Rank-ordered Data Research Articles

Methods for Enhancing the Robustness of the Generalized Contrast-to-Noise Ratio.

The generalized contrast-to-noise ratio (gCNR) is a new but increasingly popular metric for measuring lesion detectability due to its use of probability distribution functions that increase robustness against transformations and dynamic range alterations. The value of these kinds of metrics has become increasingly important as it becomes clear that traditional metrics can be arbitrarily boosted with advanced beamforming or the right kinds of postprocessing. The gCNR works well for most cases; however, we will demonstrate that for some specific cases the implementation of gCNR using histograms requires careful consideration, as histograms can be poor estimates of probability density functions (PDFs) when designed improperly. This is demonstrated with simulated lesions by altering the amount of data and the number of bins used in the calculation, as well as by introducing some extreme transformations that are represented poorly by uniformly spaced histograms. In this work, the viability of a parametric gCNR implementation is tested, more robust methods for implementing histograms are considered, and a new method for estimating gCNR using empirical cumulative distribution functions (eCDFs) is shown. The most consistent methods found were to use histograms on rank-ordered data or histograms with variable bin widths, or to use eCDFs to estimate the gCNR.

Using a Nominal Group Technique to Inform a Curriculum of a Short Learning Programme for Peer Mentor Training in a Health Sciences Context.

The purpose of this study was to explore the use of a modified nominal group technique (mNGT) to inform the curriculum of a Short Learning Programme for peer mentors in the Bachelor of Clinical Medical Practice (BCMP) program. An mNGT was used to achieve group consensus. Research participants included academic staff and students of the BCMP program called clinical associate (ClinA) students. Two sessions of the nominal group techniques (NGTs) were conducted. Two questions were presented: (1) what should be the learning outcomes of a Short Learning Programme for peer mentors for ClinA students? and (2) what learning activities should be included to achieve the intended learning outcomes? mNGT groups were both concluded in < 2 h and the costs involved were minimal. The priority outcomes of academic staff were to promote and encourage a positive, inclusive environment to enhance student morale; and to provide insight into the roles that peer mentors should fulfill. The primary objectives of academic staff were to foster and support a welcoming, inclusive atmosphere to boost student morale, as well as to offer guidance on the responsibilities that peer mentors should undertake. The top priorities of students were to provide insight into the role of a ClinA and the personal development of peer mentors. Learning activities suggested included time management and personal growth of peer mentors, "how to be an effective mentor," and leadership skills. The outcomes formulated by research participants reflected the graduate attributes listed by the University of Pretoria as well as generic attributes described by international scholars. A common NGT was an inexpensive and time-saving way to obtain rank-ordered data from research participants. This modified method ensured an equitable and inclusive approach, ensuring buy-in from all stakeholders, and is useful in the development of a curriculum for Short Learning Programmes. Both staff and students converged on common outcomes related to academic, psychosocial, and ClinA role support MeSH Terms: Consensus; Curriculum; Humans; Leadership; Mentors; Students.

Popular Attitudes Toward the Distribution of Vaccines Against COVID‐19: The Swiss Case

With the arrival of vaccines against the novel coronavirus in late 2020, the issue of how vaccines should be distributed and which groups should be prioritized has become salient. We study popular attitudes toward the distribution of COVID‐19 vaccines and how these have changed over the course of the pandemic in Switzerland, drawing on data from two rounds of an original public opinion survey conducted in the spring and winter of 2020. We find that the public supports prioritizing vulnerable groups such as health care workers or the elderly. We also find a notable degree of cross‐generational solidarity: younger age cohorts prioritize the elderly, while older groups prioritize (typically younger) health care workers. We then examine whether this finding is not in fact driven by vaccine hesitancy. This is not the case for older age groups, whose solidarity thus seems to be genuine. Vaccine hesitancy is an issue among younger groups, however.

A Time-Series Rank Ordering Control System Data-Driven Fault Detection Approach for HVAC Systems in Buildings

Abstract About 41% of total energy consumption in the United States of year 2014 is used for heating and air conditioning, which is about 40 quadrillion (40 × 1015) British thermal units (BTUs). Despite the fact that people have been working on fault detection and diagnosis (FDD) for heating, ventilation, and air conditioning (HVAC) systems for a long time, very few publications have focused on scalability and low cost. To address this challenge, we will propose an approach that focuses on control system data. Several machine learning algorithms are introduced for data exploration (e.g., DBSCAN, k-means) and analysis, rank-ordered weather data are used to define comparable days, a control system data focused model free approach is presented as well, and finally, fault detection is carried out by implementing anomaly algorithms (local outlier factor and isolation forest). Hidden faults were detected with a detection rate up to 90%+. The threshold parameter can be determined by selecting an acceptable true positive and false positive rate pair, which can be visualized using receiver operating characteristic (ROC) curves and is demonstrated in this article. A simulation model that is used to generate about 250 GB of data is used to evaluate the performance of various algorithms.

Research on intergenerational transmission of Chinese residents’ income: Based on data from ten surveys of Chinese Family Tracking Survey from 1989 to 2015

This article uses the rank-ordered probit estimation method and data from the 10 Chinese Family Tracking Survey from 1989 to 2015 to systematically study how the family background, especially the parental income, of urban and rural residents in China since its opening affects the intergenerational transmission of income and income inequality. The results show the following: ① The higher the income of parents is, the higher the income of their offspring. When parents are middle income or above, the probability of their children earning an upper-middle or high income increases significantly. ② Although the income of mothers is low, its impact on children’s income is greater than that of the father’s income. If the mother’s income is middle, upper-middle, or high income, it will increase the probability of her children earning a high income by 12.17%, 28.16% and 45.90%, respectively, while the corresponding influence from the father’s income is 9.62%, 20.69% and 43.82%. ③ For children, the degree of intergenerational income inequality is greater for women than for men, and it is higher in cities than in rural areas. ④ The intergenerational transmission of income is persistent across multiple generations, but the transmission from parents is much higher than from grandparents. It is also difficult for the offspring of a lower-income couple to obtain a higher income. These conclusions are robust to examining different samples and examining the predicted impact of various measures of family background on the income of offspring. Based on the results, this article puts forward policy recommendations to improve intergenerational income consolidation and reduce income inequality.

A Comparative Analysis of Productivity Improvement Techniques in Educational Institution of Holy Cross College

This study aims to explore and evaluate productivity improvement techniques that have a significant impact on the performance of faculty employees at Holy Cross College's Education Institution. The considered techniques are named as follows: Technology-based, Employee-Based, Material-Based, Process-Based, Product-Based, and Task-Based. Participants include Holy Cross College's teaching personnel. This study utilized an online survey with questionnaire that aims to identify the level of provision and level of importance of each productivity improvement techniques. The collected data were organized and used Related-Samples Friedman's Two-Way Analysis of Variance by Ranks to evaluate the rank-ordered data set productivity improvement techniques premised on common criteria of faculty assigned roles. Additionally, Paired Sample Statistics, Correlation and Test were conducted to find out the relationship of productivity improvement techniques’ level of provision and importance. The findings and recommendations for the possible integration of productivity enhancement techniques that should be highlighted and maintained in educational institutions were given. Results shown the task-based approach is the most commonly utilized and preferred productivity improvement technique among teachers. While the technology-based strategy has the highest correlation in this pandemic period.

Semiparametric estimation of the random utility model with rank-ordered choice data

We propose semiparametric methods for estimating random utility models using rank-ordered choice data. Our primary method is the generalized maximum score (GMS) estimator. With partially rank-ordered data, the GMS estimator allows for arbitrary forms of interpersonal heteroskedasticity. With fully rank-ordered data, the GMS estimator becomes considerably more flexible, allowing for random coefficients and alternative-specific heteroskedasticity and correlations. The GMS estimator has a non-standard asymptotic distribution and a convergence rate of N−1∕3. We proceed to construct its smoothed version which is asymptotically normal with a faster convergence rate of N−d∕(2d+1), where d≥2 increases in the strength of smoothness assumptions.

An application of a rank ordered probit modeling approach to understanding level of interest in autonomous vehicles

Surveys of behavior could benefit from information about people’s relative ranking of choice alternatives. Rank ordered data are often collected in stated preference surveys where respondents are asked to rank hypothetical alternatives (rather than choose a single alternative) to better understand their relative preferences. Despite the widespread interest in collecting data on and modeling people’s preferences for choice alternatives, rank-ordered data are rarely collected in travel surveys and very little progress has been made in the ability to rigorously model such data and obtain reliable parameter estimates. This paper presents a rank ordered probit modeling approach that overcomes limitations associated with prior approaches in analyzing rank ordered data. The efficacy of the rank ordered probit modeling methodology is demonstrated through an application of the model to understand preferences for alternative configurations of autonomous vehicles (AV) using the 2015 Puget Sound Regional Travel Study survey data set. The methodology offers behaviorally intuitive model results with a variety of socio-economic and demographic characteristics, including age, gender, household income, education, employment and household structure, significantly influencing preference for alternative configurations of AV adoption, ownership, and shared usage. The ability to estimate rank ordered probit models offers a pathway for better utilizing rank ordered data to understand preferences and recognize that choices may not be absolute in many instances.

Bayesian ROC curve estimation under binormality using an ordinal category likelihood

ABSTRACTReceiver operating characteristic (ROC) curve has been widely used in medical diagnosis. Various methods are proposed to estimate ROC curve parameters under the binormal model. In this paper, we propose a Bayesian estimation method from the continuously distributed data which is constituted by the truth-state-runs in the rank-ordered data. By using an ordinal category data likelihood and following the Metropolis–Hastings (M–H) procedure, we compute the posterior distribution of the binormal parameters, as well as the group boundaries parameters. Simulation studies and real data analysis are conducted to evaluate our Bayesian estimation method.

A Latent Class Nested Logit Model for Rank-Ordered Data with Application to Cork Oak Reforestation

We analyze stated ranking data collected from recreational visitors to the Alcornocales Natural Park (ANP) in Spain. The ANP is a large protected area which comprises mainly cork oak woodlands. The visitors ranked cork oak reforestation programs delivering different sets of environmental (reforestation technique, biodiversity, forest surface) and social (jobs and recreation sites created) outcomes. We specify a novel latent class nested logit model for rank-ordered data to estimate the distribution of willingness-to-pay for each outcome. Our modeling approach jointly exploits recent advances in discrete choice methods. The results suggest that prioritizing biodiversity would increase certainty over public support for a reforestation program. In addition, a substantial fraction of the visitor population are willing to pay more for the social outcomes than the environmental outcomes, whereas the existing reforestation subsidies are often justified by the environmental outcomes alone.

Abstract P1-10-27: Self-reported symptoms and interference issues in breast cancer patients

Abstract BACKGROUND: Breast cancer and its treatments produce multiple symptoms that significantly impact patient quality of life (QOL). Distress and impaired function are the most commonly referred symptoms [Cleeland CS, 2007]. Routine cancer care assessment of patient-reported outcomes (PROs), including symptoms, function, and QOL, has been shown to improve symptom management, identification of psychosocial problems, and patient-provider communication. The Symptom Inventory Tool (SIT) is an assessment tool that captures the patients' perceived symptom burden for real-time clinical intervention, taken at the point of no intervention (baseline) and every 21 days or greater. The SIT is comprised of 27 questions utilizing the M.D. Anderson Symptom Inventory tool (MDASI) [Cleeland CS, Cancer 2013], and validated assessment instrument with 8 questions added and a free text box by Cancer Treatment Centers of America (CTCA). CTCA is a national network of five hospitals that specialize in cancer treatment and integrative oncology. PATIENTS &amp; METHODS: Patients reported symptoms intensity using 19-item MD Anderson Symptom Inventory (MDASI) and 8 additional questions created by CTCA (constipation, swelling, mouth soreness, bleeding, sexual interest, family, hope &amp; QOL). Symptoms were rated "at the worst" on an 11-point numeric scale ranging from 0 ('no present") to 10 ("as bad as you can imagine") in the previous 24 hours. SIT became an integral part of patient care at CTCA beginning in 2012. RESULTS: From July 2012 to February 2015, a total of 3,740 outpatients with breast cancer were evaluated at CTCA. A total of 13,852 assessments were analyzed. The assessments consisted of 3,513 completed at baseline, 2,237 completed at the 2nd follow up (FU), and 8,014 completed at 3rd FU or greater. Median age was 50 (range, 17-88), 60% of patients were ER+. Race: White (68%), Black (29%), and other (3%). Disease extension: locoregional (86%) and metastatic (13.6%). The average time since cancer was diagnosed were 35 months, and 50.7% of the patients received prior systemic therapy: chemotherapy (55%), hormone-therapy (41%), and immunotherapy (4%). Mean, standard deviation and inter quartile ranges at baseline assessment are depicted in. Table 1.Patient Reported SymptomBaseline assessment statisticsPercentage of patients with severe symptoms at baseline and reporting a clinically significant change (2 points) at 2nd SIT assessment Mean +/- STDInterquartile range (IQR)Significant decreaseNo changeDistress3.0 +/- 3.0[0.5]695 (31.3%)594 (26.8%)414 (18.7%)Sadness2.5 +/- 2.9[0.4]622 (28%)718 (32.3%)358 (16.1%)Disturbed Sleep3.3 +/- 3.2[0.6]550 (24.8%)517 (23.3%)642 (28.9%)Mood2.6 +/- 2.7[0.4]549 (24.7%)678 (30.5%)447 (20.1%)Pain2.7 +/- 3.0[0.5]523 (23.9%)675 (30.8%)519 (23.7%)*IQR is a measure of variability, based on dividing a data set into quartiles. Quartiles divide a rank-ordered data set into four equal parts CONCLUSIONS: The SIT was successful in identifying symptoms burden and interference with life issues in breast cancer patients. Distress, sadness, disturbed sleep, mood and pain were the most common reported symptoms. Early identification of patient burden symptoms allowed immediate intervention and improvement in approximately a quarter of patients. Citation Format: Alvarez RH, Hartman S, Bosch B, Kendrick D, Cohen L, Fridman J, Ottersen D, Walcott K, Ware S, Castro I, Thomas J, Niu J, Ahn E, Denny D, Markman M. Self-reported symptoms and interference issues in breast cancer patients. [abstract]. In: Proceedings of the Thirty-Eighth Annual CTRC-AACR San Antonio Breast Cancer Symposium: 2015 Dec 8-12; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2016;76(4 Suppl):Abstract nr P1-10-27.

Birth and death master equation for the evolution of complex networks

Master equations for the evolution of complex networks with positive (birth) and negative (death) transition probabilities per unit time are analyzed. Explicit equations for the time evolution of the total number of nodes and for the relative node frequencies are given. It is shown that, in the continuous limit, the master equation reduces to a Fokker–Planck equation (FPE). The basic dynamical function for its stationary solution is the ratio between its drift and diffusion coefficients. When this ratio is approximated by partial fractions (Padé’s approximants), a hierarchy of stationary solutions of the FPE is obtained analytically, which are expressed as an exponential times the product of powers of monomials and binomials. It is also shown that if the difference between birth and death transition probabilities goes asymptotically to zero, the exponential factor in the solution is absent. Fits to real complex network probability distribution functions are shown. Comparison with rank-ordered data shows that, in general, the value of this exponential factor is close to unity, evidencing crossovers among power-law scale invariant regimes which might be associated to an underlying criticality and are related to a generalization of the beta distribution. The time dependent solution is also obtained analytically in terms of hyper-geometric functions. It is also shown that the FPE has similarity solutions. The limitations of the approach here presented are also discussed.

The Perceived Unreliability of Rank-Ordered Data: An Econometric Origin and Implications

The problem of unstable coefficients in the rank-ordered logit model has been traditionally interpreted as a sign that survey respondents fail to provide reliable ranking responses. This paper shows that the problem may embody the inherent sensitivity of the model to stochastic misspecification instead. Even a minor departure from the postulated random utility function can induce the problem, for instance when rank-ordered logit is estimated whereas the true additive disturbance is iid normal over alternatives. Related implications for substantive analyses and further modelling are explored. In general, a well-specified random coefficient rank-ordered logit model can mitigate, though not eliminate, the problem and produce analytically useful results. The model can also be generalised to be more suitable for forecasting purposes, by accommodating that stochastic misspecification matters less for individuals with more deterministic preferences. An empirical analysis using an Australian nursing job preferences survey shows that the estimates behave in accordance with these implications.

Using spectral analysis and multinomial logit regression to explain households’ choice patterns

Many methods are available to analyze rank-ordered data. We used spectral analysis to identify the most preferred option of Formosan subterranean termites (FSTs) control as ranked by Louisiana homeowners. Respondents were asked to rank four termite control methods from the most preferred option to the least preferred option. Spectral analysis of complete ranked data indicated that the most preferred FST control choice is a relatively cheap ($0.13/square foot) option of a liquid treatment. Similarly, analysis indicated that liquid and bait treatments are the two most desired control choices. Multinomial logit analysis indicated that survey location, household pre-tax income, and knowledge of FSTs determined Louisiana homeowners’ ranking pattern choices.

Introductory Remarks by Benedict Kingsbury

Indicators are increasingly important in global governance. They are one element of governance by information, and one expression of the growing importance of numerically expressed data and statistics in governance. (1) What are indicators, and what do they have to do with international law? These brief introductory remarks address these two questions. WHAT ARE INDICATORS? Indicators are not sharply different in nature and significance from other forms of quantification or other modes for simplifying and expressing data. Nonetheless, indicators have a cluster of features which, in aggregate, make special consideration of them useful. For purposes of inquiry into indicators as an important emerging technology in the practice of global governance, Davis, Kingsbury, and Merry define indicators in the following way: An indicator is a named collection of rank-ordered data that purports to represent the past or projected performance of different units. The data are generated through a process that simplifies raw data about a complex social phenomenon. The data, in this simplified and processed form, are capable of being used to compare particular units of analysis (such as countries or institutions or corporations), synchronically or over time, and to evaluate their performance by reference to one or more standards. (2) This working definition subsumes indexes, rankings, and composites which aggregate different indicators, although such aggregations or mash-up compilations raise many special issues. HOW ARE INDICATORS CONNECTED TO INTERNATIONAL LAW? Indicators frequently operate as standards. Indicators typically embody (although usually only implicitly rather than explicitly) an ideal, either through an understanding of what would make a good society or a better state of affairs, or through an account of a particular problem to be overcome. Many indicators also embody a view of causation by measuring elements which contribute to realization of the ideal or to the worsening or amelioration of the problem. Indicators are distinctive in that (typically) the indicator simultaneously articulates the standard and applies it. The flow of costs and benefits as incentives to perform better on an indicator may often be greater than the flows attached to legally binding instruments. Indicator-standards can have some of the same roles and features as legal standards: (a) Indicators can operate as an expression of values and political commitments, comparable in some ways to expressive functions of law. (b) Indicators can be used as part of the regulatory process for supervision or implementation of a legal standard. (c) An indicator, especially if highly authoritative and stable over time, can provide a focal point around which to align expectations. The World Bank Group's Doing Business indicators, Freedom House's Freedom in the World indicator, the World Economic Forum's Global Competitiveness Index, and the U.S. State Department's Trafficking in Persons indicator each seem to have operated as a focal point aligning expectations and influencing behavior, as have the U.S. News & World Report rankings of law schools within the United States. The influence of a focal point on behavior is heightened if use of the indicator becomes sufficiently embedded that network effects result. The system of letter-graded credit ratings for sovereign bonds is so embedded in legal rules and market practices (including requirements that some entities invest only in bonds rated as investment grade) that network effects result, making major changes to the system more costly and less likely. (d) Some of the pathways through which indicators can influence expectations, social categories, status relations, behavior, and even identities are similar to those applicable to international legal instruments. These include naming, shaming, praising/ blaming, emulation, acculturation, information changing beliefs or strategic calculations, behavioral or identity adaptations of the indicated, empowerment or redefinition of the indicators promulgator, altering external power structures, altering distributions of power within an entity, and building or intensifying networks. …

Antidepressant Medication Adherence

Nonadherence to antidepressant medication significantly contributes to the undertreatment of depression in primary care populations. The purpose of this study was to survey primary care patients' adherence to antidepressant medication to better understand factors associated with nonadherence. Participants with a history of being prescribed an antidepressant for at least 4 weeks were recruited from a primary care research network. Subjects completed a demographic survey, the Patient Health Questionnaire (PHQ), the Beck Depression Inventory-II (BDI-II), the Medical Outcomes Study (MOS) 36-Item Short-Form Health Survey, the Interpersonal Support Evaluation List, the Stages of Change Scale, the Medication Adherence Scale, and the MOS measure of adherence. Differences between adherent and nonadherent patients were compared using chi(2) for discrete variables, independent t tests for continuous variables, and Mann-Whitney U tests for rank-ordered data. Data were collected from April 1, 2001 to April 1, 2004. Approximately 80% (N = 148) of individuals approached for this study agreed to participate. The overall sample was primarily white and female. The PHQ diagnoses at study entry were dysthymic disorder (8.8%, n = 13), major depressive disorder (31.8%, n = 47), "double depression" (both dysthymic disorder and major depressive disorder, 29.7%, n = 44), and no depression (16.2%, n = 24.) The mean BDI-II score for the total sample was 19.9. Nonadherent patients reported being more careless about taking their medications, were more worried about side effects, were less satisfied with their physicians, were under the age of 40 years, and were more likely to have asked for a specific antidepressant. Nonadherent patients also indicated being at lower stages of change. Individually tailoring education to patient preference and stage of change is recommended to promote adherence.

A framework for analyzing rank-ordered data with application to automobile demand

In this paper, we develop a general random utility framework for analyzing data on individuals’ rank-orderings. Specifically, we show that in the case with three alternatives one can express the probability of a particular rank-ordering as a simple function of first choice probabilities. This framework is applied to specify and estimate models of household demand for conventional gasoline cars and alternative fuel vehicles in Shanghai based on rank-ordered data obtained from a stated preference survey. Subsequently, the framework is extended to allow for random effects in the utility specification to allow for intrapersonal correlation in tastes across stated preference questions. The preferred model is then used to calculate demand probabilities and elasticities and the distribution of willingness-to-pay for alternative fuel vehicles.

Recovery Deficiency Following Tree Mortality in Mangroves of Two Caribbean Islands: Field Survey and Statistical Classification

Mangrove species are well adapted to the harsh ecological conditions of their environment throughout the tropics. However, in the islands of Guadeloupe and Martinique (Lesser Antilles), deficient forest recovery was evidenced in 43 mangrove sites (>1000 m2) affected by apparently natural tree mortality. Such sites were recorded from four chronological sets of aerial photographs between 1950 and 1995, and field-investigated in terms of environment and vegetation characteristics. Given the speculative relationship between the slow-regenerating vegetation and its present environment within non-steady state, disturbed sites, statistical analyses arbitrarily matching physicochemical and biological data were primarily avoided. On one hand, principal component analysis (PCA), combined with an agglomerative hierarchical classification, was performed on environmental, rank-ordered data; on the other hand, multidimensional scaling (MDS) was implemented on vegetation data. Discriminant analyses (DA) further characterized the environment/vegetation interrelationships for each site type. Ultimately, three main types of mortality sites have been distinguished among the study areas. One type clustered the sites showing the lowest salinity values and the highest surge vulnerability whose dominant mangrove species is Rhizophora. Another type presented highly saline sites having clayey soils with pure, stunted, Avicennia stands. The last type consisted of peculiar forest gaps on deep, compact, peat soils. During the rainy season, these sites turned into shallow ponds scattered with living, young Rhizophora and large, standing, dead Avicennia. The authors suggest that this classification may serve as a comprehensive framework to test subsequent hypotheses (hurricanes, droughts…) on the origins of natural massive tree mortality and the causes of recovery deficiency in mangroves of the Caribbean.

Modeling Passengers' Preferences on a Short-Haul Domestic Airline with Rank-Ordered Data

In recent years, interest in finding methods to measure and analyze airline passengers' preferences has been growing. The current state of the air transportation industry encourages the implementation of tools and methodologies for such purposes. Initial modeling results of research on the preferences of domestic airline users are presented. A field survey (computerized questionnaire on a laptop computer) was conducted in five of Israel's domestic airports. Respondents were asked to rank four alternatives as main level-of-service variables. Separate models were estimated for three passenger trip purposes: personal, tourism, and business. The results of single-choice and rank-ordered logit models are compared for all available observations. The results indicate that the combination of first- and second-rank data sets produces coefficient estimates that are efficient but not significantly better than those of the single-choice logit models.

Multinomial probit estimation without nuisance parameters

Summary A feasible multinomial estimation procedure is derived, which does not require parameterization of the elements in the covariance matrix. The estimation is carried out using a simulated expectation-maximization algorithm, where the covariance structure is evaluated based on a set of score functions, while the structural coefficients are derived using standard multinomial probit (MNP) conditional on the given covariance structure. This methodology is demonstrated using a Monte Carlo simulation on both rank-ordered and non-ranked data, and on a real data set involving the choice of local residential telephone service. For limited finite samples, the procedure is shown to be superior to conventional MNP since it is faster, involves fewer parameters, and generates estimates with smaller variances.