Ivy Liu

The Analysis of Ordered Categorical Data: An Overview and a Survey of Recent Developments

This article review methodologies used for analyzing ordered categorical (ordinal) response variables. We begin by surveying models for data with a single ordinal response variable. We also survey recently proposed strategies for modeling ordinal response variables when the data have some type of clustering or when repeated measurement occurs at various occasions for each subject, such as in longitudinal studies. Primary models in that case includemarginal models andcluster-specific (conditional) models for which effects apply conditionally at the cluster level. Related discussion refers to multi-level and transitional models. The main emphasis is on maximum likelihood inference, although we indicate certain models (e.g., marginal models, multi-level models) for which this can be computationally difficult. The Bayesian approach has also received considerable attention for categorical data in the past decade, and we survey recent Bayesian approaches to modeling ordinal response variables. Alternative, non-model-based, approaches are also available for certain types of inference.

Strategies for Modeling a Categorical Variable Allowing Multiple Category Choices

This article discusses strategies for modeling a categorical variable when subjects can select any subset of the categories. With c outcome categories, the models relate to a c-dimensional binary response, with each component indicating whether a particular category is chosen. The strategies are the following: (1) Using logit models directly for the marginal distribution of each component; this accounts for dependence among the component responses but does not treat the dependence as an integral part of the model. (2) Using logit models containing subject random effects to generate the dependence among the components; this approach is limited by implying nonnegative associations having a certain exchangeability. (3) Using loglinear modeling; quasi-symmetric ones are useful but are limited to estimation of within-subject effects. Marginal logit models less fully describe the dependence patterns for the data but require fewer assumptions and focus more directly on the effects of greatest substantive interest.

Fitting stratified proportional odds models by amalgamating conditional likelihoods

Classical methods for fitting a varying intercept logistic regression model to stratified data are based on the conditional likelihood principle to eliminate the stratum-specific nuisance parameters. When the outcome variable has multiple ordered categories, a natural choice for the outcome model is a stratified proportional odds or cumulative logit model. However, classical conditioning techniques do not apply to the general K-category cumulative logit model (K>2) with varying stratum-specific intercepts as there is no reduction due to sufficiency; the nuisance parameters remain in the conditional likelihood. We propose a methodology to fit stratified proportional odds model by amalgamating conditional likelihoods obtained from all possible binary collapsings of the ordinal scale. The method allows for categorical and continuous covariates in a general regression framework. We provide a robust sandwich estimate of the variance of the proposed estimator. For binary exposures, we show equivalence of our approach to the estimators already proposed in the literature. The proposed recipe can be implemented very easily in standard software. We illustrate the methods via three real data examples related to biomedical research. Simulation results comparing the proposed method with a random effects model on the stratification parameters are also furnished.

The relationship between income and health using longitudinal data from New Zealand

Background Evidence for a cross-sectional relationship between income and health is strong but is probably biased by substantial confounding. Longitudinal data with repeated income and health measures on the same individuals can be analysed to control completely for time-invariant confounding, giving a more accurate estimate of the impact of short-term changes in income on health. Methods 4 years of annual data (2002–2005) from the New Zealand longitudinal Survey of Family, Income and Employment were used to investigate the relationship between annual household income and self-rated health (SRH) using a fixed-effects ordinal logistic regression model. Possible effect modification of the income–SRH relationship by poverty and baseline health was tested with interactions. Results An increase in income of

Gaussian Based Particle Swarm Optimisation and Statistical Clustering for Feature Selection

10 000 over the past year increased the odds of reporting better SRH by 1% (OR 1.01, 95% CI 1.00 to 1.02). Poor baseline health significantly modified the association between income and SRH. A

Filter based backward elimination in wrapper based PSO for feature selection in classification

10 000 increase in income increased the odds of better SRH by 10% for those with two or more chronic conditions. Poverty or deprivation did not modify the income–health association. Conclusions The overall small, positive, but statistically non-significant, income–health effect size is consistent with similar analyses from other longitudinal studies. Despite the overwhelming consensus that income matters for health over the medium and long-term, evidence free of time-invariant confounding for the short-run association remains elusive. However, measurement error in income and health has probably biased estimates towards the null.

Fishing for a solution: can collaborative resource management reduce poverty and support conservation?

Feature selection is an important but difficult task in classification, which aims to reduce the number of features and maintain or even increase the classification accuracy. This paper proposes a new particle swarm optimisation (PSO) algorithm using statistical clustering information to solve feature selection problems. Based on Gaussian distribution, a new updating mechanism is developed to allow the use of the clustering information during the evolutionary process of PSO based on which a new algorithm (GPSO) is developed. The proposed algorithm is examined and compared with two traditional algorithms and a PSO based algorithm which does not use clustering information on eight benchmark datasets of varying difficulty. The results show that GPSO can be successfully used for feature selection to reduce the number of features and achieve similar or even better classification performance than using all features. Meanwhile, it achieves better performance than the two traditional feature selection algorithms. It maintains the classification performance achieved by the standard PSO for feature selection algorithm, but significantly reduces the number of features and the computational cost.

Graphical diagnostics to check model misspecification for the proportional odds regression model.

The advances in data collection increase the dimensionality of the data (i.e. the total number of features) in many fields, which arises a challenge to many existing feature selection approaches. This paper develops a new feature selection approach based on particle swarm optimisation (PSO) and a local search that mimics the typical backward elimination feature selection method. The proposed algorithm uses a wrapper based fitness function, i.e. the classification error rate. The local search is performed only on the global best and uses a filter based measure, which aims to take the advantages of both filter and wrapper approaches. The proposed approach is tested and compared with three recent PSO based feature selection algorithms and two typical traditional feature selection methods. Experiments on eight benchmark datasets show that the proposed algorithm can be successfully used to select a significantly smaller number of features and simultaneously improve the classification performance over using all features. The proposed approach outperforms the three PSO based algorithms and the two traditional methods.

Particle Swarm Optimisation and Statistical Clustering for Feature Selection

Protected area management in developing countries faces the challenges of building support for conservation among neighbouring residents and monitoring the social and ecological impacts of conservation programming. This study examined a collaborative resource management (CRM) programme at Kibale National Park (Uganda) that permits residents to fish inside the Park. Like other integrated conservation and development programmes, the goals are to help alleviate poverty and encourage support for conservation and conservation-related behaviours. The programmes impact was empirically analysed using an 81 item personal survey, with 94 CRM fishers and 91 comparison group respondents, and additional data from semi-structured interviews and document review. Fishers’ annual income was significantly greater (median = US

Gaussian Transformation Based Representation in Particle Swarm Optimisation for Feature Selection

376.02 yr −1 ) than that of the comparison group (median = US