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I had a statistic class where a Logistic Regression (or what I thought a Logistic Regression is) was set up on some ecotoxicological data (dose-response curve) and the nlstools package was used for this purpose. So far when I came across the Logistic Regression I only used the glm and I am not sure what is the difference between these two approaches. When applying both approaches on the same data there was a clear difference between the fitted curves. So, it seems like there is a difference between the Logistic Regression and the nonlinear Regression with the logit function but my google search has not helped me yet. It would be nice if you guys could help me understand that.

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You seem to be confused betwen two different models which both uses the term logistic, but else has little in common:

  1. Logistic regression, used with binary responses. Here the logistic function is used to model the conditional probability for success, given the observed values of the predictor variables $X$.

  2. Nonlinear regression for a numerical response variable, with the conditional expectation for the response $Y$ modeled via a logistic (or logit) curve. Typically estimated via nonlinear least squares. For examples see Regression with nonlinear function (almost logistic) or Confidence intervals for values estimated from the nonlinear regression model.

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