Abstract not found

this paper on the likelihood-based (and approximate likelihood) methods most readily available (given current usage patterns of existing software) to statisticians and substantive researchers making frequent use of multilevel models: ML and REML in VC models, and MQL and PQL in RELR models. Other promising likelihood-based approaches-- including (a) methods based on Gaussian quadrature (e.g., Pinheiro and Bates 1995); (b) the nonparametric maximum likelihood methods of Airkin (1999a); (c) the Laplace-approximation approach of Raudenbush et al. (1999); (d) the work on hierarchical generalised linear models of Lee and Nelder (2000); and (e) interval estimation based on ranges of values of the param- eters for which the log likelihood is within a certain distance of its maximum, for instance using profile likelihood (e.g., Longford 2000)--are not addressed here. It is evident from the recent applied literature that, from the point of view of multilevel analyses currently being conducted to inform educational and health policy choices and other substantive decisions, the use of methods (a-e) is not (yet) as widespread as REML and quasi-likelihood approaches. Statisticians are well aware that the highly skewed repeated-sampling distributions of ML estimators of random-effects variances in multilevel models with small sample sizes are not likely to lead to good coverage properties for large-sample Gaussian approximate interval estimates of the form r 2-F 1.96 (2), but with few exceptions the profession has not (yet) responded to this by making software for improved likelihood interval estimates widely available to multilevel modellers. In Sections 3 and 4 we document the extent of the poor coverage behaviour of the Gaussian approach, and we offer several simple approximation ...

This paper develops a procedure for measuring how much is gained, and at what precision, by students in a pre-test and post-test situation against a target score on the post-test. We define our productivity index, M j , for teacher j as the ratio of estimated gains to an estimated standard that is the distance between an estimate of the pre-test score and the target score. Using language, mathematics, and reading scores on the SAT 9 for 1999 and 2000 from 75 public elementary classrooms (grades 3, 4, 5, and 6 in 2000), we employ a Bayesian implementation of a multivariate mixed model for repeated test scores from individual students who in turn are nested within teachers. Our analysis point to statistically significant gains on the whole for grades 3, 4, and 6. The strength of the approach lies in a straightforward estimation of the productivity index. Using the simulated sampling distribution of the posterior mean of the productivity index, we introduce a fuller depiction of progress in the productivity curve, or productivity profile, by calculating the probability that the index exceeds set proportions of the estimated standard. The basic model employed in this study thus contributes three essential components for sound accountability decisions. First, it estimates correlated measurement errors when using multiple measures. In doing so, we take full advantage of the informational redundancy in the measures. Second, it estimates initial status and value-added gains simultaneously. Lastly, it proposes a productivity index along with new procedures for representing the uncertainty in individual productivity estimates in the form of a productivity profile. This approach also facilitates a Bayesian e#ect-size analysis free from frequentist appeals to non-central t- or F- d...

In multilevel modelling it is common practice to assume constant variance at level 1 across individuals. In this paper we consider situations where the level{1 variance depends on predictor variables. We examine two cases using a dataset from educational research; in the rst case the variance at level 1 of a test score depends on a continuous \intake score" predictor, and in the second case the variance is assumed to dier according to gender. We contrast two maximum-likelihood methods based on iterative generalised least squares with two MCMC methods based on adaptive hybrid versions of the Metropolis-Hastings (MH) algorithm, and we use two simulation experiments to compare these four methods. We nd that all four approaches have good repeated-sampling behaviour in the classes of models we simulate. We conclude by contrasting raw- and log-scale formulations of the level{1 variance function, and we nd that adaptive MH sampling is considerably more ecient than adaptive rejection sampl...

Existing meta-learning based distributed data mining approaches do not explicitly address context heterogeneity across individual sites. This limitation constrains their applications where distributed data are not identically and independently distributed. Modeling heterogeneously distributed data with hierarchical models, this paper extends the traditional meta-learning techniques so that they can be successfully used in distributed scenarios with context heterogeneity.

Abstract not found

Invalid voting and electoral absenteeism are two important sources of abstention in compulsory voting systems. Previous studies in this area have not considered the correlation between both variables and ignored the compositional nature of the data, potentially leading to unfeasible results and discarding helpful information from an inferential standpoint. In order to overcome these problems, this paper develops a statistical model that accounts for the compositional and hierarchical structure of the data and addresses robustness concerns raised by the use of small samples that are typical in the literature. The model is applied to analyze invalid voting and electoral absenteeism in Brazilian legislative elections between 1945 and 2006 via MCMC simulations. The results show considerable differences in the determinants of both forms of non-voting: while invalid voting was strongly positively related both to political protest and to the existence of important informational barriers to voting, the influence of these variables on absenteeism is less evident. Comparisons based on posterior simulations indicate that the model developed in this paper fits the dataset better than several alternative modeling approaches and leads to different substantive conclusions regarding the effect of different predictors on the both sources of abstention.