Easier analysis and better reporting : modelling ordinal data in mathematics education research

This article presents an examination of the use of Rasch modelling in a major research project, 'Improving Middle Years Mathematics and Science' (IMYMS). It is unarguable that it is important to take students' perceptions, or views, into account when planning learning and teaching for them. The IMYMS student perceptions survey is an attempt to make visible these student viewpoints, and report them in a way that is accessible to teachers and researchers involved in the project. The project involves four clusters of schools from urban and regions of Victoria to investigate the role of mathematics and science knowledge and subject cultures in mediating change processes in the middle years of schooling. There are five secondary and twenty-eight primary schools. The project has generated both qualitative and quantitative data, with much of the qualitative data being ordinal in nature. Reporting the results of analyses for a range of audiences necessitates careful, well-designed report formats. Some useful new report formats based on Rasch modeling -the Modified Variable Map, the Ordinal Map, the Threshold Map, and the Annotated Ordinal Map - are illustrated using data from the IMYMS project. The Rasch analysis and the derived reporting formats avoid the pitfalls that exist when working with ordinal data and provide insights into the respondents' views about their experiences in schools unavailable by other approaches.

Cumulative restricted Boltzmann machines for ordinal matrix data analysis

Ordinal data is omnipresent in almost all multiuser-generated feedback - questionnaires, preferences etc. This paper investigates modelling of ordinal data with Gaussian restricted Boltzmann machines (RBMs). In particular, we present the model architecture, learning and inference procedures for both vector-variate and matrix-variate ordinal data. We show that our model is able to capture latent opinion profile of citizens around the world, and is competitive against state-of-art collaborative filtering techniques on large-scale public datasets. The model thus has the potential to extend application of RBMs to diverse domains such as recommendation systems, product reviews and expert assessments.

A two-stage dynamic group decision making method for processing ordinal information

In group decision making (GDM) problems, ordinal data provide a convenient way of articulating preferences from decision makers (DMs). A number of GDM models have been proposed to aggregate such kind of preferences in the literature. However, most of the GDM models that handle ordinal preferences suffer from two drawbacks: (1) it is difficult for the GDM models to manage conflicting opinions, especially with a large number of DMs; and (2) the relationships between the preferences provided by the DMs are neglected, and all DMs are assumed to be of equal importance, therefore causing the aggregated collective preference not an ideal representative of the group's decision. In order to overcome these problems, a two-stage dynamic group decision making method for aggregating ordinal preferences is proposed in this paper. The method consists of two main processes: (i) a data cleansing process, which aims to reduce the influence of conflicting opinions pertaining to the collective decision prior to the aggregation process; as such an effective solution for undertaking large-scale GDM problems is formulated; and (ii) a support degree oriented consensus-reaching process, where the collective preference is aggregated by using the Power Average (PA) operator; as such, the relationships of the arguments being aggregated are taken into consideration (i.e., allowing the values being aggregated to support each other). A new support function for the PA operator to deal with ordinal information is defined based on the dominance-based rough set approach. The proposed GDM model is compared with the models presented by Herrera-Viedma et al. An application related to controlling the degradation of the hydrographic basin of a river in Brazil is evaluated. The results demonstrate the usefulness of the proposed method in handling GDM problems with ordinal information.

Nurse-led clinic: Effective and efficient delivery of assessment and review of patients with Hepatitis B and C

Hepatology and gastroenterology services are increasingly utilising the skills and experience of nurse practitioners and nurse specialists to help meet the increasing demand for health care. A new nurse-led assessment clinic has been established in the liver clinic at Geelong Hospital to utilise the expertise of nurses to assess and triage new patients and streamline their pathway through the health care system. The aim of this study is to quantitatively assess the first two years of operation of the nurse assessment clinic at Geelong Hospital, and to assess advantages and disadvantages of the nurse-led clinic. Data was extracted retrospectively from clinical records of new patients at the liver clinic. Quarterly one-month periods were recorded over two-years. Patients were categorised according to the path via which they saw a physician, including missed and rescheduled appointments. The number of appointments, the waiting time from referral to appointments and the number of ‘did-not-attend’ occasions were analysed before and after the institution of the nurse-led assessment clinic. The Mann-Whitney rank sum test of ordinal data was used to generate median wait times. There was shown to be a statistically significant longer waiting time for physician appointment if seen by the nurse first. The difference in waiting time was 10 days. However, there was also a reduction in the number of missed appointments at the subsequent physician clinic. Other advantages have also been identified including effective triage of patients, and organisation of appropriate investigations from the initial nurse assessment.

Ordinal Boltzmann machines for collaborative filtering

Collaborative filtering is an effective recommendation technique wherein the preference of an individual can potentially be predicted based on preferences of other members. Early algorithms often relied on the strong locality in the preference data, that is, it is enough to predict preference of a user on a particular item based on a small subset of other users with similar tastes or of other items with similar properties. More recently, dimensionality reduction techniques have proved to be equally competitive, and these are based on the co-occurrence patterns rather than locality. This paper explores and extends a probabilistic model known as Boltzmann Machine for collaborative filtering tasks. It seamlessly integrates both the similarity and cooccurrence in a principled manner. In particular, we study parameterisation options to deal with the ordinal nature of the preferences, and propose a joint modelling of both the user-based and item-based processes. Experiments on moderate and large-scale movie recommendation show that our framework rivals existing well-known methods.

Associations between fruit and vegetable intake, leisure-time physical activity, sitting time and self-rated health among older adults : cross-sectional data from the WELL study

Background
Lifestyle behaviours, such as healthy diet, physical activity and sedentary behaviour, are key elements of healthy ageing and important modifiable risk factors in the prevention of chronic diseases. Little is known about the relationship between these behaviours in older adults. The purpose of this study was to explore the relationship between fruit and vegetable (F&V) intake, leisure-time physical activity (LTPA) and sitting time (ST), and their association with self-rated health in older adults.

Methods
This cross-sectional study comprised 3,644 older adults (48% men) aged 55-65 years, who participated in the Wellbeing, Eating and Exercise for a Long Life ("WELL") study. Respondents completed a postal survey about their health and their eating and physical activity behaviours in 2010 (38% response rate). Spearman's coefficient (rho) was used to evaluate the relationship between F&V intake, LTPA and ST. Their individual and shared associations with self-rated health were examined using ordinal logistic regression models, stratified by sex and adjusted for confounders (BMI, smoking, long-term illness and socio-demographic characteristics).

Results
The correlations between F&V intake, LTPA and ST were low. F&V intake and LTPA were positively associated with self-rated health. Each additional serving of F&V or MET-hour of LTPA were associated with approximately 10% higher likelihood of reporting health as good or better among women and men. The association between ST and self-rated health was not significant in the multivariate analysis. A significant interaction was found (ST*F&V intake). The effect of F&V intake on self-rated health increased with increasing ST in women, whereas the effect decreased with increasing ST in men.

Conclusion
This study contributes to the scarce literature related to lifestyle behaviours and their association with health indicators among older adults. The findings suggest that a modest increase in F&V intake, or LTPA could have a marked effect on the health of older adults. Further research is needed to fully understand the correlates and determinants of lifestyle behaviours, particularly sitting time, in this age group.

Embedded restricted Boltzmann machines for fusion of mixed data types and applications in social measurements analysis

Analysis and fusion of social measurements is important to understand what shapes the public’s opinion and the sustainability of the global development. However, modeling data collected from social responses is challenging as the data is typically complex and heterogeneous, which might take the form of stated facts, subjective assessment, choices, preferences or any combination thereof. Model-wise, these responses are a mixture of data types including binary, categorical, multicategorical, continuous, ordinal, count and rank data. The challenge is therefore to effectively handle mixed data in the a unified fusion framework in order to perform inference and analysis. To that end, this paper introduces eRBM (Embedded Restricted Boltzmann Machine) – a probabilistic latent variable model that can represent mixed data using a layer of hidden variables transparent across different types of data. The proposed model can comfortably support largescale data analysis tasks, including distribution modelling, data completion, prediction and visualisation. We demonstrate these versatile features on several moderate and large-scale publicly available social survey datasets.

Stabilized sparse ordinal regression for medical risk stratification

The recent wide adoption of electronic medical records (EMRs) presents great opportunities and challenges for data mining. The EMR data are largely temporal, often noisy, irregular and high dimensional. This paper constructs a novel ordinal regression framework for predicting medical risk stratification from EMR. First, a conceptual view of EMR as a temporal image is constructed to extract a diverse set of features. Second, ordinal modeling is applied for predicting cumulative or progressive risk. The challenges are building a transparent predictive model that works with a large number of weakly predictive features, and at the same time, is stable against resampling variations. Our solution employs sparsity methods that are stabilized through domain-specific feature interaction networks. We introduces two indices that measure the model stability against data resampling. Feature networks are used to generate two multivariate Gaussian priors with sparse precision matrices (the Laplacian and Random Walk). We apply the framework on a large short-term suicide risk prediction problem and demonstrate that our methods outperform clinicians to a large margin, discover suicide risk factors that conform with mental health knowledge, and produce models with enhanced stability. © 2014 Springer-Verlag London.