Alvaro Mauricio Montenegro

Abstracts

2 Solving Dimensionality Problem and Finding Statistical Constructs on Latent Regression Models: A Novel Methodology with Real Data Application

Authors: Sergio Paez Moncaleano, Alvaro Mauricio Montenegro

Abstract:

This paper presents a novel statistical methodology for measuring and founding constructs in Latent Regression Analysis. This approach uses the qualities of Factor Analysis in binary data with interpretations on Item Response Theory (IRT). In addition, based on the fundamentals of submodel theory and with a convergence of many ideas of IRT, we propose an algorithm not just to solve the dimensionality problem (nowadays an open discussion) but a new research field that promises more fear and realistic qualifications for examiners and a revolution on IRT and educational research. In the end, the methodology is applied to a set of real data set presenting impressive results for the coherence, speed and precision. Acknowledgments: This research was financed by Colciencias through the project: 'Multidimensional Item Response Theory Models for Practical Application in Large Test Designed to Measure Multiple Constructs' and both authors belong to SICS Research Group from Universidad Nacional de Colombia.

Keywords: dimensionality, item response theory, factorial analysis, submodel theory

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1 Multidimensional Item Response Theory Models for Practical Application in Large Tests Designed to Measure Multiple Constructs

Authors: Maria Fernanda Ordoñez Martinez, Alvaro Mauricio Montenegro

Abstract:

This work presents a statistical methodology for measuring and founding constructs in Latent Semantic Analysis. This approach uses the qualities of Factor Analysis in binary data with interpretations present on Item Response Theory. More precisely, we propose initially reducing dimensionality with specific use of Principal Component Analysis for the linguistic data and then, producing axes of groups made from a clustering analysis of the semantic data. This approach allows the user to give meaning to previous clusters and found the real latent structure presented by data. The methodology is applied in a set of real semantic data presenting impressive results for the coherence, speed and precision.

Keywords: semantic analysis, Dimension Reduction, factorial analysis, penalized logistic regression

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