Using M-quantile models as an alternative to random effects to model the contextual value-added of schools in London

The measurement of school performance for secondary schools in England has developed from simple measures of marginal performance at age 16 to more complex contextual value-added measures that account for pupil prior attainment and background. These models have been developed within the multilevel modelling environment (pupils within schools) but in this paper we propose an alternative using a more robust approach based on M-quantile modelling of individual pupil efficiency. These efficiency measures condition on a pupils ability and background, as do the current contextual value-added models, but as they are measured at the pupil level a variety of performance measures can be readily produced at the school and higher (local authority) levels. Standard errors for the performance measures are provided via a bootstrap approach, which is validated using a model-based simulation.School Performance, Contextual Value-Added, M-Quantile Models, Pupil Efficiency, London

Modelling the distribution of health related quality of life of advancedmelanoma patients in a longitudinal multi-centre clinical trial using M-quantile random effects regression

Health-related quality of life assessment is important in the clinical evaluation of patients with metastatic disease that may offer useful information in understanding the clinical effectiveness of a treatment. To assess if a set of explicative variables impacts on the health-related quality of life, regression models are routinely adopted. However, the interest of researchers may be focussed on modelling other parts (e.g. quantiles) of this conditional distribution. In this paper, we present an approach based on quantile and M-quantile regression to achieve this goal. We applied the methodologies to a prospective, randomized, multi-centre clinical trial. In order to take into account the hierarchical nature of the data we extended the M-quantile regression model to a three-level random effects specification and estimated it by maximum likelihood

Estimating regional income indicators under transformations and access to limited population auxiliary information

Spatially disaggregated income indicators are typically estimated by using model-based methods that assume access to auxiliary information from population micro-data. In many countries like Germany and the UK population micro-data are not publicly available. In this work we propose small area methodology when only aggregate population-level auxiliary information is available. We use data-driven transformations of the response to satisfy the parametric assumptions of the used models. In the absence of population micro-data, appropriate bias-corrections for small area prediction are needed. Under the approach we propose in this paper, aggregate statistics (means and covariances) and kernel density estimation are used to resolve the issue of not having access to population micro-data. We further explore the estimation of the mean squared error using the parametric bootstrap. Extensive model-based and design-based simulations are used to compare the proposed method to alternative methods. Finally, the proposed methodology is applied to the 2011 Socio-Economic Panel and aggregate census information from the same year to estimate the average income for 96 regional planning regions in Germany

Using M-quantile models as an alternative to random effects to model the contextual value-added of schools in London

The measurement of school performance for secondary schools in England has developed from simple measures of marginal performance at age 16 to more complex contextual value-added measures that account for pupil prior attainment and background. These models have been developed within the multilevel modelling environment (pupils within schools) but in this paper we propose an alternative using a more robust approach based on M-quantile modelling of individual pupil efficiency. These efficiency measures condition on a pupils ability and background, as do the current contextual value-added models, but as they are measured at the pupil level a variety of performance measures can be readily produced at the school and higher (local authority) levels. Standard errors for the performance measures are provided via a bootstrap approach, which is validated using a model-based simulation

Estimation of Linear and Non-Linear Indicators using Interval Censored Income Data

Among a variety of small area estimation methods, one popular approach for the estimation of linear and non-linear indicators is the empirical best predictor. However, parameter estimation using standard maximum likelihood methods is not possible, when the dependent variable of the underlying nested error regression model, is censored to specific intervals. This is often the case for income variables. Therefore, this work proposes an estimation method, which enables the estimation of the regression parameters of the nested error regression model using interval censored data. The introduced method is based on the stochastic expectation maximization algorithm. Since the stochastic expectation maximization method relies on the Gaussian assumptions of the error terms, transformations are incorporated into the algorithm to handle departures from normality. The estimation of the mean squared error of the empirical best predictors is facilitated by a parametric bootstrap which captures the additional uncertainty coming from the interval censored dependent variable. The validity of the proposed method is validated by extensive model-based simulations

Outlier robust small area estimation

Recently proposed outlier robust small area estimators can be substantially biased when outliers are drawn from a distribution that has a different mean from that of the rest of the survey data. This naturally leads one to consider an outlier robust bias correction for these estimators. We develop this idea, proposing two different analytical mean-squared error estimators for the ensuing bias-corrected outlier robust estimators. Simulations based on realistic outlier-contaminated data show that the bias correction proposed often leads to more efficient estimators. Furthermore, the mean-squared error estimation methods proposed appear to perform well with a variety of outlier robust small area estimators