[c(8,9)],
                disparity = ML.dev[iter],
                deviance = Deviance,
                fit[12],  
                df.residual = N - np -k+1, 
                df.null = N-1,
                fit[18],
                call = call,
                formula = formula,
                random = rform,
                data = list(subset(data,select=1:ddim[2])),
                model = list(XZ),
                weights = list(w0),
                offset = list(off0),
                mass.points = list(mass.points),
                masses = list(masses),               
                sdev = list(list(sdev=sdev, sdevk=sdevk)),
                shape = list(list(shape=shape,shapek=shapek)),
                rsdev = list(rsdev),
                post.prob = list(post.prob),
                post.int =  list(post.int),
                ebp = list(ebp),
                EMiter = iter - 1,
                EMconverged = converged,
                lastglm = list(fit),
                Misc=list(list(Disparity.trend=ML.dev,EMTrajectories=followmass, res=R,ylim=ylim,lambda=lambda,mform=mform1, mform2=mform2, tol=tol0))
                )
      class(fit) <-'glmmNPML'
  } else {
      # glmmGQ output
      
      fit <- c( fit[1],
                residuals = list(ebp.residuals),
                fitted.values = list(ebp.fitted),
                fit[c(8,9)],
                disparity = ML.dev[iter],
                deviance = Deviance,
                fit[12],  
                df.residual = N-np,
                df.null = N-1,
                fit[18],
                call = call,
                formula = formula,
                random = rform,
                data = list(subset(data,select=1:ddim[2])),
                model = list(XZ),
                weights = list(w0),
                offset = list(off0), 
                mass.points = list(mass.points),
                masses = list(gqz(k0, minweight=1e-50)$weight),          
                sdev = list(list(sdev=sdev, sdevk=sdevk)),
                shape = list(list(shape=shape,shapek=shapek)),
                rsdev = fit$coef[["z"]],
                post.prob = list(post.prob),
                post.int =  list(post.int),
                ebp = list(ebp),
                EMiter = iter - 1,
                EMconverged = converged,
                lastglm = list(fit),
                Misc=list(list(Disparity.trend=ML.dev,  lambda=lambda, mform=mform1, mform2=mform2, tol=tol0))
                )
      class(fit) <-'glmmGQ'
  }
  fit
}