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.

Evaluating Measurement Invariance with Censored Ordinal Data: A Monte Carlo Comparison of Alternative Model Estimators and Scales of Measurement

Evaluations of measurement invariance provide essential construct validity evidence. However, the quality of such evidence is partly dependent upon the validity of the resulting statistical conclusions. The presence of Type I or Type II errors can render measurement invariance conclusions meaningless. The purpose of this study was to determine the effects of categorization and censoring on the behavior of the chi-square/likelihood ratio test statistic and two alternative fit indices (CFI and RMSEA) under the context of evaluating measurement invariance. Monte Carlo simulation was used to examine Type I error and power rates for the (a) overall test statistic/fit indices, and (b) change in test statistic/fit indices. Data were generated according to a multiple-group single-factor CFA model across 40 conditions that varied by sample size, strength of item factor loadings, and categorization thresholds. Seven different combinations of model estimators (ML, Yuan-Bentler scaled ML, and WLSMV) and specified measurement scales (continuous, censored, and categorical) were used to analyze each of the simulation conditions. As hypothesized, non-normality increased Type I error rates for the continuous scale of measurement and did not affect error rates for the categorical scale of measurement. Maximum likelihood estimation combined with a categorical scale of measurement resulted in more correct statistical conclusions than the other analysis combinations. For the continuous and censored scales of measurement, the Yuan-Bentler scaled ML resulted in more correct conclusions than normal-theory ML. The censored measurement scale did not offer any advantages over the continuous measurement scale. Comparing across fit statistics and indices, the chi-square-based test statistics were preferred over the alternative fit indices, and ΔRMSEA was preferred over ΔCFI. Results from this study should be used to inform the modeling decisions of applied researchers. However, no single analysis combination can be recommended for all situations. Therefore, it is essential that researchers consider the context and purpose of their analyses.

Multidimensional item response theory models with general and specific latent traits for ordinal data

The aim of the thesis is to propose a Bayesian estimation through Markov chain Monte Carlo of multidimensional item response theory models for graded responses with complex structures and correlated traits. In particular, this work focuses on the multiunidimensional and the additive underlying latent structures, considering that the first one is widely used and represents a classical approach in multidimensional item response analysis, while the second one is able to reflect the complexity of real interactions between items and respondents. A simulation study is conducted to evaluate the parameter recovery for the proposed models under different conditions (sample size, test and subtest length, number of response categories, and correlation structure). The results show that the parameter recovery is particularly sensitive to the sample size, due to the model complexity and the high number of parameters to be estimated. For a sufficiently large sample size the parameters of the multiunidimensional and additive graded response models are well reproduced. The results are also affected by the trade-off between the number of items constituting the test and the number of item categories. An application of the proposed models on response data collected to investigate Romagna and San Marino residents' perceptions and attitudes towards the tourism industry is also presented.

A new DEA model for technology selection in the presence of ordinal data

This paper suggests a data envelopment analysis (DEA) model for selecting the most efficient alternative in advanced manufacturing technology in the presence of both cardinal and ordinal data. The paper explains the problem of using an iterative method for finding the most efficient alternative and proposes a new DEA model without the need of solving a series of LPs. A numerical example illustrates the model, and an application in technology selection with multi-inputs/multi-outputs shows the usefulness of the proposed approach. © 2012 Springer-Verlag London Limited.

Rank regression for analyzing ordinal qualitative data for treatment comparison

Ordinal qualitative data are often collected for phenotypical measurements in plant pathology and other biological sciences. Statistical methods, such as t tests or analysis of variance, are usually used to analyze ordinal data when comparing two groups or multiple groups. However, the underlying assumptions such as normality and homogeneous variances are often violated for qualitative data. To this end, we investigated an alternative methodology, rank regression, for analyzing the ordinal data. The rank-based methods are essentially based on pairwise comparisons and, therefore, can deal with qualitative data naturally. They require neither normality assumption nor data transformation. Apart from robustness against outliers and high efficiency, the rank regression can also incorporate covariate effects in the same way as the ordinary regression. By reanalyzing a data set from a wheat Fusarium crown rot study, we illustrated the use of the rank regression methodology and demonstrated that the rank regression models appear to be more appropriate and sensible for analyzing nonnormal data and data with outliers.

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.

Calculation of sample size for stroke trials assessing functional outcome: comparison of binary and ordinal approaches

Background Many acute stroke trials have given neutral results. Sub-optimal statistical analyses may be failing to detect efficacy. Methods which take account of the ordinal nature of functional outcome data are more efficient. We compare sample size calculations for dichotomous and ordinal outcomes for use in stroke trials. Methods Data from stroke trials studying the effects of interventions known to positively or negatively alter functional outcome – Rankin Scale and Barthel Index – were assessed. Sample size was calculated using comparisons of proportions, means, medians (according to Payne), and ordinal data (according to Whitehead). The sample sizes gained from each method were compared using Friedman 2 way ANOVA. Results Fifty-five comparisons (54 173 patients) of active vs. control treatment were assessed. Estimated sample sizes differed significantly depending on the method of calculation (Po00001). The ordering of the methods showed that the ordinal method of Whitehead and comparison of means produced significantly lower sample sizes than the other methods. The ordinal data method on average reduced sample size by 28% (inter-quartile range 14–53%) compared with the comparison of proportions; however, a 22% increase in sample size was seen with the ordinal method for trials assessing thrombolysis. The comparison of medians method of Payne gave the largest sample sizes. Conclusions Choosing an ordinal rather than binary method of analysis allows most trials to be, on average, smaller by approximately 28% for a given statistical power. Smaller trial sample sizes may help by reducing time to completion, complexity, and financial expense. However, ordinal methods may not be optimal for interventions which both improve functional outcome

Environments For Healthy Living (EFHL) Griffith birth cohort study : characteristics of sample and profile of antenatal exposures

Background The Environments for Healthy Living (EFHL) study is a repeated sample, longitudinal birth cohort in South East Queensland, Australia. We describe the sample characteristics and profile of maternal, household, and antenatal exposures. Variation and data stability over recruitment years were examined. Methods Four months each year from 2006, pregnant women were recruited to EFHL at routine antenatal visits on or after 24 weeks gestation, from three public maternity hospitals. Participating mothers completed a baseline questionnaire on individual, familial, social and community exposure factors. Perinatal data were extracted from hospital birth records. Descriptive statistics and measures of association were calculated comparing the EFHL birth sample with regional and national reference populations. Data stability of antenatal exposure factors was assessed across five recruitment years (2006–2010 inclusive) using the Gamma statistic for ordinal data and chi-squared for nominal data. Results Across five recruitment years 2,879 pregnant women were recruited which resulted in 2904 live births with 29 sets of twins. EFHL has a lower representation of early gestational babies, fewer still births and a lower percentage of low birth weight babies, when compared to regional data. The majority of women (65%) took a multivitamin supplement during pregnancy, 47% consumed alcohol, and 26% reported having smoked cigarettes. There were no differences in rates of a range of antenatal exposures across five years of recruitment, with the exception of increasing maternal pre-pregnancy weight (p=0.0349), decreasing rates of high maternal distress (p=0.0191) and decreasing alcohol consumption (p<0.0001). Conclusions The study sample is broadly representative of births in the region and almost all factors showed data stability over time. This study, with repeated sampling of birth cohorts over multiple years, has the potential to make important contributions to population health through evaluating longitudinal follow-up and within cohort temporal effects.

Combined analysis of categorical and numerical descriptors of Australian groundnut accessions using nonlinear principal component analysis

For users of germplasm collections, the purpose of measuring characterization and evaluation descriptors, and subsequently using statistical methodology to summarize the data, is not only to interpret the relationships between the descriptors, but also to characterize the differences and similarities between accessions in relation to their phenotypic variability for each of the measured descriptors. The set of descriptors for the accessions of most germplasm collections consists of both numerical and categorical descriptors. This poses problems for a combined analysis of all descriptors because few statistical techniques deal with mixtures of measurement types. In this article, nonlinear principal component analysis was used to analyze the descriptors of the accessions in the Australian groundnut collection. It was demonstrated that the nonlinear variant of ordinary principal component analysis is an appropriate analytical tool because subspecies and botanical varieties could be identified on the basis of the analysis and characterized in terms of all descriptors. Moreover, outlying accessions could be easily spotted and their characteristics established. The statistical results and their interpretations provide users with a more efficient way to identify accessions of potential relevance for their plant improvement programs and encourage and improve the usefulness and utilization of germplasm collections.

Autoavaliação do estado de saúde: associação com fatores sociodemográficos, hábitos de vida, morbidade e experiência de discriminação racial em inquérito populacional no Brasil

A autoavaliação do estado de saúde (AAS) é um indicador de saúde amplamente utilizado e influenciado por uma grande variedade de fatores. Em particular, existem evidências crescentes de que a discriminação racial é um importante fator de risco para eventos mórbidos em saúde e seu impacto na saúde da população brasileira ainda é pouco explorado. No primeiro artigo, o objetivo principal é investigar a associação entre AAS e fatores sociodemográficos, comportamentais e de morbidade. No segundo artigo, o objetivo é estimar a associação entre discriminação racial e diferentes desfechos em saúde, a saber, AAS, morbidade física e depressão ajustando por variáveis sociodemográficas, comportamentos relacionados à saúde e Índice de Massa Corporal, na população de pretos e pardos. O presente estudo possui delineamento seccional, baseado nos dados do inquérito de abrangência nacional Pesquisa Dimensão Social das Desigualdades. Os entrevistados responderam a questionários estruturados e suas medidas antropométricas foram aferidas. No primeiro artigo, foram avaliados 12.324 indivíduos, entre chefes de família e cônjuges, com idade maior ou igual a 20 anos. No segundo artigo, foram avaliados 3.863 chefes de família que responderam a pergunta sobre discriminação racial e que se classificaram como pretos e pardos. AAS foi avaliada por meio de pergunta obtida do instrumento de qualidade de vida SF-36 e, para o primeiro artigo, foi analisada de forma dicotômica em AAS boa (categorias de resposta excelente, muito boa e boa) e AAS ruim (categorias de resposta razoável e ruim). No segundo artigo, esse desfecho foi analisado utilizando-se as 5 categorias de resposta. As análises foram realizadas utilizando-se modelos de regressão logística uni e multivariados, para dados binários (artigo 1) ou ordinais (artigo 2). Os resultados foram apresentados na forma de Odds Ratios com os respectivos intervalos de 95% de confiança. Maior faixa etária, analfabetismo, tabagismo, obesidade e doenças crônicas estiveram associados a maior chance de AAS ruim. Para cada incremento na faixa de renda, observou-se uma redução de 20% na chance de relatar AAS ruim. Atividade física esteve associada a menor chance de AAS ruim. No segundo artigo, exposição à discriminação racial esteve associada com aumento na chance de relato de pior AAS, de morbidade física e de depressão. O presente estudo identificou a influência de diversos fatores sociais, demográficos, comportamentos relacionados à saúde e morbidade física na AAS. O estudo demonstrou ainda que a discriminação racial está associada negativamente aos três desfechos em saúde avaliados (AAS, morbidade física e depressão). Esses resultados podem traçar um perfil de subgrupos populacionais mais vulneráveis, ou seja, com maior risco de contrair doenças ou de procurar o serviço de saúde por uma doença já existente, auxiliando na definição de populações-alvo para o adequado planejamento de políticas e de programas de promoção de saúde.

Teleconsultation in sexual and reproductive health for young adults through mobile devices: Experience in Colombia

Background: Sexual risk behaviors associated with poor information on sexuality have contributed to major public health problems in the area of sexual and reproductive health in teenagers and young adults in Colombia. Objective: To measure the perception of changes in sexual and reproductive risk behavior after the use of a teleconsultation service via mobile devices in a sample of young adults. Methods: A before and after observational study was designed, where a mobile application to inquire about sexual and reproductive health was developed. The perception of changes in sexual and reproductive health risk behaviors in a sample of young adults after the use of the application was measured using the validated survey “Family Health International (FHI) – Behavioral Surveillance Survey (BSS) – Survey for Adults between 15 to 40 Years”. Non-probabilistic convenience recruitment was undertaken through the study´s web page. Participants answered the survey online before and after the use of the mobile application for a six month period (intervention). For the inferential analysis, data was divided into three groups (dichotomous data, discrete quantitative data, and ordinal data), to compare the results of the questions between the first and the second survey. For all tests, a confidence interval of 95% was established. For dichotomous data, the Chi-squared test was used. For quantitative data, we used the Student’s t-test, and for ordinal data, the Mann-Whitney-Wilcoxon test. Results: A total of 257 subjects were registered in the study and met the selection criteria. The pre-intervention survey was answered by 232 subjects, and 127 completely answered the post-intervention survey, of which 54.3% did not use the application, leaving an effective population of 58 subjects for analysis. 53% (n=31) were female, and 47% (n=27) were male. The mean age was 21 years, ranging between 18 and 40 years. The differences between the answers on the first and the second survey were not statistically significant. The main risk behaviors identified in the population were homosexual relations, non-use of condoms, sexual relations with non-regular and commercial partners, the use of psychoactive substances, and ignorance about the symptoms of sexually transmitted diseases and HIV transmission. Conclusions: Although there were no differences between the pre- and post-intervention results, the study revealed different risk behaviors among the participating subjects. These findings highlight the importance of promoting educational strategies on this matter and the importance of providing patients with easily accessible tools with reliable health 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.

Indicador multivariado policórico: proposta de indicador para o diagnóstico da aprendizagem organizacional

Pós-graduação em Engenharia Mecânica - FEG

Studies in the role of the public school teacher,

Includes bibliographies.