Unknown error messages in R using nls() with SSlogis() and predict()

Question

I'm fitting a logistic model (self-starting; SSlogis) to data of multiple populations of birds using nls(). My goal is to fit an expected function to the data (using only part of each dataset) and display a measure of the variance about the expectation on a graph. I then want to fit and plot the observed function (using the entire dataset for each population) to determine if the observed dynamics fell within the variance of the expectation. Here's my code as currently written to accomplish this:

    CE.mod = nls(CE.observed ~ SSlogis(t.CattleEgret, Asym, xmid, scal))

    with(collapse.data, plot(CE.time, CE.obs))

    CE.extrap = predict(CE.mod, data.frame(t.CattleEgret = CE.time))
    lines(CE.time, CE.extrap)

    CE.se.fit = sqrt(apply(attr(CE.extrap, "gradient"), 1, function(x) 
    sum(vcov(CE.mod)*outer(x,x))))

    matplot(CE.time, CE.extrap+outer(CE.se.fit, qnorm(c(0.5, 0.025, 0.975))),
    type = "l", lty = c(1,1,1), ylab = "Abundance (# per party hour)",
    xlab = "Time (year)", main = "Cattle Egret Collapse Analysis", 
    pch = 15, font.lab = 2, font.axis = 2, cex = 4, cex.lab = 1.5, 
    cex.axis = 2, cex.main = 2, frame.plot = FALSE, lwd = 4, 10)

    with(collapse.data, matpoints(CE.time, CE.obs, pch = 15, cex = 3))
    lines(CE.time, predict(nls(CE.obs ~ SSlogis(log(CE.time), 
    Asym, xmid, scal))), lty = 3, lwd = 4)

Where (from the "collapse.data" file):

    t.CattleEgret = c(1:20)
    CE.time = c(1:45)
    CE.obs = c(0.3061324, 0.0000100, 0.2361211, 0.5058240, 2.0685032, 2.1944544, 
               4.2689494, 4.9508297, 3.1334720, 3.6570752, 5.6753381, 10.9133183,
               5.4518257, 20.4166979, 15.9741054, 19.0970426, 13.7559959, 14.1358153, 
               15.9986416, 29.6762828, 10.3760667, 8.4284488, 6.1060359, 3.7099982, 
               3.3584060, 2.5981386, 2.5697082, 2.8091952, 5.5487979, 1.6505442,
               2.2696972, 2.1835692, 3.6747876, 4.8307886, 3.5019731, 2.8397137,
               1.8605288, 11.1848738, 2.6268683, 4.1215127, 2.3996210, 2.6569938, 
               2.1987387, 3.0267252, 2.4420927)
    CE.observed = c(0.3061324, 0.0000100, 0.2361211, 0.5058240, 2.0685032, 2.1944544, 
               4.2689494, 4.9508297, 3.1334720, 3.6570752, 5.6753381, 10.9133183,
               5.4518257, 20.4166979, 15.9741054, 19.0970426, 13.7559959, 14.1358153, 
               15.9986416, 29.6762828)

That code works fine and produces a figure like this:

If, however, I remove the "log()" from the final line of the code so as to write this:

    lines(CE.time, predict(nls(CE.obs ~ SSlogis(CE.time, 
    Asym, xmid, scal))), lty = 3, lwd = 4),

The line will not plot and I receive this error:

    Error in nls(y ~ 1/(1 + exp((xmid - x)/scal)), data = xy, start = list(xmid = 
    aux[1L],  : step factor 0.000488281 reduced below 'minFactor' of 0.000976562

which I cannot alter, even if I play around with the nls.controls and change the 'minFactor' value. I also get this error message following the initial line defining the mod (the ##.mod portion) for some populations.

Also, for some populations I receive an error message following the final line of code that reports this:

    Error in qr.solve(QR.B, cc) : singular matrix 'a' in solve

I can think of no rationalization for natural log-transforming the data, and I'm left to assume that I have simply altered the data (in this case arbitrarily logged it) in such a way to allow the predict() and SSlogis() functions to function properly, but I don't know why. I haven't been able to find any suitable answers in any forums to such an issue. Any help would be greatly appreciated.

*Update: I've attempted to implement the nlsLM function as recommended by Roland (below). That does indeed clean up the portion of code with the confusing log() use:

    lines(CE.time, predict(nlsLM(CE.obs ~ Asym/(1 + exp((xmid - CE.time)/scal)), start 
    = list(Asym = max(CE.obs), xmid = popsizetime[1], scal = 1), control = 
    nls.lm.control(maxiter = 1000))

However, for other populations I run into the same error message as above at the initial model specification:

    ChMa.mod = nls(ChMa.observed ~ SSlogis(t.ChestnutMannikin, Asym, xmid, scal))

    Error in nls(y ~ 1/(1 + exp((xmid - x)/scal)), data = xy, start = list(xmid = 
    aux[1L],  : step factor 0.000488281 reduced below 'minFactor' of 0.000976562

Switched to:

    ChMa.mod = nlsLM(ChMa.observed ~ Asym/(1 + exp((xmid - t.ChestnutMannikin)/
scal)), start = list(Asym = max(ChMa.obs), xmid = popsizetime[2], 
scal = 1), control = nls.lm.control(maxiter = 1000))

Where

    ChMa.observed = c(4.02785074, 0.33847154, 0.99029776, 2.86516540, 0.59588068, 
    0.01334333, 2.07693362, 0.62485994, 3.48979515, 3.67785202, 20.84180181)
    t.ChestnutMannikin = c(1:11)
    popsizetime[2] = 11

While this switch does avoid the error message, nlsLM evaluates the function but does not evaluate the gradient. Without the evaluation of the gradient I cannot use the se.fit code and therefore cannot obtain an estimate of the variance for plotting.

Answer 1

I've found the answer to my problems: I need to add a component of my model that generates a gradient for the function I'm regressing with nlsLM.

    log.model = function(t.RedventedBulbul, Asym, xmid, scal) {
            numericDeriv(quote(Asym/(1 + exp((xmid - t.RedventedBulbul)/scal))),
            c("Asym", "xmid", "scal"), parent.frame())
    }