[R] What's wrong with my code ?

[ronggui]

I try to code the ULS factor analysis descrbied in
ftp://ftp.spss.com/pub/spss/statistics/spss/algorithms/ factor.pdf
# see PP5-6

factanal.fit.uls <- function(cmat, factors, start=NULL, lower = 0.005,
control = NULL, ...)
{
  FAfn <- function(Psi, S, q)
  {
    Sstar <- S - diag(Psi)
    E <- eigen(Sstar, symmetric = TRUE, only.values = TRUE)
    e <- E$values[-(1:q)]
    e <- sum(e^2/2)
    e
  }

  FAgr <- function(Psi, S, q)
  {
    Sstar <- S - diag(Psi)
    E <- eigen(Sstar, symmetric = TRUE)
    L <- E$vectors[, -(1:q), drop = FALSE]
    e <- E$values[-(1:q)]
    gr <- 2*Psi*((L^2)%*%e)
    gr
  }

  p <- ncol(cmat)
  if(is.null(start))
    start <- (1 - 0.5*factors/p)/diag(solve(cmat))
  res <- optim(start, FAfn,
                 FAgr,
          method="L-BFGS-B",
          lower = lower, upper = 1,
          control = c(list(fnscale=1,
          parscale = rep(0.01, length(start))), control),
          q = factors, S = cmat)
res
}

covmat <-
structure(c(1, 0.0920030858518061, 0.053952442382614, -0.0380048634941013,
0.237986469993129, 0.243144461077282, 0.0920030858518061, 1,
0.328163804480881, 0.142002180914605, -0.139369611642031, -0.0670944471678571,
0.053952442382614, 0.328163804480881, 1, 0.267648727315665, -0.0549987508157441,
-0.107488501744669, -0.0380048634941013, 0.142002180914605, 0.267648727315665,
1, -0.0566976575082817, -0.132943658387513, 0.237986469993129,
-0.139369611642031, -0.0549987508157441, -0.0566976575082817,
1, 0.352367996102745, 0.243144461077282, -0.0670944471678571,
-0.107488501744669, -0.132943658387513, 0.352367996102745, 1), .Dim = c(6L,
6L), .Dimnames = list(c("bg2cost1", "bg2cost2", "bg2cost3", "bg2cost4",
"bg2cost5", "bg2cost6"), c("bg2cost1", "bg2cost2", "bg2cost3",
"bg2cost4", "bg2cost5", "bg2cost6")))


> factanal.fit.uls(covmat,2)
$par
bg2cost1 bg2cost2 bg2cost3 bg2cost4 bg2cost5 bg2cost6
0.7454829 0.7191459 0.6969019 0.7611750 0.6940870 0.6930580

$value
[1] 0.02167674

$counts
function gradient
    21     21

$convergence
[1] 52

$message
[1] "ERROR: ABNORMAL_TERMINATION_IN_LNSRCH"

-- 
Ronggui Huang
Department of Sociology
Fudan University, Shanghai, China