[R] nls with weights

[Antje]

Hi there,

I don't have much experience with fitting at all and I'd like to get 
some advice how to use the "weights"-argument with nls correctly.

I have created some data with a sigmoidal curve shape. Each y-Value was 
generated by the mean of three values. A standard deviation was 
calculated too.

Now, I'd like to weight the data points respective to its standard 
deviation. If this is very high, the datapoint should be considered less 
important than a datapoint with a low standard deviation.

I've tested it with the following code but I'd like to know whether I 
should change anything applying the weights. I've only guessed what 
could give a nice result...

Further, I'd like to know, why I get an error message, if I change the 
bottom-parameter to min(yData)??? Can anybody explain, why it ends up with:

"singular gradient"

8< ------------------------------------------------------- >8

sigmoid <- function(x, bottom, top, slope, logec50) { bottom + (top - 
bottom) / (1 + 10^((logec50-x)*slope)) }


xData <- seq(-10,10,1.2)
yData1 <- sigmoid(xData,10,1,-0.2,3) + rnorm(1:length(xData), sd = 0.5)
yData2 <- sigmoid(xData,10,1,-0.2,3) + rnorm(1:length(xData), sd = 0.2)
yData3 <- sigmoid(xData,10,1,-0.2,3) + rnorm(1:length(xData), sd = 1.1)
yMat <- rbind(yData1, yData2, yData3)

yData <- apply(yMat, 2, mean)
yDataSd <- apply(yMat, 2, sd)

plot(yData ~ xData, ylim = c(min(yData - yDataSd), max(yData + yDataSd)))
arrows(xData, yData - yDataSd, xData, yData + yDataSd, angle = 90, 
length = 0.1, code = 3)

# without weights
model <- nls(yData ~ sigmoid(xData,bottom, top, slope, logec50), start = 
list(bottom = yData[1], top = max(yData), slope = 0.5, logec50 = 
median(xData)), trace = TRUE)

lines(xData, predict(model), col ="blue")

# with weights
model <- nls(yData ~ sigmoid(xData,bottom, top, slope, logec50), start = 
list(bottom = yData[1], top = max(yData), slope = 0.5, logec50 = 
median(xData)), weights = 1 / (yDataSd^2), trace = TRUE)

lines(xData, predict(model), col ="green")