arXiv subjects

Marco Doretti

Publications and source records attributed to Marco Doretti.

7 recordsLinked to original sources

arXiv2026

Modeling within-department homogeneity in research quality rankings: an application to the Italian ISPD

In this paper, we consider the academic department ranking system of Italy, which is based on a performance index named Indice Standardizzato di Performance Dipartimentale (ISPD). While critiques to the ISPD have been moved for its marked tendency to polarization, we here formalize a yet unexplored determinant of this phenomenon, that is, the presence of within-department homogeneity among the standardized scores used to build the index. We account for this intra-departmental correlation by modeling it as a function of departments' size. The proposed model, estimated via Maximum Likelihood, allows to build a fairer ranking procedure via the definition of a properly adjusted version of the ISPD. The estimation framework is also adapted to fit publicly available data, which are coarsened by rounding and/or left-truncated. To this end, a novel probability distribution termed Betoidal is introduced. Empirical evidence in favor of the proposed model is found in the 2017 and 2022 data. Moreover, a simulation study shows that the adjusted index significantly overcomes not only the original ISPD, but also other more data-demanding competing proposals.

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arXiv2025

Handling outcome-dependent missingness with binary responses: A Heckman-like model

In regression models with missing outcomes, selection bias can arise when the missingness mechanism depends on the outcome itself. This proposal focuses on an extension of the Heckman model to a setting where the outcome is binary and both the selection process and the outcome are modeled through logistic regression. A correction term analogous to the inverse Mills' ratio is derived based on relative risks. Under given assumptions, such a strategy provides an effective tool for bias correction in the presence of informative missingness.

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arXiv2024

Interval identification of natural effects in the presence of outcome-related unmeasured confounding

With reference to a binary outcome and a binary mediator, we derive identification bounds for natural effects under a reduced set of assumptions. Specifically, no assumptions about confounding are made that involve the outcome; we only assume no unobserved exposure-mediator confounding as well as a condition termed partially constant cross-world dependence (PC-CWD), which poses fewer constraints on the counterfactual probabilities than the usual cross-world independence assumption. The proposed strategy can be used also to achieve interval identification of the total effect, which is no longer point identified under the considered set of assumptions. Our derivations are based on postulating a logistic regression model for the mediator as well as for the outcome. However, in both cases the functional form governing the dependence on the explanatory variables is allowed to be arbitrary, thereby resulting in a semi-parametric approach. To account for sampling variability, we provide delta-method approximations of standard errors in order to build uncertainty intervals from identification bounds. The proposed method is applied to a dataset gathered from a Spanish prospective cohort study. The aim is to evaluate whether the effect of smoking on lung cancer risk is mediated by the onset of pulmonary emphysema.

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arXiv2022

Mediation analysis with case-control sampling: Identification and estimation in the presence of a binary mediator

With reference to a stratified case-control procedure based on a binary variable of primary interest, we derive the expression of the distortion induced by the sampling design on the parameters of the logistic model of a secondary variable. This is particularly relevant when performing mediation analysis (possibly in a causal framework) with stratified case-control data in settings where both the outcome and the mediator are binary. Our identification result opens the way to M-estimation and Maximum Likelihood estimation. We then conduct a simulation study showing the gain in efficiency of the estimators of both the outcome and mediator model parameters w.r. to existing methods, based on weighting. As an illustrative example, we reanalyze a German case-control dataset in order to investigate whether the effect of reduced immunocompetency on listeriosis onset is mediated by the intake of gastric acid suppressors.

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arXiv2021

Path Analysis for Binary Random Variables

The decomposition of the overall effect of a treatment into direct and indirect effects is here investigated with reference to a recursive system of binary random variables. We show how, for the single mediator context, the marginal effect measured on the log odds scale can be written as the sum of the indirect and direct effects plus a residual term that vanishes under some specific conditions. We then extend our definitions to situations involving multiple mediators and address research questions concerning the decomposition of the total effect when some mediators on the pathway from the treatment to the outcome are marginalized over. Connections to the counterfactual definitions of the effects are also made. Data coming from an encouragement design on students' attitude to visit museums in Florence, Italy, are reanalyzed. The estimates of the defined quantities are reported together with their standard errors to compute p-values and form confidence intervals.

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arXiv2018

Exact parametric causal mediation analysis for a binary outcome with a binary mediator

A parametric expression for causal natural direct and indirect effects is derived for the setting of a binary outcome with a binary mediator. The proposed effect decomposition does not require the outcome to be rare and generalizes the existing ones, allowing for interactions between both the exposure and the mediator and confounding covariates. Further, it outlines the relationship between the causal effects and the correspondent pathway-specific logistic regression parameters, in parallel with results derived under the rare outcome assumption. Formulae for standard errors, obtained via the delta method, are also given. A simulation study is implemented which compares these estimators to a number of competing ones. An empirical application to data coming from a microfinance experiment performed in Bosnia and Herzegovina is illustrated as an example.

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arXiv2018

On marginal and conditional parameters in logistic regression models

A fundamental research question is how much a variation in a covariate influences a binary response variable in a logistic regression model, both directly or through mediators. We derive the exact formula linking the parameters of marginal and conditional regression models with binary mediators when no conditional independence assumptions can be made. The formula has the appealing property of being the sum of terms that vanish whenever parameters of the conditional models vanish, thereby recovering well-known results as particular cases. It also permits to quantify the distortion induced by omission of some relevant covariates, opening the way to sensitivity analysis. Also in this case, as the parameters of the conditional models are multiplied by terms that are always positive or bounded, the formula may be used to construct reasonable bounds on the parameters of interest. We assume that, conditionally on a set of covariates, the data-generating process can be represented by a Directed Acyclic Graph. We also show how the results here presented lead to the extension of path analysis to a system of binary random variables.

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