Prediction in Random Coefficient Regression Models

Bondeson, J.

doi:10.1002/bimj.4710320402

Cited by 8 publications

(3 citation statements)

References 16 publications

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“…In this case, the model is calibrated for each sampling unit (Bondeson, 1990;Lappi, 1991;Vonesh and Chinchilli, 1997). For a new, additional observation, the vector of random parameters $ b can be predicted using eq.…”

Section: Calibrationmentioning

confidence: 99%

Stand and tree-level variability on stem form and tree volume in Pinus pinea L.: A multilevel random components approach

Calama

Montero

2006

For. syst.

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Stem analysis data from 536 sampled trees located in 36 permanent sample plots were used to develop a taper function which allows flexible end products volume estimation for stone pine (Pinus pinea L.) in Spain. To alleviate inference problems derived from high correlation among observations a multilevel linear mixed approach, including random coefficients varying at both plot and tree levels, was used. The proposed taper function expresses the section diameter as a function of breast height diameter and relative height of the section, showing a logical behaviour at both breast and total height. Between and within plot stem form variability was explained by including explanatory covariates as basal area or distance independent competition indices.Mixed models allow calibration of the model for new locations, by predicting random coefficients if additional stem form measurements are available. Several alternatives of calibration, considering section diameters measured at different heights in a variable number of trees per plot, were compared between them, and with the basic marginal model and the marginal model including covariates. The best calibration alternative was to use additional section diameter measurements taken at 0.5 m height above ground. This model results in substantial improvement in stem form and single tree volume predictive ability over previously existing volume functions for the species, allowing size end-use classification for timber products.Key words: taper function; random coefficients; calibration; multilevel models; Pinus pinea ResumenVariabilidad a nivel de parcela y de árbol de la forma de fuste y del volumen individual en Pinus pinea L.: una aproximación multinivel con componentes aleatorios En el presente trabajo se han utilizado los datos del análisis de perfil de 536 árboles tipo de la especie Pinus pinea L, procedentes de 36 parcelas de experimentación, para desarrollar una función de perfil para la especie que permita la estimación de volúmenes individuales y una clasificación flexible de productos maderables de acuerdo a las dimensiones del fuste. Para reducir los problemas de inferencia estadística asociados con la alta correlación identificada entre las observaciones se ha propuesto la formulación de la función de perfil como un modelo mixto lineal multinivel, incluyendo parámetros aleatorios al nivel de árbol y parcela. La función de perfil desarrollada define el diámetro de la sección en función del diámetro normal y la altura relativa de la sección, y presenta comportamiento lógico en la predicción de diámetro a las alturas normal y total. La variabilidad sistemática en la forma del árbol identificada entre parcelas y entre árboles dentro de una misma parcela queda explicada mediante la inclusión de covariables tales como el área basimétrica o índices de competencia.Los modelos mixtos permiten calibrar la función de perfil para nuevas localizaciones, al predecir los parámetros aleatorios a partir de un número reducido de mediciones adicionales de la forma de fuste....

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Section: Calibrationmentioning

confidence: 99%

Stand and tree-level variability on stem form and tree volume in Pinus pinea L.: A multilevel random components approach

Calama

Montero

2006

For. syst.

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“…Contributions from a frequentist stance include Swamy (1970), Rosenberg (1973), Rao (1975), Harville (1976), Ware and Wu (1981), Strenio et al (1983), Kackar and Harville (1984), Reinsel (1984Reinsel ( , 1985, Bondeson (1990), Candel (2004Candel ( , 2007, Afshartous and de Leeuw (2005) and Frees and Kim (2006). References with a Bayesian perspective include Lindley and Smith (1972), Smith (1973), Fearn (1975) and Strenio et al (1983).…”

Section: Introductionmentioning

confidence: 99%

Prediction in Multilevel Generalized Linear Models

Skrondal

Rabe‐Hesketh

2009

Journal of the Royal Statistical Society Series A: Statistics in Society

184

142

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Summary. We discuss prediction of random effects and of expected responses in multilevel generalized linear models. Prediction of random effects is useful for instance in small area estimation and disease mapping, effectiveness studies and model diagnostics. Prediction of expected responses is useful for planning, model interpretation and diagnostics. For prediction of random effects, we concentrate on empirical Bayes prediction and discuss three different kinds of standard errors; the posterior standard deviation and the marginal prediction error standard deviation (comparative standard errors) and the marginal sampling standard deviation (diagnostic standard error). Analytical expressions are available only for linear models and are provided in an appendix. For other multilevel generalized linear models we present approximations and suggest using parametric bootstrapping to obtain standard errors. We also discuss prediction of expectations of responses or probabilities for a new unit in a hypothetical cluster, or in a new (randomly sampled) cluster or in an existing cluster. The methods are implemented in gllamm and illustrated by applying them to survey data on reading proficiency of children nested in schools. Simulations are used to assess the performance of various predictions and associated standard errors for logistic random-intercept models under a range of conditions.

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“…Ao se considerar a distribuição binomial na família exponencial, tem-se que a função de ligação canônicaé dada por Swamy (1970), Rosenberg (1973), Rao (1975), Harville (1976), Ware e Wu (1981), Strenio et al (1983), Kackar e Harville (1984), Reinsel (1984), Reinsel (1985), Bondeson (1990), Candel (2004), Candel (2007)…”

Section: Modelo De Regressão Logísticaunclassified

Métodos de predição para modelo logístico misto com k efeitos aleatórios

Tamura¹

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Prediction in Random Coefficient Regression Models

Cited by 8 publications

References 16 publications

Stand and tree-level variability on stem form and tree volume in Pinus pinea L.: A multilevel random components approach

Stand and tree-level variability on stem form and tree volume in Pinus pinea L.: A multilevel random components approach

Prediction in Multilevel Generalized Linear Models

Métodos de predição para modelo logístico misto com k efeitos aleatórios

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