Giulia Roli

Estimation of Causal Effects in Latent Strata with an Encouragement for Response

We consider a new approach to deal with non ignorable non response on an outcome variable, in a causal inference framework. Assuming that a binary instrumental variable for non response is available, we provide a likelihood-based approach to identify and estimate heterogeneous causal effects of a binary treatment on specific latent subgroups of units, named principal strata, defined by the non response behavior under each level of the treatment and of the instrument. We show that, within each stratum, non response is ignorable and respondents can be properly compared by treatment status. In order to assess our method and its robustness when the usually invoked assumptions are relaxed or misspecified, we simulate data to resemble a real experiment conducted on a panel survey which compares different methods of reducing panel attrition.

Evaluating the Effects of Subsidies to Firms with Nonignorably Missing Outcomes

In the paper, the effects of subsidies to Tuscan handicraft firms are evaluated; the study is affected by missing outcome values, which cannot be assumed missing at random. We tackle this problem within a causal inference framework. By exploiting Principal Stratification and the availability of an instrument for the missing mechanism, we conduct a likelihood-based analysis, proposing a set of plausible identification assumptions. Causal effects are estimated on (latent) subgroups of firms, characterized by their response behavior.

A new approach to spatial entropy measures

Entropy is widely employed in many applied sciences to measure the heterogeneity of observations. Recently, many attempts have been made to build entropy measures for spatial data, in order to capture the influence of space over the variable outcomes. The main limit of these developments is that all indices are computed conditional on a single distance and do not cover the whole spatial configuration of the phenomenon under study. Moreover, most of them do not satisfy the desirable additivity property between local and global spatial measures. This work reviews some recent developments, based on univariate distributions, and compares them to a new approach which considers the properties of entropy measures linked to bivariate distributions. This perspective introduces substantial innovations. Firstly, Shannon’s entropy may be decomposed into two terms: spatial mutual information, accounting for the role of space in determining the variable outcome, and spatial global residual entropy, summarizing the remaining heterogeneity carried by the variable itself. Secondly, these terms both satisfy the additivity property, being sums of partial entropies measuring what happens at different distance classes. The proposed indices are used for measuring the spatial entropy of a marked point pattern on rainforest tree species. The new entropy measures are shown to be more informative and to answer a wider set of questions than the current proposals of the literature.

A Model-based Approach to Measure School Achievements in Latent Groups of Students: A Simulation Study

In this article, we present a model-based framework to estimate the educational attainments of students in latent groups defined by unobservable or only partially observed features that are likely to affect the outcome distribution, as well as being interesting to be investigated. We focus our attention on the case of students in the first year of the upper secondary schools, for which the teachers’ suggestion at the end of their lower educational level toward the subsequent type of school is available. We use this information to develop latent strata according to the compliance behavior of students simplifying to the case of binary data for both counseled and attended school (i.e., academic or technical institute). We consider a likelihood-based approach to estimate outcome distributions in the latent groups and propose a set of plausible assumptions with respect to the problem at hand. In order to assess our method and its robustness, we simulate data resembling a real study conducted on pupils of the province of Bologna in year 2007/2008 to investigate their success or failure at the end of the first school year.

Hierarchical Bayesian Models for the Estimation of Correlated Effects in Multilevel Data: A Simulation Study to Assess Model Performance

In this article, we aim at assessing hierarchical Bayesian modeling for the analysis of multiple exposures and highly correlated effects in a multilevel setting. We exploit an artificial data set to apply our method and show the gains in the final estimates of the crucial parameters. As a motivating example to simulate data, we consider a real prospective cohort study designed to investigate the association of dietary exposures with the occurrence of colon-rectum cancer in a multilevel framework, where, e.g., individuals have been enrolled from different countries or cities. We rely on the presence of some additional information suitable to mediate the final effects of the exposures and to be arranged in a level-2 regression to model similarities among the parameters of interest (e.g., data on the nutrient compositions for each dietary item).

A Review of Multilevel Modeling: Some Methodological Issues and Advances

Multilevel modeling is a recently new class of statistical methods to handle nested data. Mainly thanks to the wide range of applicability and the great increase of statistical softwares, in the last decades multilevel modeling has enjoyed an explosion of published papers and books in both methodological and application field. Currently, there is a need to not only develop the research on multilevel approach for the analysis of complex data, but also to have instructions to properly address the usage. This work aims at summarizing methodological aspects related to multilevel models, illustrating good-practices, advantages, and limits by reviewing applications in various fields, such as socio-economic, educational, health, and medical sciences. We further focus our attention on the latest advances of multilevel modeling towards, e.g., the inclusion of latent variables and the Bayesian approach.

A Propensity Score Matching Method to Study the Achievement of Students in Upper Secondary Schools

In the paper, we investigate the effects of family characteristics on the achievement of students in the first year of the upper secondary schools of the province of Bologna. In particular, we focus our attention on the number of siblings as potential causal factor influencing the outcome. We employ a matching strategy based on propensity score to create treatment groups, corresponding to the values of the factor under study, with the same distribution of observed covariates. As a result, students are stratified in blocks according to the propensity score to obtain estimates of the average treatment effect using nearest neighbour matching. In order to further compare the achievements of students of upper secondary schools in the city of Bologna with those in the other towns of the province, we show that valid inference is assured by controlling for family characteristics whose influence on the outcome has been previously assessed.

The Longevity Pattern in Emilia Romagna, Italy: A Spatio-temporal Analysis

In this chapter, we investigate the pattern of longevity in an Italian region at a municipality level in two different periods. Spatio-temporal modeling is used to tackle at both periods the random variations in the occurrence of long-lived individuals, due to the rareness of such events in small areas. This method allows to exploit the spatial proximity smoothing the observed data, as well as to control for the effects of a set of regressors. As a result, clusters of areas characterized by extreme indexes of longevity are well identified and the temporal evolution of the phenomenon can be depicted. A joint analysis of male and female longevity by cohort in the two periods is conducted specifying a set of hierarchical Bayesian models.