The effect of area of residence over the life course on subsequent mortality

Summary.  Life course epidemiology concentrates on the contribution that social or physical exposures have across the life course on adult health. It is known that the area of residence can affect health, but little is known about the effect of the area of residence across the life course. We examine the contribution that area of residence in 1960, 1970, 1980 and 1990 made on subsequent mortality for 49736 male inhabitants of Oslo in 1990. We compare the performance of multiple-membership and cross-classified multilevel models on these data with a correlated cross-classified model that was developed for this.     

The transition from university to work: a multilevel approach to the analysis of the time to obtain the first job

The aim of the paper is to characterize the factors that determine the transition from university to work as well as to evaluate the effectiveness of universities and course programmes with respect to the labour market outcomes of their graduates. The study is focused on the analysis of the time to obtain the first job, taking into account the graduates' characteristics and the effects pertaining to course programmes and universities. For this a three-level discrete time survival model is used, where the logit of the hazard—conditionally on the random effects at course programme and university level—is a linear function of the covariates. The analysis is accomplished by using a large data set from a survey on job opportunities for the 1992 Italian graduates.     

The complexity of school and neighbourhood effects and movements of pupils on school differences in models of educational achievement

Summary.  Traditional studies of school differences in educational achievement use multilevel modelling techniques to take into account the nesting of pupils within schools. However, educational data are known to have more complex non-hierarchical structures. The potential importance of such structures is apparent when considering the effect of pupil mobility during secondary schooling on educational achievement. Movements of pupils between schools suggest that we should model pupils as belonging to the series of schools that are attended and not just their final school. Since these school moves are strongly linked to residential moves, it is important to explore additionally whether achievement is also affected by the history of neighbourhoods that are lived in. Using the national pupil database, this paper combines multiple membership and cross-classified multilevel models to explore simultaneously the relationships between secondary school, primary school, neighbourhood and educational achievement. The results show a negative relationship between pupil mobility and achievement, the strength of which depends greatly on the nature and timing of these moves. Accounting for pupil mobility also reveals that schools and neighbourhoods are more important than shown by previous analysis. A strong primary school effect appears to last long after a child has left that phase of schooling. The additional effect of neighbourhoods, in contrast, is small. Crucially, the rank order of school effects across all types of pupil is sensitive to whether we account for the complexity of the multilevel data structure.     

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.     

Generalized linear mixed models for ordered responses in complex multilevel structures: effects beneath the school or college in education

Summary.  The complexities of educational processes and structure and the need for disentangling effects beneath the level of the school or college are discussed. Ordinal response multilevel crossed random-effects models for educational grades are introduced. Weighted random effects for teacher contributions are then added. Estimation methodology is reviewed. Specially written macros for quasi-likelihood with second-order terms are described. The application discusses General Certificate of Education at advanced level grades cross-classified by student and teaching group within a number of institutions. The methods handle teacher effects where several teachers contribute to provision and where each teacher deals with several groups. Some methodological lessons are drawn for sparse data and the use of extra-multinomial variation. Developments of the analysis yield conclusions about the sources of variation in educational progress, and particularly the effect of teachers.     

Fitting logistic multilevel models with crossed random effects via Bayesian Integrated Nested Laplace Approximations: a simulation study

Fitting cross-classified multilevel models with binary response is challenging. In this setting a promising method is Bayesian inference through Integrated Nested Laplace Approximations (INLA), which performs well in several latent variable models. We devise a systematic simulation study to assess the performance of INLA with cross-classified binary data under different scenarios defined by the magnitude of the variances of the random effects, the number of observations, the number of clusters, and the degree of cross-classification. In the simulations INLA is systematically compared with the popular method of Maximum Likelihood via Laplace Approximation. By an application to the classical salamander mating data, we compare INLA with the best performing methods. Given the computational speed and the generally good performance, INLA turns out to be a valuable method for fitting logistic cross-classified models.     

Inter-university variations in undergraduate non-completion rates: A statistical analysis by subject of study

SUMMARY Non-completion of higher education degree courses is a considerable problem, incurring costs on the taxpayer, higher education institutions and the students who fail to complete. Closer examination of the data reveals that non-completion rates in higher education vary substantially across institutions and by subject of degree. The purpose of this paper is to investigate, within each of 13 broad subject categories, the potential determinants of inter-university variations in non-completion rates. Published data are used to compute university non-completion rates over four time periods and to construct corresponding explanatory variables which could potentially be related to non-completion rates. The explanatory variables measure the characteristics (both academic and socioeconomic) of students recruited by universities and the characteristics of the institutions themselves. The significance of the relationship between the possible explanatory variables and non-completion rates within each given subject is assessed using both weighted leastsquares and weighted logit analysis. The conclusions drawn from the results of each technique are identical, and, therefore, for interpretation reasons, only the results of the weighted least-squares analysis are reported. As expected, the academic quality of student entrants is an important determinant of non-completion rates in the majority of subjects, although the magnitude of the effect varies according to subject. Variables reflecting the age and gender mix of university entrants are generally not significantly related to noncompletion rates. The characteristics of institutions which are significantly related to non-completion rates in specific subjects include the staff student ratio and the length of the degree course     

Meta-analysis using multilevel models with an application to the study of class size effects

Meta-analysis is formulated as a special case of a multilevel (hierarchical data) model in which the highest level is that of the study and the lowest level that of an observation on an individual respondent. Studies can be combined within a single model where the responses occur at different levels of the data hierarchy and efficient estimates are obtained. An example is given from studies of class sizes and achievement in schools, where study data are available at the aggregate level in terms of overall mean values for classes of different sizes, and also at the student level.     

On the mean residual life of a generalized k-out-of-n system

A generalized k-out-of-n system consists of N modules in which the i th module is composed of n_i components in parallel. The system failswhen at least f components in the whole system or at least k consecutive modules have failed. In this article, we obtain the mean residual life function of such a generalized k-out-of-n system under different conditions, namely, when the number of components in each module is equal or unequal and when the components of the system are independent or exchangeable.     

In Memoriam: Frank Wilcoxon

A mosaic is a graphical display of cross-classified data in which each count is represented by a rectangle of area proportional to the count. The positions and sides of the rectangles are set to encourage comparisons between counts in the figures. Mosaics are useful for discovering unusually high or small counts and for discovering dependencies between variables. In principle, mosaics may be used for any number of cross-classifying variables, but six seems to be a practical maximum. A mosaic is given for a four-way classification of Nielsen ratings.     

Evaluation of missing data mechanisms in two and three dimensional incomplete tables

The analysis of incomplete contingency tables is a practical and an interesting problem. In this paper, we provide characterizations for the various missing mechanisms of a variable in terms of response and non-response odds for two and three dimensional incomplete tables. Log-linear parametrization and some distinctive properties of the missing data models for the above tables are discussed. All possible cases in which data on one, two or all variables may be missing are considered. We study the missingness of each variable in a model, which is more insightful for analyzing cross-classified data than the missingness of the outcome vector. For sensitivity analysis of the incomplete tables, we propose easily verifiable procedures to evaluate the missing at random (MAR), missing completely at random (MCAR) and not missing at random (NMAR) assumptions of the missing data models. These methods depend only on joint and marginal odds computed from fully and partially observed counts in the tables, respectively. Finally, some real-life datasets are analyzed to illustrate our results, which are confirmed based on simulation studies.     

An L1-type estimator of multivariate location and shape

The main goal of the paper is to specify a suitable multivariate multilevel model for polytomous responses with a non-ignorable missing data mechanism in order to determine the factors which influence the way of acquisition of the skills of the graduates and to evaluate the degree programmes on the basis of the adequacy of the skills they give to their graduates. The application is based on data gathered by a telephone survey conducted, about two years after the degree, on the graduates of year 2000 of the University of Florence. A multilevel multinomial logit model for the response of interest is fitted simultaneously with a multilevel logit model for the selection mechanism by means of maximum likelihood with adaptive Gaussian quadrature. In the application the multilevel structure has a crucial role, while selection bias results negligible. The analysis of the empirical Bayes residuals allows to detect some extreme degree programmes to be further inspected.     

Determining the optimal allocation of testing resource for modular software system using dynamic programming

Abstract

Reliability is a major concern in the process of software development because unreliable software can cause failure in the computer system that can be hazardous. A way to enhance the reliability of software is to detect and remove the faults during the testing phase, which begins with module testing wherein modules are tested independently to remove a substantial number of faults within a limited resource. Therefore, the available resource must be allocated among the modules in such a way that the number of faults is removed as much as possible from each of the modules to achieve higher software reliability. In this article, we discuss the problem of optimal resource allocation of the testing resource for a modular software system, which maximizes the number of faults removed subject to the conditions that the amount of testing-effort is fixed, a certain percentage of faults is to be removed and a desired level of reliability is to be achieved. The problem is formulated as a non linear programming problem (NLPP), which is modeled by the inflection S-shaped software reliability growth models (SRGM) based on a non homogeneous Poisson process (NHPP) which incorporates the exponentiated Weibull (EW) testing-effort functions. A solution procedure is then developed using a dynamic programming technique to solve the NLPP. Furthermore, three special cases of optimum resource allocations are also discussed. Finally, numerical examples using three sets of software failure data are presented to illustrate the procedure developed and to validate the performance of the strategies proposed in this article. Experimental results indicate that the proposed strategies may be helpful to software project managers for making the best decisions in allocating the testing resource. In addition, the results are compared with those of Kapur et al. (2004), Huang and Lyu (2005), and Jha et al. (2010) that are available in the literature to deal the similar problems addressed in this article. It reveals that the proposed dynamic programming method for the testing-resource allocation problem yields a gain in efficiency over other methods.     

Synthesizing categorical datasets to enhance inference

A common data analysis setting consists of a collection of datasets of varying sizes that are all relevant to a particular scientific question, but which include different subsets of the relevant variables, presumably with some overlap. Here, we demonstrate that synthesizing cross-classified categorical datasets drawn from an incompletely cross-classified common population, where many of the sets are incomplete (i.e., one or more of the classification variables is unobserved), but at least one is completely observed is expected to reduce uncertainty about the cell probabilities in the associated multi-way contingency table as well as for derived quantities such as relative risks and odds ratios. The use of the word “expected” here is the key point. When synthesizing complete datasets from a common population, we are assured to reduce uncertainty. However, when we work with a log-linear model to explain the complete table, because this model cannot be fitted to any of the incomplete datasets, improvement is not assured. We provide technical clarification of this point as well as a series of simulation examples, motivated by an adverse birth outcomes investigation, to illustrate what can be expected under such synthesis.     

When is a seamless study desirable? Case studies from different pharmaceutical sponsors

Background: Inferentially seamless studies are one of the best‐known adaptive trial designs. Statistical inference for these studies is a well‐studied problem. Regulatory guidance suggests that statistical issues associated with study conduct are not as well understood. Some of these issues are caused by the need for early pre‐specification of the phase III design and the absence of sponsor access to unblinded data. Before statisticians decide to choose a seamless IIb/III design for their programme, they should consider whether these pitfalls will be an issue for their programme. Methods: We consider four case studies. Each design met with varying degrees of success. We explore the reasons for this variation to identify characteristics of drug development programmes that lend themselves well to inferentially seamless trials and other characteristics that warn of difficulties. Results: Seamless studies require increased upfront investment and planning to enable the phase III design to be specified at the outset of phase II. Pivotal, inferentially seamless studies are unlikely to allow meaningful sponsor access to unblinded data before study completion. This limits a sponsor's ability to reflect new information in the phase III portion. Conclusions: When few clinical data have been gathered about a drug, phase II data will answer many unresolved questions. Committing to phase III plans and study designs before phase II begins introduces extra risk to drug development. However, seamless pivotal studies may be an attractive option when the clinical setting and development programme allow, for example, when revisiting dose selection. Copyright © 2014 John Wiley & Sons, Ltd.     

Graduate and undergraduate modular instruction

Undergraduate modular instruction at the University of Kentucky is at present designed to afford students every opportunity to complete successfully more of the material usually tought in un unter gratuvate 3-credit service course with minimum risk to themselves. Graduate modules enable students to design a statistics program better suited to their individual needs. In all cases, the price is a heavier load on faculty and administration, but the reward is a generally enthusiastic reception by the students     

Bayesian binary quantile regression for the analysis of Bachelor-to-Master transition

The multi-cycle organization of modern university systems stimulates the interest in studying the progression to higher level degree courses during the academic career. In particular, after the achievement of the first level qualification (Bachelor degree), students have to decide whether to continue their university studies, by enrolling in a second level (Master) programme, or to conclude their training experience. In this work we propose a binary quantile regression (BQR) approach to analyse the Bachelor-to-Master transition phenomenon with the adoption of the Bayesian inferential perspective. In addition to the traditional predictors of academic outcomes, such as the personal characteristics and the field of study, different aspects of student's performance are considered. Moreover, the role of a new contextual variable, representing the type of university regulations experienced during the academic path, is investigated. The utility of the Bayesian BQR to characterize the non-continuation decision after the first cycle studies is illustrated with an application to administrative data of Bachelor graduates at the School of Economics of Sapienza University of Rome. The method favourably compares with more conventional model specifications concerning the conditional mean of the binary response.     

Teacher shortages, teacher contracts and their effect on education in Africa

Summary.  To enhance primary enrolment rates, many African countries have launched large teacher recruitment programmes in recent years. Given tight budgetary constraints, teachers are no longer employed in civil service positions, but on the basis of (fixed term) contracts typically implying considerably lower salaries and a sharply reduced amount of professional training. We analyse the effect of this change on educational quality in Niger, Togo and Mali, on the basis of very informative data, which are comparable across these countries. We use a variety of estimation techniques, including a non-parametric estimation of quantile treatment effects. Our results demonstrate that contract teachers tend to reduce inequalities in student outcomes. Overall, the effects are positive in Mali, somewhat mixed in Togo and negative in Niger. This ordering is consistent with theoretical expectations related to the manner in which contract teacher programmes were implemented differently in each of the three countries under study.     

A multilevel exploration of the role of interviewers in survey non-response

This paper illustrates the use of multilevel statistical modelling of cross-classified data to explore interviewers' influence on survey non-response. The results suggest that the variability in whole household refusal and non-contact rates is due more to the influence of interviewers than to the influence of areas. The results from separate logistic regression models are compared with the results from multinomial models using a polytomous dependent variable (refusals, non-contacts and responses). Using the cross-classified multilevel approach allows us to estimate correlations between refusals and non-contacts, suggesting that interviewers who are good at reducing whole household refusals are also good at reducing whole household non-contacts.     

Analysis of repeated categorical responses from fully and partially cross-classified data

Many follow-up studies involve categorical data measured on the same individual at different times. Frequently, some of the individuals are missing one or more of the measurements. This results in a contingency table with both fully and partially cross-classified data. Two models can be used to analyze data of this type: (i) The multiple-sample model, in which all the study subjects with the same configuration of missing observations are considered a separate sample. (ii) The single-sample model, which assumes that the missing observations are the result of a mechanism causing subjects to lose the informtion from one or some of the measurements. In this work we compare the two approaches and show that under certain conditions, the two models yield the same maximum likelihood estimates of the cell probabilities in the underlying contingency table.