Robustness of parameter estimation procedures in multilevel models when random effects are MEP distributed. (English) Zbl 1157.62034

Summary: We examine maximum likelihood estimation procedures in multilevel models for two level nesting structures. Usually, for fixed effects and variance components estimation, level-one error terms and random effects are assumed to be normally distributed. Nevertheless, in some circumstances this assumption might not be realistic, especially as concerns random effects. Thus we assume for random effects the family of multivariate exponential power distributions (MEP); subsequently, by means of Monte Carlo simulation procedures, we study robustness of maximum likelihood estimators under the normality assumption when, actually, random effects are MEP distributed.


62H12 Estimation in multivariate analysis
62F35 Robustness and adaptive procedures (parametric inference)
65C05 Monte Carlo methods


Full Text: DOI


[1] Fang K-T, Kotz S, Ng K-W (1990) Symmetric multivariate and related distributions. Monograph on statistics and applied probability, vol 39. Chapman and Hall, London · Zbl 0699.62048
[2] Ferrari PA, Solaro N (2002) Una proposta per le componenti erratiche del modello multilivello. In: Studi in onore di Angelo Zanella. Vita e Pensiero, Milano, pp 273–291
[3] Gómez E, Gómez-Villegas MA, Marin JM (1998) A multivariate generalization of the power exponential family of distributions. Commun Stat Theory Meth 27:589–600 · Zbl 0895.62053
[4] Gori E, Vittadini G (1999) La valutazione dell’efficienza ed efficacia dei servizi alla persona. Impostazione e metodi. In: Qualità e valutazione nei servizi di pubblica utilità. ETAS, pp 121–241
[5] Hollander M, Wolfe DA (1973) Nonparametric statistical methods. Wiley, New York · Zbl 0277.62030
[6] Johnson ME (1987) Multivariate statistical simulation. Wiley, New York · Zbl 0604.62056
[7] Kreft IGG (1996) Are multilevel techniques necessary? An overview, including simulation studies. Technical report: http://www.calstatela.edu/ faculty/ikreft
[8] Laird NM, Ware JH (1982) Random-effects models for longitudinal data. Biometrics 38:963–974 · Zbl 0512.62107
[9] Lindsey JK (1999) Models for repeated measurements. Oxford University Press, Oxford · Zbl 1274.62011
[10] Maas CJM, Hox JJ (2004) The influence of violations of assumptions on multilevel parameter estimates and their standard errors. Comput Stat Data Anal 46:427–440 · Zbl 1429.62085
[11] Mardia KV (1970) Measures of multivariate skewness and kurtosis with applications. Biometrika 57:519–530 · Zbl 0214.46302
[12] Pinheiro JC, Bates MB (2000) Mixed-effects models in S and S-Plus. Springer, Berlin Heidelberg New York · Zbl 0953.62065
[13] Snijders TAB, Bosker RJ (1999) Multilevel analysis – an introduction to basic and advanced multilevel modeling. SAGE Publications, London · Zbl 0953.62127
[14] Solaro N (2004) Random variate generation from multivariate exponential power distribution. Statistica Applicazioni II, 2:25–44
[15] Verbeke G, Lesaffre E (1997) The effect of misspecifying the random-effects distribution in linear mixed models for longitudinal data. Comput Stat Data Anal 23:541–556 · Zbl 0900.62374
[16] Verbeke G, Molenberghs G (2000) Linear mixed models for longitudinal data. Springer, Berlin Heidelberg New York · Zbl 0956.62055
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.