A partial dependence factorial analysis to deal with selection bias in observational studis

This thesis presents a creative and practical approach to dealing with the problem of selection bias. Selection bias may be the most important vexing problem in program evaluation or in any line of research that attempts to assert causality. Some of the greatest minds in economics and statistics have scrutinized the problem of selection bias, with the resulting approaches – Rubin’s Potential Outcome Approach(Rosenbaum and Rubin,1983; Rubin, 1991,2001,2004) or Heckman’s Selection model (Heckman, 1979) – being widely accepted and used as the best fixes. These solutions to the bias that arises in particular from self selection are imperfect, and many researchers, when feasible, reserve their strongest causal inference for data from experimental rather than observational studies. The innovative aspect of this thesis is to propose a data transformation that allows measuring and testing in an automatic and multivariate way the presence of selection bias. The approach involves the construction of a multi-dimensional conditional space of the X matrix in which the bias associated with the treatment assignment has been eliminated. Specifically, we propose the use of a partial dependence analysis of the X-space as a tool for investigating the dependence relationship between a set of observable pre-treatment categorical covariates X and a treatment indicator variable T, in order to obtain a measure of bias according to their dependence structure. The measure of selection bias is then expressed in terms of inertia due to the dependence between X and T that has been eliminated. Given the measure of selection bias, we propose a multivariate test of imbalance in order to check if the detected bias is significant, by using the asymptotical distribution of inertia due to T (Estadella et al. 2005) , and by preserving the multivariate nature of data. Further, we propose the use of a clustering procedure as a tool to find groups of comparable units on which estimate local causal effects, and the use of the multivariate test of imbalance as a stopping rule in choosing the best cluster solution set. The method is non parametric, it does not call for modeling the data, based on some underlying theory or assumption about the selection process, but instead it calls for using the existing variability within the data and letting the data to speak. The idea of proposing this multivariate approach to measure selection bias and test balance comes from the consideration that in applied research all aspects of multivariate balance, not represented in the univariate variable- by-variable summaries, are ignored. The first part contains an introduction to evaluation methods as part of public and private decision process and a review of the literature of evaluation methods. The attention is focused on Rubin Potential Outcome Approach, matching methods, and briefly on Heckman’s Selection Model. The second part focuses on some resulting limitations of conventional methods, with particular attention to the problem of how testing in the correct way balancing. The third part contains the original contribution proposed , a simulation study that allows to check the performance of the method for a given dependence setting and an application to a real data set. Finally, we discuss, conclude and explain our future perspectives.

Inference on copula-based correlation structures

We propose an extension of the approach provided by Kluppelberg and Kuhn (2009) for inference on second-order structure moments. As in Kluppelberg and Kuhn (2009) we adopt a copula-based approach instead of assuming normal distribution for the variables, thus relaxing the equality in distribution assumption. A new copula-based estimator for structure moments is investigated. The methodology provided by Kluppelberg and Kuhn (2009) is also extended considering the copulas associated with the family of Eyraud-Farlie-Gumbel-Morgenstern distribution functions (Kotz, Balakrishnan, and Johnson, 2000, Equation 44.73). Finally, a comprehensive simulation study and an application to real financial data are performed in order to compare the different approaches.

Epidemiology and population genetics of Podosphaera fusca and Golovinomyces orontii, causal agents of cucurbit powdery mildew

In 2010, 2011 and 2012 growing seasons, the occurrence of the ascomycetes Podosphaera fusca and Golovinomyces orontii, causal agents of powdery mildew disease, was monitored on cultivated cucurbits located in Bologna and Mantua provinces to determine the epidemiology of the species. To identify the pathogens, both morphological and molecular identifications were performed on infected leaf samples and a Multiplex-PCR was performed to identify the mating type genes of P. fusca isolates. The investigations indicated a temporal succession of the two species with the earlier infections caused by G. orontii, that seems to be the predominant species till the middle of July when it progressively disappears and P. fusca becomes the main species infecting cucurbits till the end of October. The temporal variation is likely due to the different overwintering strategies of the two species instead of climatic conditions. Only chasmothecia of P. fusca were recorded and mating type alleles ratio tended to be 1:1. Considering that only chasmothecia of P. fusca were found, molecular-genetic analysis were carried out to find some evidence of recombination within this species by MLST and AFLP methods. Surprisingly, no variations were observed within isolates for the 8 MLST markers used. According to this result, AFLP analysis showed a high similarity within isolates, with SM similarity coefficient ranging between 0.91-1.00 and also, sequencing of 12 polymorphic bands revealed identity to some gene involved in mutation and selection. The results suggest that populations of P. fusca are likely to be a clonal population with some differences among isolates probably due to agricultural practices such as fungicides treatments and cultivated hosts. Therefore, asexual reproduction, producing a lot of fungal biomass that can be easily transported by wind, is the most common and useful way to the spread and colonization of the pathogen.

Obsessed With Work: A multi-causal and multi-rater approach to workaholism

Workaholism is defined as the combination of two underlying dimensions: working excessively and working compulsively. The present thesis aims at achieving the following purposes: 1) to test whether the interaction between environmental and personal antecedents may enhance workaholism; 2) to develop a questionnaire aimed to assess overwork climate in the workplace; 3) to contrast focal employees’ and coworkers’ perceptions of employees’ workaholism and engagement. Concerning the first purpose, the interaction between overwork climate and person characteristics (achievement motivation, perfectionism, conscientiousness, self-efficacy) was explored on a sample of 333 Dutch employees. The results of moderated regression analyses showed that the interaction between overwork climate and person characteristics is related to workaholism. The second purpose was pursued with two interrelated studies. In Study 1 the Overwork Climate Scale (OWCS) was developed and tested using a principal component analysis (N = 395) and a confirmatory factor analysis (N = 396). Two overwork climate dimensions were distinguished, overwork endorsement and lacking overwork rewards. In Study 2 the total sample (N = 791) was used to explore the association of overwork climate with two types of working hard: work engagement and workaholism. Lacking overwork rewards was negatively associated with engagement, whereas overwork endorsement showed a positive association with workaholism. Concerning the third purpose, using a sample of 73 dyads composed by focal employees and their coworkers, a multitrait-multimethod matrix and a correlated trait-correlated method model, i.e. the CT-C(M–1) model, were examined. Our results showed a considerable agreement between raters on focal employees' engagement and workaholism. In contrast, we observed a significant difference concerning the cognitive dimension of workaholism, working compulsively. Moreover, we provided further evidence for the discriminant validity between engagement and workaholism. Overall, workaholism appears as a negative work-related state that could be better explained by assuming a multi-causal and multi-rater approach.

New perspectives in statistical mechanics and high-dimensional inference

The main purpose of this thesis is to go beyond two usual assumptions that accompany theoretical analysis in spin-glasses and inference: the i.i.d. (independently and identically distributed) hypothesis on the noise elements and the finite rank regime. The first one appears since the early birth of spin-glasses. The second one instead concerns the inference viewpoint. Disordered systems and Bayesian inference have a well-established relation, evidenced by their continuous cross-fertilization. The thesis makes use of techniques coming both from the rigorous mathematical machinery of spin-glasses, such as the interpolation scheme, and from Statistical Physics, such as the replica method. The first chapter contains an introduction to the Sherrington-Kirkpatrick and spiked Wigner models. The first is a mean field spin-glass where the couplings are i.i.d. Gaussian random variables. The second instead amounts to establish the information theoretical limits in the reconstruction of a fixed low rank matrix, the “spike”, blurred by additive Gaussian noise. In chapters 2 and 3 the i.i.d. hypothesis on the noise is broken by assuming a noise with inhomogeneous variance profile. In spin-glasses this leads to multi-species models. The inferential counterpart is called spatial coupling. All the previous models are usually studied in the Bayes-optimal setting, where everything is known about the generating process of the data. In chapter 4 instead we study the spiked Wigner model where the prior on the signal to reconstruct is ignored. In chapter 5 we analyze the statistical limits of a spiked Wigner model where the noise is no longer Gaussian, but drawn from a random matrix ensemble, which makes its elements dependent. The thesis ends with chapter 6, where the challenging problem of high-rank probabilistic matrix factorization is tackled. Here we introduce a new procedure called "decimation" and we show that it is theoretically to perform matrix factorization through it.

Hierarchical active inference for cognitive architectures

This thesis explores the methods based on the free energy principle and active inference for modelling cognition. Active inference is an emerging framework for designing intelligent agents where psychological processes are cast in terms of Bayesian inference. Here, I appeal to it to test the design of a set of cognitive architectures, via simulation. These architectures are defined in terms of generative models where an agent executes a task under the assumption that all cognitive processes aspire to the same objective: the minimization of variational free energy. Chapter 1 introduces the free energy principle and its assumptions about self-organizing systems. Chapter 2 describes how from the mechanics of self-organization can emerge a minimal form of cognition able to achieve autopoiesis. In chapter 3 I present the method of how I formalize generative models for action and perception. The architectures proposed allow providing a more biologically plausible account of more complex cognitive processing that entails deep temporal features. I then present three simulation studies that aim to show different aspects of cognition, their associated behavior and the underlying neural dynamics. In chapter 4, the first study proposes an architecture that represents the visuomotor system for the encoding of actions during action observation, understanding and imitation. In chapter 5, the generative model is extended and is lesioned to simulate brain damage and neuropsychological patterns observed in apraxic patients. In chapter 6, the third study proposes an architecture for cognitive control and the modulation of attention for action selection. At last, I argue how active inference can provide a formal account of information processing in the brain and how the adaptive capabilities of the simulated agents are a mere consequence of the architecture of the generative models. Cognitive processing, then, becomes an emergent property of the minimization of variational free energy.