# Fitting a Weibull function in R

I am trying to model some data that follows a sigmoid curve relationship. In my field of work (psychophysics), a Weibull function is usually used to model such relationships, rather than probit.

I am trying to create a model using R. My model will have a 'shape' and 'scale' value. In order to generate this model, I would have thought that R would need to have input vectors from both my X and Y axes (I am plotting size of a visual stimulus against the probability of it being seen). However, the R help page gives details of functions that only require either a vector of quantiles (size of stimulus) or a vector of probabilities (presumably, this means my 'probability of seeing' data).

I don't see how R could possibly fit a model on the grounds of only having half of my data (i.e. using my X axis (quantile) data, but none of my Y axis (probability of seeing) data).

Am I missing something? I'm not a statistician so I fear there's something fundamental that I've overlooked. Any help would be appreciated.

• The confusion here isn't really w/ R, it's w/ the nature of the activity you're trying to do. What you want is to use the cumulative Weibull as a link function to connect the size of your visual stimulus to the probability of it being seen. To understand more about link functions, it may help you to read my answer here: difference-between-logit-and-probit-models. Feb 7 '13 at 15:33

What you are trying to do (if I understand you correctly), is to model the probability of the stimulus being seen by a Weibull distribution... but with the Weibull parameters depending on a covariate, i.e., the size of the stimulus. So you are really doing a so-called "Weibull regression". The weibreg() function in the eha package looks like it should do what you want.