Extended linear modeling provides a flexible framework for functional estimation problems with multiple covariates. Such problems include ordinary and generalized regression, density and conditional density estimation, hazard regression, spectral density estimation and polychotomous regression. In this paper, we develop a general theory on the rate of convergence of maximum likelihood estimatio...

Cox proportional hazards regression analysis of survival data and conditional logistic regression analysis of matched case-control data are methods that are widely used by epidemiologists. Standard statistical software packages accommodate only log-linear model forms, which imply exponential exposure-response functions and multiplicative interactions. In this paper, the authors describe methods...

Cox proportional hazards regression analysis of survival data and conditional logistic regression analysis of matched case-control data are methods that are widely used by epidemiologists. Standard statistical software packages accommodate only log-linear model forms, which imply exponential exposure-response functions and multiplicative interactions. In this paper, the authors describe methods...

• As x gets bigger, so does expx. So raising θsolid with your slider will raise the numerators of p(solid circle) (1) and p(solid triangle) (3). To be precise, each time you increase θsolid by 1, you multiply those numerators by e. (And decreasing θsolid by 1 divides them by e.) • Finally, the four probabilities (1)–(4) always sum to 1 (thanks to their common denominator Z). That’s required bec...

This is yet another introduction to log-linear (“maximum entropy”) models for NLP practitioners, in the spirit of Berger (1996) and Ratnaparkhi (1997b). The derivations here are similar to Berger’s, but more details are filled in and some errors are corrected. I do not address iterative scaling (Darroch and Ratcliff, 1972), but rather give derivations of the gradient and Hessian of the dual obj...