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Regresión de rango reducido para variables predictoras y de respuesta mixtas

Mark de Rooij1, Lorenza Cotugno2, Roberta Siciliano3

  • 1Methodology and Statistics Department, Leiden University, Leiden, The Netherlands.

The British journal of mathematical and statistical psychology
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Introducimos la regresión de rango reducido mixta generalizada (GMR3), un método de regresión versátil para variables predictoras y de respuesta mixta. Los estudios de simulación demuestran su robusto rendimiento en varios tipos de datos y tamaños de muestra.

Palabras clave:
Algoritmo de las MMModelos lineales generalizadosRegresión multivariadaescalado óptimo

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Área de la Ciencia:

  • Las estadísticas
  • Las economías
  • Ciencia de los datos

Sus antecedentes:

  • El análisis de regresión es crucial para comprender las relaciones entre las variables.
  • Los métodos existentes a menudo luchan con tipos mixtos de variables predictoras y de respuesta.
  • La regresión de rango reducido es efectiva para datos de alta dimensión, pero generalmente requiere tipos de variables específicos.

Objetivo del estudio:

  • Introducir un nuevo método de regresión, la regresión mixta generalizada de rango reducido (GMR3), capaz de manejar diversos tipos de variables.
  • Desarrollar un algoritmo eficiente para la estimación de la probabilidad máxima en GMR3.
  • Evaluar el rendimiento y el comportamiento de GMR3 a través de estudios de simulación y una aplicación empírica.

Principales métodos:

  • El método GMR3 propuesto incorpora un escalamiento óptimo para las variables predictoras categóricas.
  • Se deriva un algoritmo de majorización-minimización para la estimación de la máxima probabilidad.
  • Se llevan a cabo extensos estudios de simulación para evaluar el rendimiento con diferentes variables y configuraciones de datos.

Principales resultados:

  • Los estudios de simulación confirman la eficacia del algoritmo GMR3 en varias combinaciones de variables predictivas y de respuesta.
  • Simulaciones adicionales investigan el comportamiento del modelo con respecto al rango verdadero y al tamaño de la muestra.
  • Una aplicación que utiliza los datos de las encuestas del Eurobarómetro de 2023 demuestra la utilidad práctica de la GMR3.

Conclusiones:

  • GMR3 proporciona un marco flexible y potente para el análisis de regresión con tipos de datos mixtos.
  • El algoritmo de majorización-minimización derivado garantiza una estimación eficiente.
  • GMR3 es una herramienta valiosa para analizar conjuntos de datos complejos en campos como las ciencias sociales y la econometría.