In this project I have studied the left-right symmetric model (LRSM) as a candidate beyond standard model theory of particle physics. The most common version of the theory, called the minimal LRSM, has been studied and tested extensively for several decades. I have therefore modied this minimal LRSM by adapting the scalar sector and computing the mass of the charged right-handed gauge bosons WR for this particular scalar sector. I carried out a study of the theory and implemented it into FeynRules, in order to simulate LHC events using MadGraph. This allowed computation of the cross-section for the decay WR to a top and a bottom quark as a function of the mass of WR , which was compared with CMS data for the same decay, with proton-proton collisions at a centre of mass energy of 13 TeV. The final result was a constraint on the mass of WR , with a lower bound of 3 TeV.

Item response theory models (IRT) are increasingly becoming established in social science research, particularly in the analysis of performance or attitudinal data in psychology, education, medicine, marketing and other fields where testing is relevant. We propose the R package eRm (extended Rasch modeling) for computing Rasch models and several extensions. A main characteristic of some IRT models, the Rasch model being the most prominent, concerns the separation of two kinds of parameters, one that describes qualities of the subject under investigation, and the other relates to qualities of the situation under which the response of a subject is observed. Using conditional maximum likelihood (CML) estimation both types of parameters may be estimated independently from each other. IRT models are well suited to cope with dichotomous and polytomous responses, where the response categories may be unordered as well as ordered. The incorporation of linear structures allows for modeling the effects of covariates and enables the analysis of repeated categorical measurements. The eRm package fits the following models: the Rasch model, the rating scale model (RSM), and the partial credit model (PCM) as well as linear reparameterizations through covariate structures like the linear logistic test model (LLTM), the linear rating scale model (LRSM), and the linear partial credit model (LPCM). We use an unitary, efficient CML approach to estimate the item parameters and their standard errors. Graphical and numeric tools for assessing goodness-of-fit are provided. (authors' abstract)

Item response theory models (IRT) are increasingly becoming established in social science research, particularly in the analysis of performance or attitudinal data in psychology, education, medicine, marketing and other fields where testing is relevant. We propose the R package eRm (extended Rasch modeling) for computing Rasch models and several extensions. A main characteristic of some IRT models, the Rasch model being the most prominent, concerns the separation of two kinds of parameters, one that describes qualities of the subject under investigation, and the other relates to qualities of the situation under which the response of a subject is observed. Using conditional maximum likelihood (CML) estimation both types of parameters may be estimated independently from each other. IRT models are well suited to cope with dichotomous and polytomous responses, where the response categories may be unordered as well as ordered. The incorporation of linear structures allows for modeling the effects of covariates and enables the analysis of repeated categorical measurements. The eRm package fits the following models: the Rasch model, the rating scale model (RSM), and the partial credit model (PCM) as well as linear reparameterizations through covariate structures like the linear logistic test model (LLTM), the linear rating scale model (LRSM), and the linear partial credit model (LPCM). We use an unitary, efficient CML approach to estimate the item parameters and their standard errors. Graphical and numeric tools for assessing goodness-of-fit are provided. (author's abstract) / Series: Research Report Series / Department of Statistics and Mathematics

The aim of the monograph is to contribute towards bridging the gap between methodological developments that have evolved in the social sciences, in particular in psychometric research, and methods of statistical modelling in a more general framework. The first part surveys certain special psychometric models (often referred to as Rasch family of models) that share common properties: separation of parameters describing qualities of the subject under investigation and parameters related to properties of the situation under which the response of a subject is observed. Using conditional maximum likelihood estimation, both types of parameters may be estimated independently from each other. In particular, the Rasch model, the rating scale model, the partial credit model, hybrid types, and linear extensions thereof are treated. The second part reviews basic ideas of generalized linear models (GLMs) as an an excellent framework for unifying different approaches and providing a natural, technical background for model formulation, estimation and testing. This is followed by a short introduction to the software package GLIM chosen to illustrate the formulation of psychometric models in the GLM framework. The third part is the main part of this monograph and shows the application of generalized linear models to psychometric approaches. It gives a unified treatment of Rasch family models in the context of log-linear models and contains some new material on log-linear longitudinal modelling. The last part of the monograph is devoted to show the usefulness of the latent variable approach in a variety of applications, such as panel, cross-over, and therapy evaluation studies, where standard statistical analysis does not necessarily lead to satisfactory results. (author´s abstract) / Series: Research Report Series / Department of Statistics and Mathematics