A review of some models for the analysis of contingency tables : a thesis presented in partial fulfilment of the requirements for the degree of Master of Arts in Statistics at Massey University

Some models proposed for the analysis of contingency tables are reviewed and illustrated with examples. These include standard loglinear models; models which are suitable for ordinal categorical variables such as ordinal loglinear, log­ multiplicative and logit models, and models based on an underlying distribution for the response; and models for incomplete and square tables. Estimation methods and inference are also discussed

Selection of Ordinally Scaled Independent Variables

Ordinal categorial variables are a common case in regression modeling. Although the case of ordinal response variables has been well investigated, less work has been done concerning ordinal predictors. This article deals with the selection of ordinally scaled independent variables in the classical linear model, where the ordinal structure is taken into account by use of a difference penalty on adjacent dummy coefficients. It is shown how the Group Lasso can be used for the selection of ordinal predictors, and an alternative blockwise Boosting procedure is proposed. Emphasis is placed on the application of the presented methods to the (Comprehensive) ICF Core Set for chronic widespread pain. The paper is a preprint of an article accepted for publication in the Journal of the Royal Statistical Society Series C (Applied Statistics). Please use the journal version for citation

Bayesian inference through encompassing priors and importance sampling for a class of marginal models for categorical data

We develop a Bayesian approach for selecting the model which is the most supported by the data within a class of marginal models for categorical variables formulated through equality and/or inequality constraints on generalised logits (local, global, continuation or reverse continuation), generalised log-odds ratios and similar higher-order interactions. For each constrained model, the prior distribution of the model parameters is formulated following the encompassing prior approach. Then, model selection is performed by using Bayes factors which are estimated by an importance sampling method. The approach is illustrated through three applications involving some datasets, which also include explanatory variables. In connection with one of these examples, a sensitivity analysis to the prior specification is also considered

Discriminatively Trained Latent Ordinal Model for Video Classification

We study the problem of video classification for facial analysis and human action recognition. We propose a novel weakly supervised learning method that models the video as a sequence of automatically mined, discriminative sub-events (eg. onset and offset phase for "smile", running and jumping for "highjump"). The proposed model is inspired by the recent works on Multiple Instance Learning and latent SVM/HCRF -- it extends such frameworks to model the ordinal aspect in the videos, approximately. We obtain consistent improvements over relevant competitive baselines on four challenging and publicly available video based facial analysis datasets for prediction of expression, clinical pain and intent in dyadic conversations and on three challenging human action datasets. We also validate the method with qualitative results and show that they largely support the intuitions behind the method.Comment: Paper accepted in IEEE TPAMI. arXiv admin note: substantial text overlap with arXiv:1604.0150