Giuseppe Porro

Multivariate Matching Methods That Are Monotonic Imbalance Bounding

We introduce a new “Monotonic Imbalance Bounding” (MIB) class of matching methods for causal inference with a surprisingly large number of attractive statistical properties. MIB generalizes and extends in several new directions the only existing class, “Equal Percent Bias Reducing” (EPBR), which is designed to satisfy weaker properties and only in expectation. We also offer strategies to obtain specific members of the MIB class, and analyze in more detail a member of this class, called Coarsened Exact Matching, whose properties we analyze from this new perspective. We offer a variety of analytical results and numerical simulations that demonstrate how members of the MIB class can dramatically improve inferences relative to EPBR-based matching methods.

Every tweet counts? How sentiment analysis of social media can improve our knowledge of citizens’ political preferences with an application to Italy and France

The growing usage of social media by a wider audience of citizens sharply increases the possibility of investigating the web as a device to explore and track political preferences. In the present paper we apply a method recently proposed by other social scientists to three different scenarios, by analyzing on one side the online popularity of Italian political leaders throughout 2011, and on the other the voting intention of French Internet users in both the 2012 presidential ballot and the subsequent legislative election. While Internet users are not necessarily representative of the whole population of a country’s citizens, our analysis shows a remarkable ability for social media to forecast electoral results, as well as a noteworthy correlation between social media and the results of traditional mass surveys. We also illustrate that the predictive ability of social media analysis strengthens as the number of citizens expressing their opinion online increases, provided that the citizens act consistently on these opinions.

Missing data imputation, matching and other applications of random recursive partitioning

Applications of the random recursive partitioning (RRP) method are described. This method generates a proximity matrix which can be used in non-parametric matching problems such as hot-deck missing data imputation and average treatment effect estimation. RRP is a Monte Carlo procedure that randomly generates non-empty recursive partitions of the data and calculates the proximity between observations as the empirical frequency in the same cell of these random partitions over all the replications. Also, the method in the presence of missing data is invariant under monotonic transformations of the data but no other formal properties of the method are known yet. Therefore, Monte Carlo experiments were conducted in order to explore the performance of the method. A companion software is available as a package for the R statistical environment.

Teachers’ evaluations and students’ achievement: a ‘deviation from the reference’ analysis

Several studies show that teachers make use of grading practices to affect students’ effort and achievement. Generally linearity is assumed in the grading equation, while it is everyone’s experience that grading practices are frequently non‐linear. Representing grading practices as linear can be misleading both from a descriptive and a prescriptive viewpoint. Here we propose to identify grading practices as ‘deviations from a reference’, which is a fully non‐parametric criterion, and measure their effects on achievement based on this classification. To show the effectiveness of our approach, we apply the methodology to a data‐set on Italian lower secondary school.

Missing Data Imputation, Classification, Prediction and Average Treatment Effect Estimation Via Random Recursive Partitioning

In this paper we describe some applications of the Random Recursive Partitioning (RRP) method. This method generates a proximity matrix which can be used in non parametric hot-deck missing data imputation, classification, prediction, average treatment effect estimation and, more generally, in matching problems. RRP is a Monte Carlo procedure that randomly generates non-empty recursive partitions of the data and evaluates the proximity between observations as the empirical frequency they fall in the same cell of these random partitions over all the replications. RRP works also in the presence of missing data and is invariant under monotonic transformations of the data. No other formal properties of the method are known yet, therefore Monte Carlo experiments are provided in order to explore the performance of the method. A companion software is available in the form of a package for the R statistical environment.

Average Treatment Effect Estimation Via Random Recursive Partitioning

A new matching method is proposed for the estimation of the average treatment effect of social policy interventions (e. g. , training programs or health care measures. Given an outcome variable, a treatment and a set of pre-treatment covariates, the method is based on the examination of random recursive partitions of the space of covariates using regression trees. A regression tree is grown either on the treated or on the untreated individuals {\it only} using as response variable a random permutation of the indexes 1,. . . ,n (n being the number of units involved), while the indexes for the other group are predicted using this tree. The procedure is replicated in order to rule out the effect of specific permutations. The average treatment effect is estimated in each tree by matching treated and untreated in the same terminal nodes. The final estimator of the average treatment effect is obtained by averaging on all the trees grown. The method does not require any specific model assumption apart from the trees complexity, which does not affect the estimator though. We show that this method is either an instrument to check whether two samples can be matched (by any method) and, when this is feasible, to obtain reliable estimates of the average treatment effect. We further propose a graphical tool to inspect the quality of the match. The method has been applied to the National Supported Work Demonstration data, previously analyzed by Lalonde (1986) and others.