Fence methods for mixed model selection

Many model search strategies involve trading off model fit with model complexity in a penalized goodness of fit measure. Asymptotic properties for these types of procedures in settings like linear regression and ARMA time series have been studied, but these do not naturally extend to nonstandard situations such as mixed effects models, where simple definition of the sample size is not meaningful. This paper introduces a new class of strategies, known as fence methods, for mixed model selection, which includes linear and generalized linear mixed models. The idea involves a procedure to isolate a subgroup of what are known as correct models (of which the optimal model is a member). This is accomplished by constructing a statistical fence, or barrier, to carefully eliminate incorrect models. Once the fence is constructed, the optimal model is selected from among those within the fence according to a criterion which can be made flexible. In addition, we propose two variations of the fence. The first is a stepwise procedure to handle situations of many predictors; the second is an adaptive approach for choosing a tuning constant. We give sufficient conditions for consistency of fence and its variations, a desirable property for a good model selection procedure. The methods are illustrated through simulation studies and real data analysis.Comment: Published in at http://dx.doi.org/10.1214/07-AOS517 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Advocating mixed-methods approaches in health research

This methods paper provides researchers in Nepal with a broad overview of the practical and philosophical aspects of mixed-methods research. The three authors have a wide-ranging expertise in planning and conducting mixed-methods studies. The paper outlines the different paradigms or philosophies underlying quantitative and qualitative methods and some of the on-going debates about mixed-methods. The paper further highlights a number of practical issues, such as (a) the particular mix and order of quantitative and qualitative methods; (b) the way of integrating methods from different philosophical stance; and (c) how to synthesise mixed-methods findings

Mirror-Descent Methods in Mixed-Integer Convex Optimization

In this paper, we address the problem of minimizing a convex function f over a convex set, with the extra constraint that some variables must be integer. This problem, even when f is a piecewise linear function, is NP-hard. We study an algorithmic approach to this problem, postponing its hardness to the realization of an oracle. If this oracle can be realized in polynomial time, then the problem can be solved in polynomial time as well. For problems with two integer variables, we show that the oracle can be implemented efficiently, that is, in O(ln(B)) approximate minimizations of f over the continuous variables, where B is a known bound on the absolute value of the integer variables.Our algorithm can be adapted to find the second best point of a purely integer convex optimization problem in two dimensions, and more generally its k-th best point. This observation allows us to formulate a finite-time algorithm for mixed-integer convex optimization

Investigating information systems with mixed-methods research

Mixed-methods research, which comprises both quantitative and qualitative components, is widely perceived as a means to resolve the inherent limitations of traditional single method designs and is thus expected to yield richer and more holistic findings. Despite such distinctive benefits and continuous advocacy from Information Systems (IS) researchers, the use of mixed-methods approach in the IS field has not been high. This paper discusses some of the key reasons that led to this low application rate of mixed-methods design in the IS field, ranging from misunderstanding the term with multiple-methods research to practical difficulties for design and implementation. Two previous IS studies are used as examples to illustrate the discussion. The paper concludes by recommending that in order to apply mixed-methods design successfully, IS researchers need to plan and consider thoroughly how the quantitative and qualitative components (i.e. from data collection to data analysis to reporting of findings) can be genuinely integrated together and supplement one another, in relation to the predefined research questions and the specific research contexts

Chow-Lin Methods in Spatial Mixed Models

Missing data in dynamic panel models occur quite often since detailed recording of the dependent variable is often not possible at all observation points in time and space. In this paper we develop classical and Bayesian methods to complete missing data in panel models. The Chow-Lin (1971) method is a classical method for completing dependent disaggregated data and is successfully applied in economics to disaggregate aggregated time series. We will extend the space-time panel model in a new way to include cross-sectional and spatially correlated data. The missing disaggregated data will be obtained either by point prediction or by a numerical (posterior) predictive density. Furthermore, we point out that the approach can be extended to more complex models, like ow data or systems of panel data. The panel Chow-Lin approach will be demonstrated with examples involving regional growth for Spanish regions.Space-time interpolation, Spatial panel econometrics, MCMC, Spatial Chow-Lin, missing regional data, Spanish provinces, MCMC, NUTS: nomenclature of territorial units for statistics

Outcomes of Orphanhood in Ethiopia: A Mixed Methods Study

The paper addresses the question of whether parental death always has a strongly negative effect on children’s outcomes using quantitative and qualitative data from Young Lives, a longitudinal study of childhood poverty in Ethiopia. It investigates the validity of potential mediating factors identified by other studies in Sub-Saharan Africa using data from the whole sample (n = 973) and explores these processes in-depth through the experiences of three orphans in one community in Addis Ababa. The paper concludes that the outcomes of orphans and non-orphans in poor communities are not significantly different, supporting the need to address vulnerability at a societal level. Nonetheless, specific groups, for example, older female children who have lost their mothers, may face particular risks that should be addressed with targeted interventions