Modelling rankings in R: the PlackettLuce package

This paper presents the R package PlackettLuce, which implements a generalization of the Plackett-Luce model for rankings data. The generalization accommodates both ties (of arbitrary order) and partial rankings (complete rankings of subsets of items). By default, the implementation adds a set of pseudo-comparisons with a hypothetical item, ensuring that the underlying network of wins and losses between items is always strongly connected. In this way, the worth of each item always has a finite maximum likelihood estimate, with finite standard error. The use of pseudo-comparisons also has a regularization effect, shrinking the estimated parameters towards equal item worth. In addition to standard methods for model summary, PlackettLuce provides a method to compute quasi standard errors for the item parameters. This provides the basis for comparison intervals that do not change with the choice of identifiability constraint placed on the item parameters. Finally, the package provides a method for model-based partitioning using covariates whose values vary between rankings, enabling the identification of subgroups of judges or settings that have different item worths. The features of the package are demonstrated through application to classic and novel data sets.Comment: In v2: review of software implementing alternative models to Plackett-Luce; comparison of algorithms provided by the PlackettLuce package; further examples of rankings where the underlying win-loss network is not strongly connected. In addition, general editing to improve organisation and clarity. In v3: corrected headings Table 4, minor edit

VizRank: Data Visualization Guided by Machine Learning

Data visualization plays a crucial role in identifying interesting patterns in exploratory data analysis. Its use is, however, made difficult by the large number of possible data projections showing different attribute subsets that must be evaluated by the data analyst. In this paper, we introduce a method called VizRank, which is applied on classified data to automatically select the most useful data projections. VizRank can be used with any visualization method that maps attribute values to points in a two-dimensional visualization space. It assesses possible data projections and ranks them by their ability to visually discriminate between classes. The quality of class separation is estimated by computing the predictive accuracy of k-nearest neighbor classifier on the data set consisting of x and y positions of the projected data points and their class information. The paper introduces the method and presents experimental results which show that VizRank's ranking of projections highly agrees with subjective rankings by data analysts. The practical use of VizRank is also demonstrated by an application in the field of functional genomics

Towards Comparative and Aggregate Vulnerability: An Analysis of Welfare Distributions in Rural Provinces in Thailand and Vietnam

Several measures of vulnerability to poverty have been suggested in the literature. In practise, only little is known about the robustness of vulnerability comparisons based on these often quite specific measures. The theory of stochastic orders can be applied to shed some light on such issues. In the DFG research project "Impact of Shocks on the Vulnerability to Poverty: Consequences for Development of Emerging Southeast Asian Economies" (DFG FOR 756), an extensive panel survey was carried out in six rural provinces of Thailand and Vietnam in 2007. We establish cumulative distribution functions for income and consumption at the provincial level and search for stochastic dominance relations between these distributions. Our comparisons allow for initial, but quite robust conclusions on welfare and provide benchmarks for assessing the vulnerability to poverty in the research regions. --welfare distribution,stochastic ordering,vulnerability

Diversity and Polarization of Research Performance: Evidence from Hungary

Measuring the intellectual diversity encoded in publication records as a proxy to the degree of interdisciplinarity has recently received considerable attention in the science mapping community. The present paper draws upon the use of the Stirling index as a diversity measure applied to a network model (customized science map) of research profiles, proposed by several authors. A modified version of the index is used and compared with the previous versions on a sample data set in order to rank top Hungarian research organizations (HROs) according to their research performance diversity. Results, unexpected in several respects, show that the modified index is a candidate for measuring the degree of polarization of a research profile. The study also points towards a possible typology of publication portfolios that instantiate different types of diversity

The simultaneous valuation of states from multiple instruments using ranking and VAS data: methods and preliminary results

Background: Previous methods of empirical mapping involve using regressions on patient or general population self-report data from datasets involving two or more instruments. This approach relies on overlap in the descriptive systems of the measures, but key dimensions may not be present in both measures. Furthermore this assumes it is appropriate to use different instruments on the same population, which may not be the case for all patient groups. The aim of the study described here is to develop a new method of mapping using general population preferences for hypothetical health states defined by the descriptive systems of different measures. This paper presents a description of the methods used in the study and reports on the results of the valuation study including details about the respondents, feasibility and quality (e.g. response rate, completion and consistency) and descriptive results on VAS and ranking data. The use of these results to estimate mapping functions between instruments will be presented in a companion paper. Methods: The study used interviewer administered versions of ranking and VAS techniques to value 13 health states defined by each of 6 instruments: EQ-5D (generic), SF-6D (generic), HUI2 (generic for children), AQL-5D (asthma specific), OPUS (social care specific), ICECAP (capabilities). Each interview involved 3 ranking and visual analogue scale (VAS) tasks with states from 3 different instruments where each task involves the simultaneous valuation of multiple instruments. The study includes 13 health and well-being states for each instrument (16 for EQ-5D) that reflect a range of health state values according to the published health state values for each instrument and each health state is valued approximately 75-100 times. Results: The sample consists of 499 members of the UK general population with a reasonable spread of background characteristics (response rate=55%). The study achieved a completion rate of 99% for all states included in the rank and rating tasks and 94.8% of respondents have complete VAS responses and 97.2% have complete rank responses. Interviewers reported that it is doubtful for 4.1% of respondents that they understood the tasks, and 29.3% of respondents stated that they found the tasks difficult. The results suggest important differences in the range of mean VAS and mean rank values per state across instruments, for example mean VAS values for the worst state vary across instruments from 0.075 to 0.324. Respondents are able to change the ordering of states between the rank and VAS tasks and 12.0% of respondents have one or more differences in their rank and VAS orderings for every task. Conclusions: This study has demonstrated the feasibility of simultaneously valuing health states from different preference-based instruments. The preliminary analysis of the results presented here provides the basis for a new method of mapping between measures based on general population preferences.preference-based measures of health; quality of life; mapping; visual analogue scale; ranking

The simultaneous valuation of states from multiple instruments using ranking and VAS data: methods and preliminary results

Background: Previous methods of empirical mapping involve using regressions on patient or general population self-report data from datasets involving 2 or more instruments. This approach relies on overlap in the descriptive systems of the measures, but key dimensions may not be present in both measures. Furthermore, this assumes it is appropriate to use different instruments on the same population, which may not be the case for all patient groups. The aim of the study described here is to develop a new method of mapping using general population preferences for hypothetical health states defined by the descriptive systems of different measures. This paper presents a description of the methods used in the study and reports on the results of the valuation study including details about the respondents, feasibility and quality (e.g. response rate, completion and consistency) and descriptive results on VAS and ranking data. The use of these results to estimate mapping functions between instruments will be presented in a companion paper. Methods: The study used interviewer administered versions of ranking and VAS techniques to value 13 health states defined by each of 6 instruments: EQ-5D (generic), SF-6D (generic), HUI2 (generic for children), AQL-5D (asthma specific), OPUS (social care specific), ICECAP (capabilities). Each interview involved 3 ranking and visual analogue scale (VAS) tasks with states from 3 different instruments where each task involves the simultaneous valuation of multiple instruments. The study includes 13 health and well-being states for each instrument (16 for EQ-5D) that reflect a range of health state values according to the published health state values for each instrument and each health state is valued approximately 75-100 times. Results: The sample consists of 499 members of the UK general population with a reasonable spread of background characteristics (response rate=55%). The study achieved a completion rate of 99% for all states included in the rank and rating tasks and 94.8% of respondents have complete VAS responses and 97.2% have complete rank responses. Interviewers reported that it is doubtful for 4.1% of respondents that they understood the tasks, and 29.3% of respondents stated that they found the tasks difficult. The results suggest important differences in the range of mean VAS and mean rank values per state across instruments; for example, mean VAS values for the worst state vary across instruments from 0.075 to 0.324. Respondents are able to change the ordering of states between the rank and VAS tasks and 12.0% of respondents have one or more differences in their rank and VAS orderings for every task. Conclusions: This study has demonstrated the feasibility of simultaneously valuing health states from different preference-based instruments. The preliminary analysis of the results presented here provides the basis for a new method of mapping between measures based on general population preferences