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New prediction method for the mixed logistic model applied in a marketing problem

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  • Tamura, Karin Ayumi
  • Giampaoli, Viviana

Abstract

When units belong to a specific group, such as employees nested within companies, the data present a hierarchical structure that can be modeled by using mixed models. In addition to fixed effects, these models estimate the random effects for each group. The problem of assigning values to the random effects for new groups in order to predict the outcome in a future period, based on the parameters previously estimated, is the focus of this article. The empirical best predictor (EBP) has been applied to the logistic mixed model, but when there is more than one random effect, the processing time required to solve the multidimensional integrals is costly. A new methodology is proposed based on linear regression that considers the relationship among the random effects and the covariates aggregated at the group level. A comparison among the linear regression prediction method (LRPM), EBP, and the ordinary logistic model is provided through simulation studies and an application study with a mobile company. The results indicate that LRPM drastically reduced the computational effort, and at the same time, maintained a similar level of prediction in relation to EBP.

Suggested Citation

  • Tamura, Karin Ayumi & Giampaoli, Viviana, 2013. "New prediction method for the mixed logistic model applied in a marketing problem," Computational Statistics & Data Analysis, Elsevier, vol. 66(C), pages 202-216.
    • Handle: RePEc:eee:csdana:v:66:y:2013:i:c:p:202-216
    DOI: 10.1016/j.csda.2013.04.006
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    References listed on IDEAS

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    1. José Lombardía, María & Sperlich, Stefan, 2012. "A new class of semi-mixed effects models and its application in small area estimation," Computational Statistics & Data Analysis, Elsevier, vol. 56(10), pages 2903-2917.
    2. Anders Skrondal & Sophia Rabe‐Hesketh, 2009. "Prediction in multilevel generalized linear models," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 172(3), pages 659-687, June.
    3. Xianzheng Huang, 2009. "Diagnosis of Random-Effect Model Misspecification in Generalized Linear Mixed Models for Binary Response," Biometrics, The International Biometric Society, vol. 65(2), pages 361-368, June.
    4. Jiming Jiang & P. Lahiri, 2006. "Mixed model prediction and small area estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(1), pages 1-96, June.
    5. Esteban, M.D. & Morales, D. & Pérez, A. & Santamaría, L., 2012. "Small area estimation of poverty proportions under area-level time models," Computational Statistics & Data Analysis, Elsevier, vol. 56(10), pages 2840-2855.
    6. R. A. Rigby & D. M. Stasinopoulos, 2005. "Generalized additive models for location, scale and shape," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(3), pages 507-554, June.
    7. Jiming Jiang & P. Lahiri, 2001. "Empirical Best Prediction for Small Area Inference with Binary Data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(2), pages 217-243, June.
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    3. Caro, Norma Patricia & Arias, Ver—nica & Ortiz, Pablo, 2017. "Predicci—n de fracaso en empresas latinoamericanas utilizando el mŽtodo del vecino más cercano para predecir efectos aleatorios en modelos mixtos || Prediction of Failure in Latin-American Companies U," Revista de Métodos Cuantitativos para la Economía y la Empresa = Journal of Quantitative Methods for Economics and Business Administration, Universidad Pablo de Olavide, Department of Quantitative Methods for Economics and Business Administration, vol. 24(1), pages 5-24, Diciembre.
    4. Erdely, Arturo, 2017. "Value at Risk and the Diversification Dogma || Valor en riesgo y el dogma de la diversificación," Revista de Métodos Cuantitativos para la Economía y la Empresa = Journal of Quantitative Methods for Economics and Business Administration, Universidad Pablo de Olavide, Department of Quantitative Methods for Economics and Business Administration, vol. 24(1), pages 209-219, Diciembre.

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