Bivariate multilevel models for the analysis of mathematics and reading pupils' achievements

The purpose of this paper is to identify a relationship between pupils' mathematics and reading test scores and the characteristics of students themselves, stratifying for classes, schools and geographical areas. The data set of interest contains detailed information about more than 500,000 students at the first year of junior secondary school in the year 2012/2013, provided by the Italian Institute for the Evaluation of Educational System. The innovation of this work is in the use of multivariate multilevel models, in which the outcome is bivariate: reading and mathematics achievement. Using the bivariate outcome enables researchers to analyze the correlations between achievement levels in the two fields and to predict statistically significant school and class effects after adjusting for pupil's characteristics. The statistical model employed here explicates account for the potential covariance between the two topics, and at the same time it allows the school effect to vary among them. The results show that while for most cases the direction of school's effect is coherent for reading and mathematics (i.e. positive/negative), there are cases where internal school factors lead to different performances in the two fields.     

Hierarchical related regression for combining aggregate and individual data in studies of socio-economic disease risk factors

Summary.  To obtain information about the contribution of individual and area level factors to population health, it is desirable to use both data collected on areas, such as censuses, and on individuals, e.g. survey and cohort data. Recently developed models allow us to carry out simultaneous regressions on related data at the individual and aggregate levels. These can reduce 'ecological bias' that is caused by confounding, model misspecification or lack of information and increase power compared with analysing the data sets singly. We use these methods in an application investigating individual and area level sociodemographic predictors of the risk of hospital admissions for heart and circulatory disease in London. We discuss the practical issues that are encountered in this kind of data synthesis and demonstrate that this modelling framework is sufficiently flexible to incorporate a wide range of sources of data and to answer substantive questions. Our analysis shows that the variations that are observed are mainly attributable to individual level factors rather than the contextual effect of deprivation.     

A multilevel Bayesian model for contextual effect of material deprivation

The relationship between socioeconomic factors and health has been studied in many circumstances. Whether the association takes place at individual level only, or also at population level (contextual effect) is still unclear. We present a multilevel hierarchical Bayesian model to investigate the joint contribution of individual and population-based socioeconomic factors to mortality, using data from the census cohort of the general population of the city of Florence, Italy (Tuscany Longitudinal Study, 1991-1995). Evidence supporting a contextual effect of deprivation on mortality at the very fine level of aggregation is found. Inappropriate modelling of individual and aggregate variables could strongly bias effect estimates.Received: 10 January 2002, Revised: 23 June 2003, The research on Tuscany Longitudinal Study (Studio Longitudinale Toscano, SLTo) was supported by the Regione Toscana Servizio Statistica.     

The case for small area microdata

Summary.  Census data are available in aggregate form for local areas and, through the samples of anonymized records (SARs), as samples of microdata for households and individuals. In 1991 there were two SAR files: a household file and an individual file. These have a high degree of detail on the census variables but little geographical detail, a situation that will be exacerbated for the 2001 SAR owing to the loss of district level geography on the individual SAR. The paper puts forward the case for an additional sample of microdata, also drawn from the census, that has much greater geographical detail. Small area microdata (SAM) are individual level records with local area identifiers and, to maintain confidentiality, reduced detail on the census variables. Population data from seven local authorities, including rural and urban areas, are used to define prototype samples of SAM. The rationale for SAM is given, with examples that demonstrate the role of local area information in the analysis of census data. Since there is a trade-off between the extent of local detail and the extent of detail on variables that can be made available, the confidentiality risk of SAM is assessed empirically. An indicative specification of the SAM is given, having taken into account the results of the confidentiality analysis.     

Multilevel analysis in social research: An application of a cross-classified model

The multilevel approach can be a fruitful methodological framework in which to formulate the micro-macro relationships existing between individuals and their contexts. Usually, place of residence is taken as proxy for context. But individuals can be classified at the same level in more than one way. For example, not only may place of residence be relevant, but birthplace, household or working relations may also be taken into account. Contextual effects can be better identified if multiple classifications are simultaneously considered. in this sense, data do not have a purely hierarchical structure but a cross-classified one, and become very important to establish whether the resulting structure affects the covariance structure of data. In this paper, some critical issues arising from application of multilevel modelling are discussed, and multilevel cross-classified models are proposed as more flexible tools to study contextual effects. A multilevel cross-classified model is specified to evaluate simultaneously the effects of women's place of birth and women's current place of residence on the choice of bearing a second child by Italian women in the mid-1990s.     

Abundance estimation with a categorical covariate subject to missing in continuous-time capture-recapture studies

Abstract

In continuous-time capture-recapture experiments, individual heterogeneity has a large effect on the capture probability. To account for the heterogeneity, we consider an individual covariate, which is categorical and subject to missing. In this article, we develop a general model to summarize three kinds of missing mechanisms, and propose a maximum likelihood estimator of the abundance. A likelihood ratio confidence interval of the abundance is also proposed. We illustrate the proposed methods by simulation studies and a real data example of a bird species prinia subflava in Hong Kong.     

Testing for unit roots in panel data using a GMM approach

For aggregated time series unit root tests are routinely applied to choose among trend and difference stationary models. Recent work demonstrates that such test can also be applied for testing panel data. However, it is well known that disaggregated data often exhibit a considerable amount of heterogeneity so that standard tests may perform poorly. To account for the heterogeneity in the data we allow for individual specific deterministics, that is, we let the time trends vary across the cross section units. It is shown that standard GMM estimators suggested for the dynamic panel data model may fail to give a valid test procedure. To overcome this difficulty, a modified GMM estimator is suggested. In a Monte Carlo study the finite sample properties of the alternative tests are compared.     

Deprivation, ill-health and the ecological fallacy

The use of ecological studies in explaining the relationship between deprivation and ill-health is widespread in many health applications. However, inferences drawn from these studies about individuals are susceptible to serious bias known as the ecological fallacy. Our paper demonstrates the ecological fallacy effect in this context but also shows how it can be considerably reduced by taking into account different population structures at the aggregate level. Two regression analyses of limiting long-term illness are performed, one at the individual level and one at the electoral ward level, using the 1991 UK census sample of anonymized records and the small area statistics. The analyses compare several measures of deprivation including the standard Carstairs index, with the separate variables which make up the indices, to determine their effectiveness in explaining rates of illness. Two of the deprivation scores are constructed using latent variable modelling techniques which enable a score to be generated at the individual level as well as at the ward level. It is shown that, given the right choice of socioeconomic variables and taking into account the age structure of the population, it should be possible to construct a single aggregate deprivation index that will explain most of the variation in rates of illness across the study region.     

Joint models for mixed categorical outcomes: a study of HIV risk perception and disease status in Mozambique

Two types of bivariate models for categorical response variables are introduced to deal with special categories such as ‘unsure’ or ‘unknown’ in combination with other ordinal categories, while taking additional hierarchical data structures into account. The latter is achieved by the use of different covariance structures for a trivariate random effect. The models are applied to data from the INSIDA survey, where interest goes to the effect of covariates on the association between HIV risk perception (quadrinomial with an ‘unknown risk’ category) and HIV infection status (binary). The final model combines continuation-ratio with cumulative link logits for the risk perception, together with partly correlated and partly shared trivariate random effects for the household level. The results indicate that only age has a significant effect on the association between HIV risk perception and infection status. The proposed models may be useful in various fields of application such as social and biomedical sciences, epidemiology and public health.     

MULTIPLE-RECORD SYSTEMS ESTIMATION USING LATENT CLASS MODELS

Capture–recapture methods (also referred to as 'multiple-record systems') have been widely used in enumerating human populations in the fields of epidemiology and public health. In this article, we introduce latent class models into multiple-record systems to account for unobserved heterogeneity in the population. Two approaches, the full and the conditional likelihood, are proposed to estimate the unknown population abundance. We also suggest rules to diagnose identifiability of the proposed latent class models. The methodologies are illustrated by two real examples: the first is to count the undercount of homelessness in the Adelaide central business district, and the second concerns the incidence of diabetes in a small Italian town.     

Heterogeneity,school-effects and the North/South achievement gap in Italian secondary education: evidence from a three-level mixed model

With the aim of assessing the extent of the differences in the context of Italian educational system, the paper applies multilevel modeling to a new administrative dataset, containing detailed information for more than 500,000 students at grade 6 in the year 2011/2012, provided by the Italian Institute for the Evaluation of Educational System. Data are grouped by classes, schools and geographical areas. Different models for each area are fitted, in order to properly address the heteroscedasticity of the phenomenon. The results show that it is possible to estimate statistically significant “school effects”, i.e., the positive/negative association of attending a specific school and the student’s test score, after a case-mix adjustment. Therefore, the paper’s most important message is that school effects are different in terms of magnitude and types in the three geographical macro areas (Northern, Central and Southern Italy) and are dependent on specific students’ and schools’ characteristics.     

Semiparametric Proportional Odds Models for Spatially Correlated Survival Data

The last decade has witnessed major developments in Geographical Information Systems (GIS) technology resulting in the need for statisticians to develop models that account for spatial clustering and variation. In public health settings, epidemiologists and health-care professionals are interested in discerning spatial patterns in survival data that might exist among the counties. This paper develops a Bayesian hierarchical model for capturing spatial heterogeneity within the framework of proportional odds. This is deemed more appropriate when a substantial percentage of subjects enjoy prolonged survival. We discuss the implementation issues of our models, perform comparisons among competing models and illustrate with data from the SEER (Surveillance Epidemiology and End Results) database of the National Cancer Institute, paying particular attention to the underlying spatial story.     

Bayesian hierarchical duration model for repeated events: an application to behavioral observations

This article presents a continuous-time Bayesian model for analyzing durations of behavior displays in social interactions. Duration data of social interactions are often complex because of repeated behaviors (events) at individual or group (e.g. dyad) level, multiple behaviors (multistates), and several choices of exit from a current event (competing risks). A multilevel, multistate model is proposed to adequately characterize the behavioral processes. The model incorporates dyad-specific and transition-specific random effects to account for heterogeneity among dyads and interdependence among competing risks. The proposed method is applied to child–parent observational data derived from the School Transitions Project to assess the relation of emotional expression in child–parent interaction to risk for early and persisting child conduct problems.     

A new spatial shift-share decomposition for the regional growth analysis: a local study of the employment based on Italian Business Statistical Register

This paper presents a new shift-share model to decompose the employment growth rate of a territorial unit by taking into consideration the association between industry mix and firm legal status effects measured in its neighborhood. We explicitly consider this kind of association to go beyond the problem of asymmetry found in a previous work. The empirical application refers to the data collected in the Italian Business Statistical Register and, in particular, regional employment figures in Friuli Venezia Giulia (NUTS2 level), for 219 territorial units (LAU2 level) and 12 Local Labour Systems (LLS), for the years 2001 and 2004.     

中国交通运输能源效率及其影响因素分析——基于三阶段DEA和GWR方法

交通运输部门能源消耗占总能耗的比重虽然不高,但是对环境造成的影响较大。交通车辆数、人口密度、交通运营线路长度、旅客和货运量等都直接影响交通能源效率。采用三阶段数据包络模型分析各地区交通运输部门的能源效率,同时考虑到相邻地区交通运输状况的相互影响,构建空间地理加权回归模型对各个地区能源消耗的影响因素进行分析。研究结果表明:各个地区交通能源效率差异与地理区位有关,但是关系不大,主要与该地区的交通运输综合密切相关;提高交通领域能源效率的主要对策是合理进行交通运输状况的分布,调配交通运输车辆和根据不同的人口密度选择交通工具。     

Shared frailty models based on reversed hazard rate for modified inverse Weibull distribution as baseline distribution

The unknown or unobservable risk factors in the survival analysis cause heterogeneity between individuals. Frailty models are used in the survival analysis to account for the unobserved heterogeneity in individual risks to disease and death. To analyze the bivariate data on related survival times, the shared frailty models were suggested. The most common shared frailty model is a model in which frailty act multiplicatively on the hazard function. In this paper, we introduce the shared gamma frailty model and the inverse Gaussian frailty model with the reversed hazard rate. We introduce the Bayesian estimation procedure using Markov chain Monte Carlo (MCMC) technique to estimate the parameters involved in the model. We present a simulation study to compare the true values of the parameters with the estimated values. We also apply the proposed models to the Australian twin data set and a better model is suggested.     

Spatial and non-spatial model-based protection procedures for the release of business microdata

In this paper we discuss methodology for the safe release of business microdata. In particular we extend the model-based protection procedure of Franconi and Stander (2002, The Statistician 51: 1–11) by allowing the model to take account of the spatial structure underlying the geographical information in the microdata. We discuss the use of the Gibbs sampler for performing the computations required by this spatial approach. We provide an empirical comparison of these non-spatial and spatial disclosure limitation methods based on the Italian sample from the Community Innovation Survey. We quantify the level of protection achieved for the released microdata and the error induced when various inferences are performed. We find that although the spatial method often induces higher inferential errors, it almost always provides more protection. Moreover the aggregated areas from the spatial procedure can be somewhat more spatially smooth, and hence possibly more meaningful, than those from the non-spatial approach. We discuss possible applications of these model-based protection procedures to more spatially extensive data sets.     

Principal components of sample estimates: an approach through symbolic data analysis

This paper deals with the analysis of datasets, where the subjects are described by the estimated means of a p-dimensional variable. Classical statistical methods of data analysis do not treat measurements affected by intrinsic variability, as in the case of estimates, so that the heterogeneity induced among subjects by this condition is not taken into account. In this paper a way to solve the problem is suggested in the context of symbolic data analysis, whose specific aim is to handle data tables where single valued measurements are substituted by complex data structures like frequency distributions, intervals, and sets of values. A principal component analysis is carried out according to this proposal, with a significant improvement in the treatment of information.     

城市医生资源与新冠肺炎防控效率

本文利用非参数估计法考察了我国城市层面的新冠肺炎病情防控效率,讨论了医生资源对防控效率的影响。结果表明,城市疫情防控措施显著降低了每日新增病例,但存在明显地区异质性,城市医生资源差异是解释防控效率异质性的重要因素。医生资源对防控效率的影响具有非线性特征,在资源紧缺城市边际促进作用更大。包括病床和医院数量在内的医疗物质投入没有产生边际影响,表明医疗物质资源还未达到约束状态。进一步分析医生职业结构发现,临床医生的作用最为显著。地区应急响应启动越早,医生资源的作用越大,因此政府相关政策是医生资源作用的有力保障。新冠肺炎疫情一定程度上暴露了我国医生资源短板,需要多措并举有效提升城市医生资源供给。     

基于EM算法的改进MLM模型及参数估计

传统的分层模型假设组与组之间独立,没有考虑组之间的相关性。而以地理单元分组的数据往往具有空间依赖性,个体不仅受本地区的影响,也可能受相邻地区的影响。此时,传统分层模型层-2残差分布的假设不再成立。为了处理空间分层数据,将空间统计和空间计量经济模型的思想引入到分层模型中,既纳入分层的思想,又顾及空间相关性,提出了空间分层线性模型,并给出了其固定效应、方差协方差成分和空间回归参数的最大似然估计,在运用EM算法时,结合运用了Fisher得分算法。