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Estimación de la matriz de covarianza no-fronteriza en modelos de efectos mixtos lineales generalizados utilizando

Tina Košuta1, Erik Langerholc1, Rok Blagus1,2

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La penalización de las matrices de covarianza de efectos aleatorios en modelos mixtos mejora las estimaciones. Este método utiliza pseudoobservaciones para una implementación más fácil y ofrece ajuste de parámetros basado en datos, mejorando la inferencia estadística.

Palabras clave:
(inverso) Wishart anterior y anterior.priores basados en datos.máximo una estimación a posteriori.penalizado con la máxima probabilidad.Las pseudoobservaciones son pseudoobservaciones.

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Área de la Ciencia:

  • Estadísticas Estadísticas Las estadísticas.
  • Modelado Estadístico Modelado Estadístico

Sus antecedentes:

  • La estimación de la probabilidad máxima en modelos de efectos mixtos lineales generalizados puede enfrentar desafíos numéricos debido a las estimaciones límite de las matrices de covarianza de efectos aleatorios.
  • Estos problemas de frontera tienen un impacto negativo en la inferencia estadística y la estabilidad del modelo.

Objetivo del estudio:

  • Desarrollar un método de estimación penalizado para matrices de covarianza de efectos aleatorios en modelos generalizados de efectos mixtos lineales.
  • Para abordar los desafíos numéricos y mejorar la precisión de la estimación de la matriz de covarianza.

Principales métodos:

  • Se introdujeron sanciones a la función de probabilidad utilizando priores condicionalmente conjugados para las matrices de covarianza o precisión de efectos aleatorios.
  • Sanciones representadas como pseudo-observaciones para integrar el método en el software de máxima probabilidad existente.
  • Desarrolló un procedimiento para construir pseudoobservaciones y un método basado en datos para establecer parámetros de penalización.

Principales resultados:

  • El enfoque penalizado propuesto demostró una mejor estimación de las matrices de covarianza de efectos aleatorios en estudios de simulación.
  • El método mostró un mejor rendimiento en comparación con los métodos de la competencia bajo escenarios realistas.
  • Aplicó con éxito el enfoque a datos del mundo real, confirmando su utilidad práctica.

Conclusiones:

  • El método de probabilidad penalizada mitiga efectivamente los problemas de estimación de límites en las matrices de covarianza de efectos aleatorios.
  • El uso de pseudoobservaciones simplifica la implementación dentro del software estadístico estándar.
  • La selección de parámetros de penalización basada en datos mejora la aplicabilidad del método cuando la información previa es limitada.