HYBRID LOG-LINEAR MODELS FOR SPATIAL INTERACTION AND STABILITY ANALYSIS(*)

SERIE RESEHRCHmElllORnnDB HYBRID LOG-LINEAR MODELS FOR SPATIAL INTERACTION AND STABILITY ANALYSIS

Bayesian Inference for Spatial Beta Generalized Linear Mixed Models

In some applications, the response variable assumes values in the unit interval. The standard linear regression model is not appropriate for modelling this type of data because the normality assumption is not met. Alternatively, the beta regression model has been introduced to analyze such observations. A beta distribution represents a flexible density family on (0, 1) interval that covers symm...

Decomposable Log-linear Models Decomposable Log-linear Models

The present paper considers discrete probability models with exact computational properties. In relation to contingency tables this means closed form expressions of the maksimum likelihood estimate and its distribution. The model class includes what is known as decomposable graphical models, which can be characterized by a structured set of conditional independencies between some variables give...

Log-Linear Models

• 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...

Log-Linear Models

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...