PROC NLIN uses ordinary nonlinear least squares, rather than maximum likelihood estimation. However, if the error term is assumed to have a distribution in the exponential family (this includes binomial, Poisson, normal, gamma, and inverse Gaussian distributions), it has been shown that an iteratively reweighted least squares approach is equivalent to maximum likelihood estimation. For more details, see the paper by Jennrich and Moore (1975) cited in the References section in the NLIN documentation.

If you want maximum likelihood estimates for a linear model with a binomial error distribution, see the LOGISTIC, GLIMMIX, or GENMOD procedures. For a linear model with a Poisson, gamma, or inverse gaussian error distribution, see the GLIMMIX or GENMOD procedures. For a linear model with a normal error distribution, see the MIXED, GLIMMIX, or GENMOD procedures. PROC PHREG and PROC LIFEREG can fit survival models using maximum likelihood estimation. Linear or nonlinear models on responses with various response distributions can be estimated by maximum likelihood in PROC NLMIXED.

If you want to maximize an explicit likelihood function in PROC NLIN, create a 'dummy' response variable that takes the value of 0 throughout the data set. Then specify the square root of twice the negative of the log-likelihood function on the right side of the model equation. Minimizing the sum of squares in this model is equivalent to maximizing twice the log-likelihood function. This method is demonstrated in the NLIN documentation example titled 'Probit Model with Likelihood Function'.