Statistical Analysis with Missing Data

This Handbook aims to provide a guide for constructing and using composite indicators for policy makers, academics, the media and other interested parties. While there are several types of composite indicators, this Handbook is concerned with those which compare and rank country performance in areas such as industrial competitiveness, sustainable development, globalisation and innovation. The Handbook aims to contribute to a better understanding of the complexity of composite indicators and to an improvement of the techniques currently used to build them. In particular, it contains a set of technical guidelines that can help constructors of composite indicators to improve the quality of their outputs. It has been prepared jointly by the OECD (the Statistics Directorate and the Directorate for Science, Technology and Industry) and the Applied Statistics and Econometrics Unit of the Joint Research Centre of the European Commission in Ispra, Italy. Primary authors from the JRC are Michela Nardo, Michaela Saisana, Andrea Saltelli and Stefano Tarantola. Primary authors from the OECD are Anders Hoffmann and Enrico Giovannini. Editorial assistance was provided by Candice Stevens, Gunseli Baygan and Karsten Olsen. The research is partly funded by the European Commission, Research Directorate, under the project KEI (Knowledge Economy Indicators), Contract FP6 No. 502529. In the OECD context, the work has benefitted from a grant from the Danish government. The views expressed are those of the authors and should not be regarded as stating an official position of either the European Commission or the OECD.

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Handbook on Constructing Composite Indicators: Methodology and User Guide

There are two kinds of tutorial articles: those that provide a primer on an established topic and those that let us in on the ground floor of something of emerging importance. The first type of tutorial can have a noted expert who has been gracious (and brave) enough to write a field guide about a particular topic. The other sort of tutorial typically involves researchers who have each been laboring on a topic for some years. Both sorts of tutorial articles are very much desired. But we, as an editorial board for both Systems and Transactions, know that there has been no logical place for them in the AESS until this series was started several years ago. With these tutorials, we hope to continue to give them a home, a welcome, and provide a service to our membership. We do not intend to publish tutorials on a regular basis, but we hope to deliver them once or twice per year. We need and welcome good, useful tutorial articles (both kinds) in relevant AESS areas. If you, the reader, can offer a topic of interest and an author to write about it, please contact us. Self-nominations are welcome, and even more ideal is a suggestion of an article that the editor(s) can solicit. All articles will be reviewed in detail. Criteria on which they will be judged include their clarity of presentation, relevance, and likely audience, and, of course, their correctness and scientific merit. As to the mathematical level, the articles in this issue are a good guide: in each case the author has striven to explain complicated topics in simple-well, tutorial-terms. There should be no (or very little) novel material: the home for archival science is the Transactions Magazine, and submissions that need to be properly peer reviewed would be rerouted there. Likewise, articles that are interesting and descriptive, but lack significant tutorial content, ought more properly be submitted to the Systems Magazine.

What is a tutorial

This Handbook is a guide for constructing and using composite indicators for policy makers, academics, the media and other interested parties. While there are several types of composite indicators, this Handbook is concerned with those which compare and rank country performance in areas such as industrial competitiveness, sustainable development, globalization and innovation.  The Handbook aims to contribute to a better understanding of the complexity of composite indicators and to an improvement of the techniques currently used to build them.  In particular, it contains a set of technical guidelines that can help constructors of composite indicators to improve the quality of their outputs.It has been prepared jointly by the OECD (the Statistics Directorate and the Directorate for Science, Technology and Industry) and the Applied Statistics and Econometrics Unit of the Joint Research Centre (JRC) of the European Commission in Ispra, Italy.

In recent times, composite indicators have gained astounding popularity in a wide variety of research areas. Their adoption by global institutions has further captured the attention of the media and policymakers around the globe, and their number of applications has surged ever since. This increase in their popularity has solicited a plethora of methodological contributions in response to the substantial criticism surrounding their underlying framework. In this paper, we put composite indicators under the spotlight, examining the wide variety of methodological approaches in existence. In this way, we offer a more recent outlook on the advances made in this field over the past years. Despite the large sequence of steps required in the construction of composite indicators, we focus particularly on two of them, namely weighting and aggregation. We find that these are where the paramount criticism appears and where a promising future lies. Finally, we review the last step of the robustness analysis that follows their construction, to which less attention has been paid despite its importance. Overall, this study aims to provide both academics and practitioners in the field of composite indices with a synopsis of the choices available alongside their recent advances.

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On the Methodological Framework of Composite Indices: A Review of the Issues of Weighting, Aggregation, and Robustness

Background Alcohol consumption causes an estimated 4% of the global disease burden, prompting goverments to impose regulations to mitigate the adverse effects of alcohol. To assist public health leaders and policymakers, the authors developed a composite indicator—the Alcohol Policy Index—to gauge the strength of a country's alcohol control policies. Methods and Findings The Index generates a score based on policies from five regulatory domains—physical availability of alcohol, drinking context, alcohol prices, alcohol advertising, and operation of motor vehicles. The Index was applied to the 30 countries that compose the Organization for Economic Cooperation and Development and regression analysis was used to examine the relationship between policy score and per capita alcohol consumption. Countries attained a median score of 42.4 of a possible 100 points, ranging from 14.5 (Luxembourg) to 67.3 (Norway). The analysis revealed a strong negative correlation between score and consumption (r ¼� 0.57; p ¼0.001): a 10-point increase in the score was associated with a one-liter decrease in absolute alcohol consumption per person per year (95% confidence interval, 0.4-1.5 l). A sensitivity analysis demonstrated the robustness of the Index by showing that countries' scores and ranks remained relatively stable in response to variations in methodological assumptions.

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Comparative analysis of alcohol control policies in 30 countries.

Overview on Latent Markov Modeling Introduction Literature review on latent Markov models Alternative approaches Example datasets Background on Latent Variable and Markov Chain Models Introduction Latent variable models Expectation-Maximization algorithm Standard errors Latent class model Selection of the number of latent classes Applications Markov chain model for longitudinal data Applications Basic Latent Markov Model Introduction Univariate formulation Multivariate formulation Model identifiability Maximum likelihood estimation Selection of the number of latent states Applications Constrained Latent Markov Models Introduction Constraints on the measurement model Constraints on the latent model Maximum likelihood estimation Model selection and hypothesis testing Applications Including Individual Covariates and Relaxing Basic Model Assumptions Introduction Notation Covariates in the measurement model Covariates in the latent model Interpretation of the resulting models Maximum likelihood estimation Observed information matrix, identifiability, and standard errors Relaxing local independence Higher order extensions Applications Including Random Effects and Extension to Multilevel Data Introduction Random-effects formulation Maximum likelihood estimation Multilevel formulation Application to the student math achievement dataset Advanced Topics about Latent Markov Modeling Introduction Dealing with continuous response variables Dealing with missing responses Additional computational issues Decoding and forecasting Selection of the number of latent states Bayesian Latent Markov Models Introduction Prior distributions Bayesian inference via reversible jump Alternative sampling Application to the labor market dataset Appendix: Software List of Main Symbols Bibliography Index

Latent Markov Models for Longitudinal Data

The paper investigates the problem of determining patterns of criminal behaviour from official criminal histories, concentrating on the variety and type of offending convictions. The analysis is carried out on the basis of a multivariate latent Markov model which allows for discrete covariates affecting the initial and the transition probabilities of the latent process. We also show some simplifications which reduce the number of parameters substantially; we include a Rasch-like parameterization of the conditional distribution of the response variables given the latent process and a constraint of partial homogeneity of the latent Markov chain. For the maximum likelihood estimation of the model we outline an EM algorithm based on recursions known in the hidden Markov literature, which make the estimation feasible also when the number of time occasions is large. Through this model, we analyse the conviction histories of a cohort of offenders who were born in England and Wales in 1953. The final model identifies five latent classes and specifies common transition probabilities for males and females between 5-year age periods, but with different initial probabilities.

A latent Markov model for detecting patterns of criminal activity

Latent Markov (LM) models represent an important class of models for the analysis of longitudinal data, especially when response variables are categorical. These models have a great potential of application in many fields, such as economics and medicine. We illustrate the R package LMest that is tailored to deal with the basic LM model and some extended formulations accounting for individual covariates and for the presence of unobserved clusters of units having the same initial and transition probabilities (mixed LM model). The main functions of the package are tailored to parameter estimation through the expectation-maximization algorithm, which is based on suitable forwardbackward recursions. The package also permits local and global decoding and to obtain standard errors for the parameter estimates. We illustrate the use of the package and its main features through some empirical examples in the fields of labour market, health, and criminology.

Lmest: An R package for latent Markov models for longitudinal categorical data

We provide a comprehensive overview of latent Markov (LM) models for the analysis of longitudinal categorical data. We illustrate the general version of the LM model which includes individual covariates, and several constrained versions. Constraints make the model more parsimonious and allow us to consider and test hypotheses of interest. These constraints may be put on the conditional distribution of the response variables given the latent process (measurement model) or on the distribution of the latent process (latent model). We also illustrate in detail maximum likelihood estimation through the Expectation–Maximization algorithm, which may be efficiently implemented by recursions taken from the hidden Markov literature. We outline methods for obtaining standard errors for the parameter estimates. We also illustrate methods for selecting the number of states and for path prediction. Finally, we mention issues related to Bayesian inference of LM models. Possibilities for further developments are given among the concluding remarks.

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Fulvia Pennoni

Papers

Comparative analysis of alcohol control policies in 30 countries.

Latent Markov Models for Longitudinal Data

A latent Markov model for detecting patterns of criminal activity

Lmest: An R package for latent Markov models for longitudinal categorical data

Latent Markov models: a review of a general framework for the analysis of longitudinal data with covariates