R/fitLORgee.R

In multgee: GEE Solver for Correlated Nominal or Ordinal Multinomial Responses

fitLORgee <- function(Y, X_mat, coeffs, ncategories, id, repeated, offset,
                      link, LORterm, marpars, ipfp.ctrl, control, IM,
                      LORem = LORem, LORstr = LORstr, add) {
  inversematrix <- function(x) inversemat(x, IM)
  tol <- control$tolerance
  maxiter <- control$maxiter
  verbose <- control$verbose
  ncategoriesm1 <- ncategories - 1
  p <- ncol(X_mat)
  Nsubs <- max(id)
  nobs <- length(id) / ncategoriesm1
  repeatednew <- as.numeric(factor(repeated))
  noccasions <- max(repeatednew)
  noccasionpairs <- choose(noccasions, 2)
  Ti_vector <- as.numeric(lapply(split(id, id), length)) / (ncategoriesm1)
  if (all(Ti_vector == 1)) {
    stop("There are no repeated responses")
  }
  sel_mat <- lapply(seq.int(2, noccasions), function(x) {
    which(lower.tri(diag(x * ncategoriesm1)))
  })
  if (any(Ti_vector < noccasions)) {
    times_mat <- lapply(split(repeatednew, id), unique)
  }
  code_mat <- combns(noccasions)
  if (link != "acl" & link != "bcl") {
    family <- make.link(link)
    linkinv <- family$linkinv
    mu.eta <- family$mu.eta
  }
  validmu <- function(mu) all(mu > 0) && all(mu < 1)
  if (LORstr == "fixed") {
    if (!is.matrix(LORterm)) {
      stop("'LORterm' must be inserted as matrix")
    }
    if (ncol(LORterm) != ncategories^2) {
      stop("'LORterm' must have ", ncategories^2, " columns")
    }
    if (nrow(LORterm) != noccasionpairs) {
      stop("'LORterm' must have ", noccasionpairs, " rows")
    }
    LORterm <- prop.table(LORterm, 1)
  }
  if (LORstr == "independence") {
    LORterm <- matrix(1 / ncategories^2, noccasionpairs, ncategories^2)
  }
  formals(ipfp)$dimension <- ncategories
  formals(ipfp)$tol <- ipfp.ctrl$tol
  formals(ipfp)$maxit <- ipfp.ctrl$maxit
  index_mat <- matrix(
    seq.int(ncategoriesm1 * noccasions), noccasions,
    ncategoriesm1, TRUE
  )
  extindex_mat <- matrix(
    seq.int(ncategories * noccasions), noccasions,
    ncategories, TRUE
  )
  id_vector <- split(seq.int(nrow(X_mat)), id)
  extid_vector <- split(seq.int(ncategories * nobs), rep.int(
    seq.int(Nsubs),
    Ti_vector * ncategories
  ))
  deriv_mat <- if (link == "acl") {
    derivacl
  } else if (link == "bcl") {
    derivbcl
  } else {
    derivmclm
  }
  eta <- drop(X_mat %*% coeffs) + offset
  if (link != "acl" & link != "bcl") {
    probexclude <- seq(ncategories, nobs * ncategories, ncategories)
    fitproball <- muprob(linkinv(eta), nobs, ncategoriesm1)
    if (!validmu(fitproball)) {
      stop("Please insert initial values")
    }
    fitprob <- fitproball[-probexclude]
    dummy <- mu.eta(eta)
  } else {
    fitprob <- exp(matrix(
      eta, length(eta) / ncategoriesm1, ncategoriesm1,
      TRUE
    ))
    fitprob <- fitprob / (1 + .rowSums(
      fitprob, nobs, ncategoriesm1,
      FALSE
    ))
    fitproball <- as.vector(t(cbind(fitprob, 1 - .rowSums(
      fitprob,
      nobs, ncategoriesm1, FALSE
    ))))
    if (!validmu(fitproball)) {
      stop("Please insert initial values")
    }
    fitprob <- as.vector(t(fitprob))
    dummy <- fitprob
  }
  if (verbose) {
    cat(
      format("Iteration",
        digits = 5, trim = TRUE, justify = "centre",
        scientific = FALSE, nsmall = 0, width = 8
      ), "\t",
      format("Criterion",
        digits = 5, trim = TRUE, justify = "centre",
        scientific = FALSE, nsmall = 5, width = 8
      ), "\n"
    )
  }
  beta_mat <- matrix(coeffs)
  crit_vector <- 20
  I0_mat <- I1_mat <- matrix(0, p, p, FALSE)
  H_mat <- matrix(0, p, 1, FALSE)
  for (iter in 1:maxiter) {
    resids <- Y - fitprob
    D_mat <- deriv_mat(dummy, ncategoriesm1, X_mat)
    for (i in 1:Nsubs) {
      Ti <- Ti_vector[[i]]
      id_ind <- id_vector[[i]]
      prob <- fitprob[id_ind]
      mat1 <- diagmod(prob)
      if (Ti == 1) {
        V_mat <- inversematrix(mat1 - tcrossprod(prob, prob))
      } else if (Ti == noccasions) {
        proball <- fitproball[extid_vector[[i]]]
        for (j in 1:(noccasions - 1)) {
          t1 <- index_mat[j, ]
          t2 <- extindex_mat[j, ]
          probrow <- proball[t2]
          for (k in (j + 1):noccasions) {
            t3 <- extindex_mat[k, ]
            index <- code_mat[code_mat[, 1] == j & code_mat[, 2] ==
              k, 3]
            ipfpfit <- ipfp(LORterm[index, ], probrow, proball[t3])
            mat1[t1, index_mat[k, ]] <- ipfpfit[
              -ncategories,
              -ncategories
            ]
          }
        }
        mat1[sel_mat[[noccasions - 1]]] <-
          aperm(mat1, c(2, 1))[sel_mat[[noccasions - 1]]]
        V_mat <- inversematrix(mat1 - tcrossprod(prob, prob))
      } else {
        Tiid <- times_mat[[i]]
        proball <- fitproball[extid_vector[[i]]]
        for (j in 1:(Ti - 1)) {
          t1 <- index_mat[j, ]
          t2 <- extindex_mat[Tiid[j], ]
          probrow <- proball[extindex_mat[j, ]]
          for (k in (j + 1):Ti) {
            t3 <- extindex_mat[Tiid[k], ]
            index <- code_mat[code_mat[, 1] == Tiid[j] & code_mat[
              ,
              2
            ] == Tiid[k], 3]
            ipfpfit <- ipfp_cpp(LORterm[index, ],
                                probrow,
                                proball[extindex_mat[k, ]],
                                ncategories,
                                ipfp.ctrl$maxit,
                                ipfp.ctrl$tol)
            mat1[t1, index_mat[k, ]] <- ipfpfit[
              -ncategories,
              -ncategories
            ]
          }
        }
        mat1[sel_mat[[Ti - 1]]] <- aperm(mat1, c(2, 1))[sel_mat[[Ti -
          1]]]
        V_mat <- inversematrix(mat1 - tcrossprod(prob, prob))
      }
      D_mat1 <- D_mat[id_ind, ]
      help_mat1 <- crossprod(D_mat1, V_mat)
      help_mat2 <- help_mat1 %*% resids[id_ind]
      I0_mat <- help_mat1 %*% D_mat1 + I0_mat
      H_mat <- help_mat2 + H_mat
      I1_mat <- tcrossprod(help_mat2, help_mat2) + I1_mat
    }
    naive_mat <- solve(I0_mat)
    robust_mat <- naive_mat %*% I1_mat %*% naive_mat
    if (any(eigen(robust_mat, TRUE, only.values = TRUE)$values <= 0)) {
      stop("Robust covariance matrix is not positive definite")
    }
    coeffsnew <- coeffs + naive_mat %*% H_mat
    crit <- max(abs(coeffs - coeffsnew) / pmax.int(abs(coeffs), 1e-06))
    crit_vector <- c(crit_vector, crit)
    beta_mat <- cbind(beta_mat, coeffsnew)
    coeffs <- coeffsnew
    eta <- drop(X_mat %*% coeffs) + offset
    if (link != "acl" & link != "bcl") {
      probexclude <- seq(ncategories, nobs * ncategories, ncategories)
      fitproball <- muprob(linkinv(eta), nobs, ncategoriesm1)
      if (!validmu(fitproball)) {
        stop("Please insert initial values")
      }
      fitprob <- fitproball[-probexclude]
      dummy <- mu.eta(eta)
    } else {
      fitprob <- exp(matrix(
        eta, length(eta) / ncategoriesm1,
        ncategoriesm1, TRUE
      ))
      fitprob <- fitprob / (1 + .rowSums(
        fitprob, nobs, ncategoriesm1,
        FALSE
      ))
      fitproball <- as.vector(t(cbind(fitprob, 1 - .rowSums(
        fitprob,
        nobs, ncategoriesm1, FALSE
      ))))
      if (!validmu(fitproball)) {
        stop("Please insert initial values")
      }
      fitprob <- as.vector(t(fitprob))
      dummy <- fitprob
    }
    I0_mat[, ] <- I1_mat[, ] <- H_mat[, ] <- 0
    if (verbose) {
      cat(
        format(round(iter, 0),
          digits = 5, trim = TRUE,
          justify = "centre", scientific = FALSE, nsmall = 0,
          width = 8
        ), "\t",
        format(round(crit, 5),
          digits = 5, trim = TRUE,
          justify = "centre", scientific = FALSE, nsmall = 5,
          width = 8
        ), "\n"
      )
    }
    if (crit <= tol) {
      break
    }
  }
  resids <- Y - fitprob
  D_mat <- deriv_mat(dummy, ncategoriesm1, X_mat)
  for (i in 1:Nsubs) {
    Ti <- Ti_vector[[i]]
    id_ind <- id_vector[[i]]
    prob <- fitprob[id_ind]
    mat1 <- diagmod(prob)
    if (Ti == 1) {
      V_mat <- inversematrix(mat1 - tcrossprod(prob, prob))
    } else if (Ti == noccasions) {
      proball <- fitproball[extid_vector[[i]]]
      for (j in 1:(noccasions - 1)) {
        t1 <- index_mat[j, ]
        probrow <- proball[extindex_mat[j, ]]
        for (k in (j + 1):noccasions) {
          index <- code_mat[code_mat[, 1] == j & code_mat[, 2] ==
            k, 3]
          ipfpfit <- ipfp(
            LORterm[index, ], probrow,
            proball[extindex_mat[k, ]]
          )
          mat1[t1, index_mat[k, ]] <- ipfpfit[
            -ncategories,
            -ncategories
          ]
        }
      }
      mat1[sel_mat[[noccasions - 1]]] <-
        aperm(mat1, c(2, 1))[sel_mat[[noccasions - 1]]]
      V_mat <- inversematrix(mat1 - tcrossprod(prob, prob))
    } else {
      Tiid <- times_mat[[i]]
      proball <- fitproball[extid_vector[[i]]]
      for (j in 1:(Ti - 1)) {
        t1 <- index_mat[j, ]
        probrow <- proball[extindex_mat[j, ]]
        for (k in (j + 1):Ti) {
          index <- code_mat[code_mat[, 1] == Tiid[j] & code_mat[
            ,
            2
          ] == Tiid[k], 3]
          ipfpfit <- ipfp(
            LORterm[index, ], probrow,
            proball[extindex_mat[k, ]]
          )
          mat1[t1, index_mat[k, ]] <- ipfpfit[
            -ncategories,
            -ncategories
          ]
        }
      }
      mat1[sel_mat[[Ti - 1]]] <- aperm(mat1, c(2, 1))[sel_mat[[Ti -
        1]]]
      V_mat <- inversematrix(mat1 - tcrossprod(prob, prob))
    }
    D_mat1 <- D_mat[id_ind, ]
    help_mat1 <- crossprod(D_mat1, V_mat)
    help_mat2 <- help_mat1 %*% resids[id_ind]
    I0_mat <- help_mat1 %*% D_mat1 + I0_mat
    I1_mat <- tcrossprod(help_mat2, help_mat2) + I1_mat
  }
  if (any(eigen(I0_mat, TRUE, only.values = TRUE)$values <= 0)) {
    warning("'Naive' covariance matrix is not positive definite")
  }
  naive_mat <- solve(I0_mat)
  robust_mat <- naive_mat %*% I1_mat %*% naive_mat
  if (any(eigen(robust_mat, TRUE, only.values = TRUE)$values <= 0)) {
    stop("Robust covariance matrix is not positive definite")
  }
  result <- list()
  result$beta_mat <- beta_mat
  result$naive <- naive_mat
  result$robust <- robust_mat
  result$crit <- crit_vector[-1]
  result$iter <- length(result$crit)
  ans <- diagmod(rep(0, ncategoriesm1 * noccasions))
  k <- 1
  for (i in 1:(noccasions - 1)) {
    for (j in (i + 1):noccasions) {
      ans[
        seq(ncategoriesm1) + ncategoriesm1 * (i - 1),
        seq(ncategoriesm1) + ncategoriesm1 * (j - 1)
      ] <-
        odds_ratio(matrix(LORterm[k, ], ncategories, ncategories))
      k <- k + 1
    }
  }
  result$theta <- ans + t(ans)
  result$conv <- (result$crit[result$iter] <= tol)
  result$linear.predictor <- eta
  result$fitted.values <- fitprob
  result$residuals <- resids
  result
}