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.

Displacement Analysis of Under-Constrained Cable-Driven Parallel Robots

This dissertation studies the geometric static problem of under-constrained cable-driven parallel robots (CDPRs) supported by n cables, with n ≤ 6. The task consists of determining the overall robot configuration when a set of n variables is assigned. When variables relating to the platform posture are assigned, an inverse geometric static problem (IGP) must be solved; whereas, when cable lengths are given, a direct geometric static problem (DGP) must be considered. Both problems are challenging, as the robot continues to preserve some degrees of freedom even after n variables are assigned, with the final configuration determined by the applied forces. Hence, kinematics and statics are coupled and must be resolved simultaneously. In this dissertation, a general methodology is presented for modelling the aforementioned scenario with a set of algebraic equations. An elimination procedure is provided, aimed at solving the governing equations analytically and obtaining a least-degree univariate polynomial in the corresponding ideal for any value of n. Although an analytical procedure based on elimination is important from a mathematical point of view, providing an upper bound on the number of solutions in the complex field, it is not practical to compute these solutions as it would be very time-consuming. Thus, for the efficient computation of the solution set, a numerical procedure based on homotopy continuation is implemented. A continuation algorithm is also applied to find a set of robot parameters with the maximum number of real assembly modes for a given DGP. Finally, the end-effector pose depends on the applied load and may change due to external disturbances. An investigation into equilibrium stability is therefore performed.

Fine Mapping of qroot-yield-1.06, a QTL for Root, Plant Vigor and Yield in Maize

Root-yield-1.06 is a major QTL affecting root system architecture (RSA) and other agronomic traits in maize. The effect of this QTL has been evaluated with the development of near isogenic lines (NILs) differing at the QTL position. The objective of this study was to fine map qroot-yield-1.06 by marker-assisted searching for chromosome recombinants in the QTL interval and concurrent root phenotyping in both controlled and field conditions, through successive generations. Complementary approaches such as QTL meta-analysis and RNA-seq were deployed in order to help prioritizing candidate genes within the QTL target region. Using a selected group of genotypes, field based root analysis by ‘shovelomics’ enabled to accurately collect RSA information of adult maize plants. Shovelomics combined with software-assisted root imaging analysis proved to be an informative and relatively highly automated phenotyping protocol. A QTL interval mapping was conducted using a segregating population at the seedling stage grown in controlled environment. Results enabled to narrow down the QTL interval and to identify new polymorphic markers for MAS in field experiments. A collection of homozygous recombinant NILs was developed by screening segregating populations with markers flanking qroot-yield-1.06. A first set of lines from this collection was phenotyped based on the adapted shovelomics protocol. QTL analysis based on these data highlighted an interval of 1.3 Mb as completely linked with the target QTL but, a larger safer interval of 4.1 Mb was selected for further investigations. QTL meta-analysis allows to synthetize information on root QTLs and two mQTLs were identified in the qroot-yield-1.06 interval. Trascriptomics analysis based on RNA-seq data of the two contrasting QTL-NILs, confirmed alternative haplotypes at chromosome bin 1.06. qroot-yield-1.06 has now been delimited to a 4.1-Mb interval, and thanks to the availability of additional untested homozygous recombinant NILs, the potentially achievable mapping resolution at qroot-yield-1.06 is c. 50 kb.