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Generalised M-quantile random-effects model for discrete response: an application to the number of visits to physicians. (English) Zbl 1523.62198

MSC:

62P10 Applications of statistics to biology and medical sciences; meta analysis

Software:

npmv
Full Text: DOI

References:

[1] AlfòMarco, MarinoMaria Francesca, RanalliMaria Giovanna, SalvatiNicola, TzavidisNikos (2020). M‐quantile regression for multivariate longitudinal data with an application to the Millennium Cohort Study. Journal of the Royal Statistical Society: Series C (Applied Statistics), https://doi.org/10.1111/rssc.12452. · doi:10.1111/rssc.12452
[2] Alfò, M., Salvati, N., & Ranalli, M. (2017). Finite mixtures of quantile and M‐quantile regression models. Statistics and Computing, 27, 547-570. · Zbl 1505.62017
[3] Bathke, A. C., Friedrich, S., Pauly, M., Konietschke, F., Staffen, W., Strobl, N., & Höller, Y. (2018). Testing mean differences among groups: Multivariate and repeated measures analysis with minimal assumptions. Multivariate Behavioral Research, 53(3), 348-359.
[4] Bathke, A. C., Harrar, S. W., & Rauf Ahmad, M. (2009). Some contributions to the analysis of multivariate data. Biometrical Journal: Journal of Mathematical Methods in Biosciences, 51(2), 285-303. · Zbl 1442.62247
[5] Borgoni, R., Del Bianco, P., Salvati, N., Schmid, T., & Tzavidis, N. (2018). Modelling the distribution of health‐related quality of life of advanced melanoma patients in a longitudinal multi‐centre clinical trial using M‐quantile random effects regression. Statistical Methods in Medical Research, 27, 549-563.
[6] Breckling, J., & Chambers, R. (1988). M‐quantiles. Biometrika, 75, 761-771. · Zbl 0653.62024
[7] Breslow, N. E., & Clayton, D. G. (1993). Approximate inference in generalized linear mixed models. Journal of the American Statistical Association, 88, 9-25. · Zbl 0775.62195
[8] Cantoni, E., & Ronchetti, E. (2001). Robust inference for generalized linear models. Journal of the American Statistical Association, 96, 1022-1030. · Zbl 1072.62610
[9] Chambers, R., Dreassi, E., & Salvati, N. (2014). Disease mapping via negative binomial regression M‐quantiles. Statistics in Medicine, 33, 4805-4824.
[10] Dawber, J. (2017). Advances in M‐quantile estimation. Australia: The University of Wollongong School of School of Mathematics and Applied Statistics.
[11] Ellis, A. R., Burchett, W. W., Harrar, S. W., & Bathke, A. C. (2017). Nonparametric inference for multivariate data: The R package npmv. Journal of Statistical Software, 76(4), 1-18.
[12] Fellner, W. H. (1986). Robust estimation of variance components. Technometrics, 28, 51-60. · Zbl 0597.62018
[13] Geraci, M., & Bottai, M. (2007). Quantile regression for longitudinal data using the asymmetric Laplace distribution. Biostatistics, 8, 140-154. · Zbl 1170.62380
[14] Geraci, M., & Bottai, M. (2014). Linear quantile mixed models. Statistics and Computing, 24, 461-479. · Zbl 1325.62010
[15] Gourieroux, C., Monfort, A., & Trognon, A. (1984). Pseudo maximum likelihood methods: Applications to Poisson models. Econometrica, 52, 701-720. · Zbl 0575.62032
[16] Hagemann, A. (2017). Cluster‐robust bootstrap inference in quantile regression models. Journal of the American Statistical Association, 112(517), 446-456.
[17] Huber, P. J. (1981). Robust statistics. New York: John Wiley and Sons. · Zbl 0536.62025
[18] ISTAT (2017). Anziani: le condizioni di salute in Italia e nell’Unione Europea. Statistiche report 26 settembre 2017, Istat.
[19] Jones, M. (1994). Expectiles and M‐quantiles are quantiles. Statistics and Probability Letters, 20, 149-153. · Zbl 0801.62012
[20] Kim, E. S., Park, N., Sun, J. K., Smith, J., & Peterson, C. (2014). Life satisfaction and frequency of doctor visits. Psychosomatic Medicine, 76, 86.
[21] Koenker, R. (2004). Quantile regression for longitudinal data. Journal of Multivariate Analysis, 91, 74-89. · Zbl 1051.62059
[22] Koenker, R. (2005). Quantile regression. Econometric Society Monographs. Cambridge: Cambridge University Press. · Zbl 1111.62037
[23] Koenker, R., & Bassett, G. (1978). Regression quantiles. Econometrica, 46, 33-50. · Zbl 0373.62038
[24] Kokic, P., Chambers, R., Breckling, J., & Beare, S. (1997). A measure of production performance. Journal of Business and Economic Statistics, 15, 445-451.
[25] Lawless, J. F. (1987). Negative binomial and mixed Poisson regression. The Canadian Journal of Statistics/La Revue Canadienne de Statistique, 15(3), 209-225. · Zbl 0632.62060
[26] Machado, J. A. F., & Silva, J. S. (2005). Quantiles for counts. Journal of the American Statistical Association, 100, 1226-1237. · Zbl 1117.62395
[27] Mc Culloch, C. (1997). Maximum likelihood algorithms for generalized linear mixed models. Journal of the American Statistical Association, 92, 162-170. · Zbl 0889.62061
[28] McCulloch, C. E., & Searle, S. R. (2001). Generalized, linear and mixed models. Canada: Wiley. · Zbl 0964.62061
[29] Newey, W. K., & Powell, J. L. (1987). Asymmetric least squares estimation and testing. Econometrica, 55, 819-847. · Zbl 0625.62047
[30] OruetaJuan F., García‐AlvarezArturo, GrandesGonzalo, Nuño‐SolinísRoberto (2015). The Origin of Variation in Primary Care Process and Outcome Indicators. Medicine, 94, (31), https://doi.org/10.1097/md.0000000000001314. · doi:10.1097/md.0000000000001314
[31] Parente, P. M., & Silva, J. M. S. (2016). Quantile regression with clustered data. Journal of Econometric Methods, 5(1), 1-15. · Zbl 1345.62182
[32] Raudenbush, S. W., Yang, M.‐L., & Yosef, M. (2000). Maximum likelihood for generalized linear models with nested random effects via high‐order, multivariate Laplace approximation. Journal of computational and Graphical Statistics, 9, 141-157.
[33] Richardson, A. M., & Welsh, A. H. (1995). Robust restricted maximum likelihood in mixed linear models. Biometrics, 51, 1429-1439. · Zbl 0875.62313
[34] Schall, R. (1991). Estimation in generalized linear models with random effects. Biometrika, 78, 719-727. · Zbl 0850.62561
[35] Schirripa Spagnolo, F., Salvati, N., D’Agostino, A., & Nicaise, I. (2020). The use of sampling weights in M ‐quantile random‐effects regression: An application to Programme for International Student Assessment mathematics scores. Journal of the Royal Statistical Society: Series C (Applied Statistics), 69(4), 991-1012.
[36] Schmid, T., Tzavidis, N., & Salvati, N. (2014). On the use of a data‐driven tuning constant in M‐quantile regression. Seminart July, 2014, University of Southampton.
[37] Sinha, S. K., & Rao, J. (2009). Robust small area estimation. Canadian Journal of Statistics, 37, 381-399. · Zbl 1177.62076
[38] Song, P., Fan, Y., & Kalbfleisch, J. (2005). Maximization by parts in likelihood inference (with discussion). Journal of the American Statistical Association, 100, 1145-1158. · Zbl 1117.62429
[39] Stevens, W. (1950). Fiducial limits of the parameter of a discontinuous distribution. Biometrika, 37, 117-129. · Zbl 0037.36701
[40] Stroup, W. W. (2013). Generalized Linear mixed models. Modern concepts, methods and applications. New York: CRC Press. · Zbl 1281.62013
[41] Torabi, M., & Shokoohi, F. (2015). Non‐parametric generalized linear mixed models in small area estimation. Canadian Journal of Statistics, 43, 82-96. · Zbl 1314.62039
[42] Tzavidis, N., Ranalli, M., Salvati, N., Dreassi, E., & Chambers, R. (2015). Robust small area prediction for counts. Statistical Methods in Medical Research, 24, 373-395.
[43] Tzavidis, N., Salvati, N., Schmid, T., Flouri, E., & Midouhas, E. (2016). Longitudinal analysis of the strengths and difficulties questionnaire scores of the Millennium Cohort Study children in England using M‐quantile random‐effects regression. Journal of the Royal Statistical Society: Series A (Statistics in Society), 179, 427-452.
[44] Wang, Y.‐G., Lin, X., Zhu, M., & Bai, Z. (2007). Robust estimation using the Huber function with a data‐dependent tuning constant. Journal of Computational and Graphical Statistics, 16(2), 468-481.
[45] White, H. (1980). A heteroskedasticity‐consistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica, 46, 817-838. · Zbl 0459.62051
[46] Zeileis, A., Kleiber, C., & Jackman, S. (2008). Regression models for count data in R. Journal of statistical software, 27, 1-25.
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