# Project

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## Robust Prediction and Model Choice in Mixed Linear Models for the Analysis of Social Sciences Data

 English title Robust Prediction and Model Choice in Mixed Linear Models for the Analysis of Social Sciences Data Victoria-Feser Maria-Pia 131906 Project funding (Div. I-III) Section des Hautes Études Commerciales HEC-FSES Université de Genève University of Geneva - GE Science of management 01.09.2011 - 30.11.2014 327'240.00
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### All Disciplines (2)

Discipline
 Science of management
 Psychology

### Keywords (11)

Small area estimation; Multilevel models; ANOVA; Growth curve models; Estimation and testing; Clustered data; time series; repeated measurements; medical data; biostatistics; data contamination

### Lay Summary (English)

Lay summary
Statistics plays an important role in the research process. To verify a theoretical statement on a given problem, experiments are set and observations made on a sample of subjects and the collected information is then analyzed through the use of statistical models and tools. One can then make inference from the sample to the unobservable population. The results of the research rely therefore heavily on the quality of the statistical analysis. Modern research in the life sciences imply the use of more and more complex models such as mixed linear models (MLM). These models allow the analysis of multivariate or clustered data, i.e. several measurements per sampled subject. They are used in many fields such as in biology, medicine, psychology, education, sociology, political sciences, economics, business. A MLM can be used for example to understand the mechanisms that make individuals choose among different media (radio, television), or to react to different stimuli or drugs in a medical setting. New or improved statistical methods are necessary because researchers become more and more aware of the potential biases induced in the results of the analysis by either the use of too simplistic statistical models and/or data contamination. In this project we will develop more or less automatic model selection procedures, which are usually based on the optimization of response prediction criteria, as well as propose correct (robust) response predictions when the distributional assumptions underlying MLM is not fully respected by the data at hand. We also aim at applying the new development for the analysis of real data sets in the social, economics and psychological sciences and, in order to make this transfer of technology as efficient as possible, these methods will also be implemented in statistical packages for their availability to the community of researchers.
 Direct link to Lay Summary Last update: 21.02.2013

### Responsible applicant and co-applicants

Name Institute
 Victoria-Feser Maria-Pia Research Center for Statistics Geneva School of Economics and Management University of Geneva

### Employees

Name Institute
 Rothen Stéphane Service d'addictologie Dépt. de santé mentale et de psychiatrie HUG
 Guerrier Stéphane Faculté d'économie et de management Université de Genève
 Orso Samuel Faculté d'économie et de management Université de Genève

### Publications

Publication
Stebler Yannick, Guerrier Stéphane, Skaloud Jan, Victoria-Feser Maria-Pia (2012), A Framework for Inertial Sensor Calibration Using Complex Stochastic Error Models, in Proceedings of IEEE/ ION PLANS 2012, Myrtle Beach, SC, USA.
Guerrier S., Waegli Adrian, Skalud J., Victoria-Feser M.-P. (2012), Fault Detection and Isolation in Multiple MEMS-IMUs Configurations, in IEEE Transactions on Aerospace and Electronic Systems, 48, 2015-2031.
Stebler Yannick, Guerrier Stéphane, Skalud Jan, Victoria-Feser Maria-Pia (2011), Constrained Expectation-Maximization Algorithm for Stochastic Inertial Error Modeling: Study of Feasibility, in Measurement Science and Technology, 22(8), 1-12.
Stebler Yannick, Guerrier Stéphane, Skaloud Jan, Victoria-Feser Maria-Pia (2011), Improving Modeling of MEMS-IMUs Operating in GNSS-denied Conditions, in Proceedings of the ION GNSS 2011, Portland, OR, USA.
Guerrier Stéphane, Molinari Roberto, Skalud Jan, Victoria-Feser Maria-Pia, An Algorithm for Automatic Inertial Sensors Calibration, in Proceedings of the ION GNSS 2013, Nashville, TN, USA.
Dupuis D. J, Victoria-Feser M.-P., Robust VIF Regression with Application to Variable Selection in Large Datasets, in Annals of Applied Statistics.
Guerrier Stéphane, Stebler Yannick, Skaloud Jan, Victoria-Feser Maria-Pia, Wavelet variance based estimation for composite stochastic processes, in Journal of the American Statistical Association, 108(503), 1021-1030.

### Scientific events

#### Active participation

Title Type of contribution Title of article or contribution Date Place Persons involved
 Inter- national Conference on Robust Statistics (ICORS) Individual talk Asymptotic and nite sample bias correction for robust estimators 08.07.2013 Saint Petersburg, Russia Guerrier Stéphane;
 International Conference on Robust Statistics (ICORS) Individual talk Robust wavelet variance based estimation for composite stochastic processes 08.07.2013 Saint Petersburg, Russia Victoria-Feser Maria-Pia;
 International Conference on Computational Statistics Individual talk Robust VIF Regression for Selection in Large Datasets 26.08.2012 Limassol, Cyprus, Cyprus Victoria-Feser Maria-Pia;
 International Conference on Robust Statsitics Individual talk Robust VIF Regression for Selection in Large Datasets 05.08.2012 Burlington, USA, United States of America Victoria-Feser Maria-Pia;
 Joint Statistical Meeting Individual talk Wavelet Variance–Based Estimation for Composite Stochastic Processes 30.07.2012 San Diego, USA, United States of America Guerrier Stéphane;

### Awards

Title Year
 Best Presentation Award, ION GNSS 2013, Nashville, TN, USA, september 2013 2013

### Abstract

Mixed linear models (MLM) are flexible models for the analysis of complexdesigns data made across many disciplines of the social sciences. It is therefore important to develop statistical tools to estimate and test thesemodels. MLM are used whenever several measurements are made on one particular unit or subject or cluster, or even nested clusters. Their particularity, which makes them also more difficult to understand and analyze, is that they include random effects that capture the variability of the clusters. Although the literature has already provided a great amount of statistical procedures, there are some important aspects that still need to be developed. In particular, more or less automatic model selection procedures, especially for the number and nature of the random effects to introduce in the model, as well a correct response prediction when the normality assumption underlying MLM is not fully respected by the data at hand, are needed.The aim of this research project is mainly to develop statistical methods todeal with these issues. We also aim at applying the new development for the analysis of real data sets in the social, economics and psychological sciences and, in order to make this transfer of technology as efficient as possible, we will also provide new functions in the statistical software R.
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