A Spectral Method for Identifiable Grade of Membership Analysis with Binary Responses.

Grade of membership (GoM) models are popular individual-level mixture models for multivariate categorical data. GoM allows each subject to have mixed memberships in multiple extreme latent profiles. Therefore, GoM models have a richer modeling capacity than latent class models that restrict each subject to belong to a single profile. The flexibility of GoM comes at the cost of more challenging identifiability and estimation problems. In this work, we propose a singular value decomposition (SVD)-based spectral approach to GoM analysis with multivariate binary responses. Our approach hinges on the observation that the expectation of the data matrix has a low-rank decomposition under a GoM model. For identifiability, we develop sufficient and almost necessary conditions for a notion of expectation identifiability. For estimation, we extract only a few leading singular vectors of the observed data matrix and exploit the simplex geometry of these vectors to estimate the mixed membership scores and other parameters. We also establish the consistency of our estimator in the double-asymptotic regime where both the number of subjects and the number of items grow to infinity. Our spectral method has a huge computational advantage over Bayesian or likelihood-based methods and is scalable to large-scale and high-dimensional data. Extensive simulation studies demonstrate the superior efficiency and accuracy of our method. We also illustrate our method by applying it to a personality test dataset.

Why not both? Rethinking categorical and continuous approaches to bilingualism.

AIMS AND OBJECTIVES: Bilingualism is a complex construct, and it can be difficult to define and model. This paper proposes that the field of bilingualism can draw from other fields of psychology, by integrating advanced psychometric models that incorporate both categorical and continuous properties. These models can unify the widespread use of bilingual and monolingual groups that exist in the literature with recent proposals that bilingualism should be viewed as a continuous variable. APPROACH: In the paper, we highlight two models of potential interest: the factor mixture model and the grade-of-membership model. These models simultaneously allow for the formation of different categories of speakers and for continuous variation to exist within these categories. We discuss how these models could be implemented in bilingualism research, including how to develop these models. When using either of the two models, researchers can conduct their analyses on either the categorical or continuous information, or a combination of the two, depending on which is most appropriate to address their research question. CONCLUSIONS: The field of bilingualism research could benefit from incorporating more complex models into definitions of bilingualism. To help various subfields of bilingualism research converge on appropriate models, we encourage researchers to pre-register their model selection and planned analyses, as well as to share their data and analysis scripts. ORIGINALITY: The paper uniquely proposes the incorporation of advanced statistical psychometric methods for defining and modeling bilingualism. SIGNIFICANCE: Conceptualizing bilingualism within the context of these more flexible models will allow a wide variety of research questions to be addressed. Ultimately, this will help to advance theory and lead to a fuller and deeper understanding of bilingualism.

A Signal Detection Model for Multiple-Choice Exams.

A model for multiple-choice exams is developed from a signal-detection perspective. A correct alternative in a multiple-choice exam can be viewed as being a signal embedded in noise (incorrect alternatives). Examinees are assumed to have perceptions of the plausibility of each alternative, and the decision process is to choose the most plausible alternative. It is also assumed that each examinee either knows or does not know each item. These assumptions together lead to a signal detection choice model for multiple-choice exams. The model can be viewed, statistically, as a mixture extension, with random mixing, of the traditional choice model, or similarly, as a grade-of-membership extension. A version of the model with extreme value distributions is developed, in which case the model simplifies to a mixture multinomial logit model with random mixing. The approach is shown to offer measures of item discrimination and difficulty, along with information about the relative plausibility of each of the alternatives. The model, parameters, and measures derived from the parameters are compared to those obtained with several commonly used item response theory models. An application of the model to an educational data set is presented.

Validation and demonstration of a new comprehensive model of Alzheimer's disease progression.

INTRODUCTION: Identifying the course of Alzheimer's disease (AD) for individual patients is important for numerous clinical applications. Ideally, prognostic models should provide information about a range of clinical features across the entire disease process. Previously, we published a new comprehensive longitudinal model of AD progression with inputs/outputs covering 11 interconnected clinical measurement domains. METHODS: Here, we (1) validate the model on an independent cohort; and (2) demonstrate the model's utility in clinical applications by projecting changes in 6 of the 11 domains. RESULTS: Survival and prevalence curves for two representative outcomes-mortality and dependency-generated by the model accurately reproduced the observed curves both overall and for patients subdivided according to risk levels using an independent Cox model. DISCUSSION: The new model, validated here, effectively reproduces the observed course of AD from an initial visit assessment, allowing users to project coordinated developments for individual patients of multiple disease features.

Performance of the Grade of Membership Model Under a Variety of Sample Sizes, Group Size Ratios, and Differential Group Response Probabilities for Dichotomous Indicators.

Social scientists are frequently interested in identifying latent subgroups within the population, based on a set of observed variables. One of the more common tools for this purpose is latent class analysis (LCA), which models a scenario involving k finite and mutually exclusive classes within the population. An alternative approach to this problem is presented by the grade of membership (GoM) model, in which individuals are assumed to have partial membership in multiple population subgroups. In this respect, it differs from the hard groupings associated with LCA. The current Monte Carlo simulation study extended on prior work on the GoM by investigating its ability to recover underlying subgroups in the population for a variety of sample sizes, latent group size ratios, and differing group response profiles. In addition, this study compared the performance of GoM with that of LCA. Results demonstrated that when the underlying process conforms to the GoM model form, the GoM approach yielded more accurate classification results than did LCA. In addition, it was found that the GoM modeling paradigm yielded accurate results for samples as small as 200, even when latent subgroups were very unequal in size. Implications for practice were discussed.

Dispersal syndromes drive the formation of biogeographical regions, illustrated by the case of Wallace's Line.

AIM: Biogeographical regions (realms) reflect patterns of co-distributed species (biotas) across space. Their boundaries are set by dispersal barriers and difficulties of establishment in new locations. We extend new methods to assess these two contributions by quantifying the degree to which realms intergrade across geographical space and the contributions of individual species to the delineation of those realms. As our example, we focus on Wallace's Line, the most enigmatic partitioning of the world's faunas, where climate is thought to have little effect and the majority of dispersal barriers are short water gaps. LOCATION: Indo-Pacific. TIME PERIOD: Present day. MAJOR TAXA STUDIED: Birds and mammals. METHODS: Terrestrial bird and mammal assemblages were established in 1-degree map cells using range maps. Assemblage structure was modelled using latent Dirichlet allocation, a continuous clustering method that simultaneously establishes the likely partitioning of species into biotas and the contribution of biotas to each map cell. Phylogenetic trees were used to assess the contribution of deep historical processes. Spatial segregation between biotas was evaluated across time and space in comparison with numerous hard realm boundaries drawn by various workers. RESULTS: We demonstrate that the strong turnover between biotas coincides with the north-western extent of the region not connected to the mainland during the Pleistocene, although the Philippines contains mixed contributions. At deeper taxonomic levels, Sulawesi and the Philippines shift to primarily Asian affinities, resulting from transgressions of a few Asian-derived lineages across the line. The partitioning of biotas sometimes produces fragmented regions that reflect habitat. Differences in partitions between birds and mammals reflect differences in dispersal ability. MAIN CONCLUSIONS: Permanent water barriers have selected for a dispersive archipelago fauna, excluded by an incumbent continental fauna on the Sunda shelf. Deep history, such as plate movements, is relatively unimportant in setting boundaries. The analysis implies a temporally dynamic interaction between a species' intrinsic dispersal ability, physiographic barriers, and recent climate change in the genesis of Earth's biotas.

An Item Response Model for True-False Exams Based on Signal Detection Theory.

A true-false exam can be viewed as being a signal detection task-the task is to detect whether or not an item is true (signal) or false (noise). In terms of signal detection theory (SDT), examinees can be viewed as performing the task by comparing the perceived plausibility of an item (a perceptual component) to a threshold that delineates true from false (a decision component). The resulting model is distinct yet is related to item response theory (IRT) models and grade of membership models, with the difference that SDT explicitly recognizes the role of examinees' perceptions in determining their response to an item. SDT also views IRT concepts such as "difficulty" and "guessing" in a different light, in that both are viewed as reflecting the same aspect-item bias. An application to a true-false algebra exam is presented and the various models are compared.

Personalized predictive modeling for patients with Alzheimer's disease using an extension of Sullivan's life table model.

BACKGROUND: Alzheimer's disease (AD) progression varies substantially among patients, hindering calculation of residual total life expectancy (TLE) and its decomposition into disability-free life expectancy (DFLE) and disabled life expectancy (DLE) for individual patients with AD. The objective of the present study was to assess the accuracy of a new synthesis of Sullivan's life table (SLT) and longitudinal Grade of Membership (L-GoM) models that estimates individualized TLEs, DFLEs, and DLEs for patients with AD. If sufficiently accurate, such information could enhance the quality of important decisions in AD treatment and patient care. METHODS: We estimated a new SLT/L-GoM model of the natural history of AD over 10 years in the Predictors 2 Study cohort: N = 229 with 6 fixed and 73 time-varying covariates over 21 examinations covering 11 measurement domains including cognitive, functional, behavioral, psychiatric, and other symptoms/signs. Total remaining life expectancy was censored at 10 years. Disability was defined as need for full-time care (FTC), the outcome most strongly associated with AD progression. All parameters were estimated via weighted maximum likelihood using data-dependent weights designed to ensure that the estimates of the prognostic subtypes were of high quality. Goodness of fit was tested/confirmed for survival and FTC disability for five relatively homogeneous subgroups defined to cover the range of patient outcomes over the 21 examinations. RESULTS: The substantial heterogeneity in initial patient presentation and AD progression was captured using three clinically meaningful prognostic subtypes and one terminal subtype exhibiting highly differentiated symptom severity on 7 of the 11 measurement domains. Comparisons of the observed and estimated survival and FTC disability probabilities demonstrated that the estimates were accurate for all five subgroups, supporting their use in AD life expectancy calculations. Mean 10-year TLE differed widely across subgroups: range 3.6-8.0 years, average 6.1 years. Mean 10-year DFLE differed relatively even more widely across subgroups: range 1.2-6.5 years, average 4.0 years. Mean 10-year DLE was relatively much closer: range 1.5-2.3 years, average 2.1 years. CONCLUSIONS: The SLT/L-GoM model yields accurate maximum likelihood estimates of TLE, DFLE, and DLE for patients with AD; it provides a realistic, comprehensive modeling framework for endpoint and resource use/cost calculations.

A new algorithm for predicting time to disease endpoints in Alzheimer's disease patients.

BACKGROUND: The ability to predict the length of time to death and institutionalization has strong implications for Alzheimer's disease patients and caregivers, health policy, economics, and the design of intervention studies. OBJECTIVE: To develop and validate a prediction algorithm that uses data from a single visit to estimate time to important disease endpoints for individual Alzheimer's disease patients. METHOD: Two separate study cohorts (Predictors 1, N = 252; Predictors 2, N = 254), all initially with mild Alzheimer's disease, were followed for 10 years at three research centers with semiannual assessments that included cognition, functional capacity, and medical, psychiatric, and neurologic information. The prediction algorithm was based on a longitudinal Grade of Membership model developed using the complete series of semiannually-collected Predictors 1 data. The algorithm was validated on the Predictors 2 data using data only from the initial assessment to predict separate survival curves for three outcomes. RESULTS: For each of the three outcome measures, the predicted survival curves fell well within the 95% confidence intervals of the observed survival curves. Patients were also divided into quintiles for each endpoint to assess the calibration of the algorithm for extreme patient profiles. In all cases, the actual and predicted survival curves were statistically equivalent. Predictive accuracy was maintained even when key baseline variables were excluded, demonstrating the high resilience of the algorithm to missing data. CONCLUSION: The new prediction algorithm accurately predicts time to death, institutionalization, and need for full-time care in individual Alzheimer's disease patients; it can be readily adapted to predict other important disease endpoints. The algorithm will serve an unmet clinical, research, and public health need.

Rebuilding Babel: finding common development solutions using cross-contextual comparisons of multidimensional well-being / Reconstruindo Babel: comparando o bem-estar multidimensional de diferentes contextos culturais em busca de soluções comuns para o desenvolvimento / Reconstruyendo Babel: la comparación del bienestar multidimensional de diferentes contextos culturales en búsqueda de soluciones comunes para el desarrollo

In this paper the theoretical tradition of coping strategies and capital portfolios is used as the basis for adaption and combination of existing methodologies to analyze well-being in rural households. Special attention is given to comparisons among different contexts. First we estimate a multidimensional measurement of poverty based on fuzzy logic for two areas of rural frontiers: Nang Rong, Thailand, and Altamira, in the Amazon Basin in Brazil. To enable a cross-contextual comparison we calculated a second estimate using a subset of shared measurements in the two areas. The findings suggest that the pattern of responses on a range of numerous key variables - including education, income and demographic dependency ratio - is robust for the model specification. It is concluded that comparative generalizations, useful in formulating cost-effective public policy interventions across contexts, could be satisfactorily identified in many situations. More generically, this approach provides researchers and policymakers with a framework for understanding the interaction of contexts with the subjective construction of well-being. The understanding of this interaction is useful for distinguishing stable corollaries of poverty from those that are volatile across contexts.

Com base na tradição teórica relativa a estratégias de sobrevivência e portfólios de capitais, propõe-se uma adaptação e combinação de metodologias existentes para análise do bem-estar em domicílios rurais, com especial atenção à comparação entre diferentes contextos. Em primeiro lugar, estimou-se uma medida multidimensional de pobreza, baseada em lógica nebulosa, para duas áreas de fronteira agrícola: Nang Rong, na Tailândia, e Altamira, no Brasil. Para que a comparação entre os contextos fosse possível, uma segunda estimativa foi obtida, utilizando-se um subconjunto das medidas presentes nas duas áreas de estudo. Os resultados sugerem que o padrão de resposta em relação a várias características-chave - por exemplo, educação, renda e razão de dependência demográfica - é robusto à especificação do modelo. Conclui-se que generalizações comparativas, úteis na formulação de políticas públicas que sejam custo-eficientes quanto à intervenção em contextos distintos, poderiam ser identificadas em diversas situações. Mais genericamente, a presente abordagem fornece aos pesquisadores e gestores de políticas um arcabouço que possibilite entender a interação do contexto com a construção subjetiva de bem-estar. A compreensão dessa interação é útil para distinguir corolários estáveis de pobreza daqueles que são voláteis em contextos distintos.

En base a la tradición teórica relativa a estrategias de supervivencia y carteras de capitales, se propone una adaptación y combinación de metodologías existentes para analizar el bienestar en viviendas rurales, con especial atención a la comparación entre diferentes contextos. En primer lugar, se estimó una medida multidimensional de pobreza, basada en lógica nebulosa, para dos áreas de frontera agrícola: Nang Rong, en Tailandia, y Altamira, en Brasil. Para que la comparación entre los contextos fuese posible, se llegó a una segunda estimación, utilizando un subconjunto de las medidas presentes en las dos áreas de estudio. Los resultados sugieren que el patrón de respuesta en relación a varias características clave - por ejemplo, educación, ingresos y razón de dependencia demográfica - es robusto en lo que concierne a la especificación del modelo. Se concluye que generalizaciones comparativas, útiles en la formulación de políticas públicas costo-eficientes en lo que se refiere a la intervención en contextos distintos, podrían identificarse en diversas situaciones. Más genéricamente, el presente abordaje ofrece a investigadores y gestores de políticas una base que posibilite entender la interacción del contexto con la construcción subjetiva de bienestar. La comprensión de esta interacción es útil para distinguir corolarios estables de pobreza de aquellos que son volátiles en contextos distintos.

Estimating Identification Disclosure Risk Using Mixed Membership Models.

Statistical agencies and other organizations that disseminate data are obligated to protect data subjects' confidentiality. For example, ill-intentioned individuals might link data subjects to records in other databases by matching on common characteristics (keys). Successful links are particularly problematic for data subjects with combinations of keys that are unique in the population. Hence, as part of their assessments of disclosure risks, many data stewards estimate the probabilities that sample uniques on sets of discrete keys are also population uniques on those keys. This is typically done using log-linear modeling on the keys. However, log-linear models can yield biased estimates of cell probabilities for sparse contingency tables with many zero counts, which often occurs in databases with many keys. This bias can result in unreliable estimates of probabilities of uniqueness and, hence, misrepresentations of disclosure risks. We propose an alternative to log-linear models for datasets with sparse keys based on a Bayesian version of grade of membership (GoM) models. We present a Bayesian GoM model for multinomial variables and offer an MCMC algorithm for fitting the model. We evaluate the approach by treating data from a recent US Census Bureau public use microdata sample as a population, taking simple random samples from that population, and benchmarking estimated probabilities of uniqueness against population values. Compared to log-linear models, GoM models provide more accurate estimates of the total number of uniques in the samples. Additionally, they offer record-level predictions of uniqueness that dominate those based on log-linear models.

Incorporando a variabilidade no processo de identificação do modelo de máximo global no Grade of Membership (GoM): considerações metodológicas / Incorporating variability in the process of identification of the global maximum model in Grade of Membership (GoM): methodological considerations / Incorporando la variabilidad en el proceso de identificación del modelo de máximo global en el Grade of Membership (GoM): consideraciones metodológicas

A disponibilidade de bases de dados cada vez mais complexas e multidimensionais é um dos principais motivadores para o aumento do número de estudos que utilizam análises multivariadas baseadas em lógica de conjuntos nebulosos. Apesar da disseminação do método Grade of Membership nos trabalhos empíricos brasileiros da área de ciências sociais e saúde, questões relativas à identificabilidade e estabilidade dos parâmetros finais estimados pelo programa GoM 3.4 não foram suficientemente aprofundadas. Dada a relevância de se obterem parâmetros únicos e estáveis, Guedes et al. (2010) propuseram um procedimento empírico para localizar um modelo de máximo global (MG) com parâmetros estáveis. Entretanto, seu localizador de MG não incorpora qualquer medida de variabilidade. Neste artigo, tal limitação é contornada por meio da utilização de uma estatística de ponderação - Máximo Global Ponderado (MGP) - semelhante ao coeficiente de variação. Esse indicador busca não penalizar de forma desproporcional situações nas quais os desvios médios, apesar de diferentes de zero, são muito pequenos. Apresentam-se evidências de que o localizador MGP reduz a distância do modelo identificado à real estrutura latente dos dados em análise, quando comparados ao modelo identificado pelo localizador não ponderado, MG.

The availability of increasingly complex and multidimensional datasets is one of the main causes for the increase in studies employing multivariate analyses based on fuzzy sets. Even though the Grade of Membership method has been widely used in Brazil for empirical studies in health and social sciences, issues regarding identifiability and stability of the final parameters estimated by GoM 3.4 software have not been thoroughly examined. Given the relevance of unique and stable parameters, Guedes et al. (2010) proposed an empirical method to locate a global maximum (GM) with stable parameters. However, the GM locator does not incorporate variability. In the present article, this limitation is circumvented by employing a weighted statistic - weight global maximum (WGM) - similar to the variation coefficient. This indicator does not affect disproportionately situations with very low mean deviations. The WGM locator is shown to decrease the distance of the identified model from the real structure, when compared with the GM locator.

La disponibilidad de bases de datos cada vez más complejas y multidimensionales es uno de los principales factores motivadores para el aumento del número de estudios que utilizan análisis multivariados basados en la lógica de conjuntos nebulosos. A pesar de la diseminación del método Grade of Membership en los trabajos empíricos brasileños dentro del área de ciencias sociales y salud, cuestiones relativas a la identificabilidad y estabilidad de los parámetros finales, estimados por el programa GoM 3.4, no fueron suficientemente profundizadas. Dada la relevancia de que se obtengan parámetros únicos y estables, Guedes et al. (2010) propusieron un procedimiento empírico para localizar un modelo de máximo global (MG) con parámetros estables. No obstante, su localizador de MG no incorpora cualquier medida de variabilidad. En este artículo, tal limitación se sortea mediante la utilización de una estadística de ponderación -Máximo Global Ponderado (MGP)- semejante al coeficiente de variación. Este indicador busca no penalizar de forma desproporcionada situaciones en las que los desvíos medios, a pesar de ser diferentes a cero, son muy pequeños. Se presentan evidencias de que el localizador MGP reduce la distancia del modelo identificado respecto a la estructura real latente de los datos en análisis, cuando se comparan con el modelo identificado por el localizador no ponderado, MG.

Urban hierarchy in the brazilian Amazon / A hierarquia urbana na Amazônia / La jerarquía urbana en la Amazonia

The Grade of Membership (GoM) model is used to outline profiles based on a heterogeneous and multidimensional database, which allows identifying clusters and describing the differences among them. In this study, GoM uses several types of variables so as to improve the understanding of the greatness and power of Amazonian cities. To accomplish this task, a model that takes into account a variety of aspects, which exceed a purely economic or demographic analysis, is proposed. Understanding the hierarchical organization of the cities in the Amazon seems to be a very important exercise in order to understand the dynamics and specific characteristics of regional urban nets. In this way, it is evident that policies which stimulate the establishment of more structured urban nets in the Amazon are needed. A more balanced population distribution throughout the territory could bring a series of benefits, especially when it comes to the offer and access to all different sorts of services.

O modelo Grade of Membership (GoM) é utilizado para delinear perfis, com base em um banco de dados heterogêneo e multidimensional, o que permite identificar grupos (clusters) e descrever as diferenças entre os mesmos. Neste trabalho, o GoM utiliza diversos tipos de variáveis, que objetivam uma maior compreensão da grandeza e da capacidade de influência das cidades amazônicas. Para cumprir tal tarefa, propõe-se um modelo que considera uma diversidade de aspectos que extrapolam as análises de ordem puramente econômica ou demográfica. Entender a organização hierárquica das cidades na Amazônia parece ser um exercício de grande importância para a compreensão do dinamismo e das especificidades das redes urbanas na região. Nesse sentido, parece evidente a necessidade de políticas que incentivem o estabelecimento de redes urbanas mais estruturadas na Amazônia. Uma distribuição mais equilibrada da população ao longo do território amazônico poderia trazer uma série de ganhos, sobretudo no que se refere à oferta e ao acesso a serviços de diversos tipos e níveis de sofisticação.

El modelo Grade of Membership (GoM) se utiliza para trazar perfiles, en base a un banco de datos heterogéneo y multidimensional, lo que permite identificar grupos (clusters) y describir las diferencias entre los mismos. En este trabajo, el GoM utiliza diversos tipos de variables, que tienen como objetivo una mayor comprensión de la grandeza y de la capacidad de influencia de las ciudades amazónicas. Para cumplir tal tarea, se propone un modelo que considera una diversidad de aspectos que extrapolan los análisis de orden puramente económico o demográfico. Entender la organización jerárquica de las ciudades en la Amazonia parece ser un ejercicio de gran importancia para la comprensión del dinamismo y de las especificidades de las redes urbanas en la región. En este sentido, parece evidente la necesidad de políticas que incentiven el establecimiento de redes urbanas más estructuradas en la Amazonia. Una distribución más equilibrada de la población a lo largo del territorio amazónico podría proporcionar una serie de beneficios, sobre todo en lo que se refiere a la oferta y acceso a servicios de diversos tipos y niveles de sofisticación.

Identificabilidade e estabilidade dos parâmetros no método Grade of Membership (GoM): considerações metodológicas e práticas / Identifiability and stability of standards in the Grade of Membership (GoM) method: methodological and practical considerations / Identificabilidad y estabilidad de los parámetros en el método Grade of Membership (GoM): consideraciones metodológicas y prácticas

O método Grade of Membership (GoM) tem sido cada vez mais utilizado por demógrafos brasileiros e tem a vantagem de possuir um parâmetro que mensura a heterogeneidade individual, com base nas correlações não-observáveis entre as categorias de resposta das variáveis de interesse, gerando um medida do grau de pertencimento de cada indivíduo a perfis extremos. Alguns autores, contudo, chamam atenção para questões importantes na calibragem dos modelos finais que utilizam o programa GoM versão 3.4, como o problema de identificabilidade - soluções múltiplas para parâmetros estimados. Neste artigo, é sugerido um procedimento capaz de identificar um modelo final com solução única que descreva os tipos puros mais fidedignos à base de dados, em uma tentativa de otimização. Para ilustrar esse processo, utilizou-se uma base de dados correspondente a um levantamento econômico e sociodemográfico de uma população de pequenos agricultores residentes ao longo da Rodovia Transamazônica, no Estado do Pará. Também identificou-se a existência de instabilidade nos parâmetros estimados pelo programa GoM 3.4, sendo proposto um método de estabilização de seus valores. Com esses procedimentos combinados, os usuários do programa GoM 3.4 poderão descrever sua base de dados de forma mais adequada e responder às críticas sobre questões de identificabilidade e estabilidade dos modelos resultantes. Essas soluções empíricas são relevantes por afetarem cálculos de prevalência e de incidência de eventos de interesse, além de trazerem consequências importantes sobre o ponto e o momento corretos para intervenções de políticas públicas ou de planejamento prospectivo em análises de projeção.

The Grade of Membership (GoM) method has been increasingly employed by Brazilian demographers, and has the advantage of including a parameter that measures individual heterogeneousness on the basis of non-observable correlations among the categories of responses to variables of interest. The parameter shows each individual's degree of membership to extreme profiles. Several authors, however, have called attention to important issues in adjusting the final models that use 3.4 Version of the GoM Program, such as the problem of identifiability - multiple solutions for estimated parameters. In this article a procedure is discussed that is able to identify a final model with a single solution that describes the pure types that are the most reliable for the database, in an attempt at streamlining. To illustrate this process, a database was used with data corresponding to an economic and sociodemographic study of a population of small farmers living along the TransAmazon Highway, in the northern State of Pará, Brazil. The existence of instability in the parameters estimated by the GoM 3.4 Program was also identified and a method of stabilization of its values was proposed. With these combined procedures, users of the GoM 3.4 Program will be able to describe their databases more adequately and respond to criticisms regarding the identifiability and stability of the resulting models. These empirical solutions are significant. Not only do they affect calculations of prevalence and incidence of events of interest, they also bring about important consequences at the correct point and correct moment for interventions of public policies or of prospective planning in projection analyses.

El método Grade of Membership (GoM) ha sido cada vez más utilizado por los demógrafos brasileños y tiene la ventaja de poseer un parámetro que mide la heterogeneidad individual, sobre la base de las correlaciones no observables entre las categorías de respuesta de las variables de interés, generando una medida del grado de pertenencia de cada individuo a perfiles extremos. Algunos autores, sin embargo, destacan cuestiones importantes en la calibración de los modelos finales que utiliza el programa GoM versión 3.4, como el problema de identificabilidad - soluciones múltiples para parámetros estimados. En este artículo, se sugiere un procedimiento capaz de identificar un modelo final con una solución única que describa los tipos puros de mayor fidelidad con respecto a la base de datos, con una intención de optimización. Para ilustrar este proceso, se utilizó una base de dados correspondiente a un relevamiento económico y socio-demográfico de una población de pequeños agricultores residentes a lo largo de la Autopista Transamazônica, en el Estado de Pará. También se identificó la existencia de inestabilidad en los parámetros estimados por el programa GoM 3.4, y se propuso un método de estabilización de sus valores. Con esos procedimientos combinados, los usuarios del programa GoM 3.4 podrán describir su base de dados en forma más adecuada y responder a las críticas sobre cuestiones de identificabilidad y estabilidad de los modelos resultantes. Estas soluciones empíricas son relevantes porque afectan cálculos de superioridad y de incidencia de eventos de interés, además de traer consecuencias importantes sobre el punto y el momento correctos para las intervenciones de políticas públicas o de planificación prospectiva en análisis de proyección.

Grade of membership analysis of multidimensional health status in adult twins / 中华疾病控制杂志

Objective To construct profiles of health status based upon physical,mental and social support items in adult twins of Qingdao.Methods Grade of Membership(GoM) model was applied to a set of 31 indicators to construct ideal profiles.Results Four health profiles were identified: pure type Ⅰ(healthy),pure type Ⅱ(personality disorders),pure type Ⅲ(psychological symptoms) and pure type Ⅳ(physiological symptoms).The most frequently occurring combination in this population was profile Ⅰ,Ⅱ,Ⅳ(14.74%),followed by profile Ⅰ,Ⅱ,Ⅲ,Ⅳ(13.44%),and then type Ⅰ(11.08%).Only 13.56% of subjects fell completely into one single pure type.Conclusions One healthy type and three non-healthy types are determined.Most individuals exhibit some of the characteristics of two or more types,holding partial membership in multiple categories.

Meio ambiente e saúde: metodologia para análise espacial da ocorrência de malária em projetos de assentamento / Environment and Health: a methodological approach for spatial assessment of malaria transmission in colonization projects in the Brazilian Amazon

A transmissão de malária em projetos de assentamento na Amazônia, definida como malária de fronteira, é resultado de um intrincado processo envolvendo fatores biológicos, ecológicos, socioeconômicos e comportamentais, apresentando uma transição temporal de altas a baixas taxas ao longo de aproximadamente oito anos. Como resultado, um dos grandes desafios é a compreensão desse processo, através da identificação das variáveis determinantes da transmissão, considerando-se dimensões temporais e espaciais. Neste artigo é apresentada uma abordagem metodológica que caracteriza perfis de risco de malária em projetos de assentamento, a partir de uma análise multidisciplinar. Composta de três etapas, a abordagem combina análise espacial, geoestatística e modelos de Grade of Membership. Os resultados ressaltam a importância de medidas de controle diferenciadas de acordo com o estágio do projeto de assentamento (implementação recente ou antiga) e o nível de transmissão em cada localidade.

Malaria at colonization sites in the Brazilian Amazon is defined as frontier malaria, a complex phenomenon including biological, ecological, socioeconomic, and behavioral issues. It follows a specific temporal transition cycle lasting approximately eight years, oscillating from extremely high rates of transmission to lower and stable ones. A broader understanding of this phenomenon that would account for its spatial and temporal idiosyncrasies is a major challenge. In this article we present a methodological approach that describes malaria risk profiles based on a multidisciplinary analysis. The approach combines spatial analysis, geostatistical tools, and fuzzy-set models. Results highlight the need for spatially and temporally targeted interventions for mitigating the spread of this disease.

La transmisión de malaria en proyectos de asentamiento en la Amazonia, definida como malaria de frontera, es el resultado de un intrincado proceso, involucrando factores biológicos, ecológicos, socioeconómicos y comportamentales, presentando una transición temporal de altas a bajas tasas a lo largo de aproximadamente ocho a±os. Como resultado, uno de los grandes desafíos es la comprensión de ese proceso, a través de la identificación de las variables determinantes de la transmisión, habiéndose considerado dimensiones temporales y espaciales. En este artículo es presentado un abordaje metodológico que caracteriza perfiles de riesgo de malaria en proyectos de asentamiento, a partir de un anßlisis multidisciplinario. Compuesto de tres etapas, el abordaje combina anßlisis espacial, geoestadística y modelos de Grade of Membership. Los resultados resaltan la importancia de medidas de control diferenciadas, de acuerdo a la etapa del proyecto de asentamiento (implementación reciente o antigua) y al nivel de transmisión en cada localidad.