Log-Likelihood, AIC, and BIC from NL?

[Cyrus Ramezani]

Folks

I am estimating a simple non-linear model using NL. I have carefully read the documentation on NL but there is an issue I have been unable to resolve: NL uses least squares to estimate the parameters. But NL also produces Log-Likelihood, BIC, and AIC. How are these values, particularly Log-Likelihood computed? Can one still do likelihood ratio test and the likes?

This is my first post and I hope I am not asking something trivial!

Thank you.

Cyrus

[Clyde Schechter]

In ordinary linear regression, the OLS estimates are identical to the maximum likelihood estimates under the assumption that the residuals are normally distributed. In fact, the same is true more generally. Under the assumption that the residuals from the non-linear model are normally distributed, least squares estimates also produces maximum likelihood estimates, and the log likelihood can be calculated from the various sums of squares in the same way that the log likelihood of a linear model can be. Once you have the log-likelihood, AIC and BIC follow directly with the usual penalties for df.

[Cyrus Ramezani]

Thank you so much Clyde. After the estimation, I used normality test (Shapiro-Wilks, and QQ plots) and reject normality. Given that, I am hesitant in using the log likelihood and in fact moving to implement MLE. I hope I am moving in the right direction.