### Abstract

The linear mixed effects model is a popular framework for analysis of continuous longitudinal responses from a sample of individuals in biomedical, agricultural, environmental, and social science applications. Inter-individual heterogeneity in features of the longitudinal profiles, such as (error-free) baseline response or rate of change, is represented explicitly by individualspecific random effects, so that inference on questions involving population or individual characteristics is possible. A standard assumption is that the random effects and within-individual errors are normally distributed, and software such as SAS proc mixed (Littell, Milliken, Stroup, and Wolfinger, 1996) or Splus lme() (Pinheiro and Bates, 2000) incorporates this assumption. Although normality of within-individual deviations may be a reasonable model for many continuous measurements, perhaps on a transformed scale, normality of the random effects implies a belief about inter-individual heterogeneity that may be unrealistic. For example, a common feature in biological contexts is skewness or heavy-tailedness of features underlying individual profiles.

Original language | English (US) |
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Title of host publication | Skew-Elliptical Distributions and Their Applications |

Subtitle of host publication | A Journey Beyond Normality |

Publisher | CRC Press |

Pages | 339-358 |

Number of pages | 20 |

ISBN (Electronic) | 9780203492000 |

ISBN (Print) | 9781584884316 |

State | Published - Jan 1 2004 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*Skew-Elliptical Distributions and Their Applications: A Journey Beyond Normality*(pp. 339-358). CRC Press.

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*Skew-Elliptical Distributions and Their Applications: A Journey Beyond Normality.*CRC Press, pp. 339-358.

**Linear mixed effects models with flexible generalized skew-elliptical random effects.** / Ma, Yanyuan; Genton, Marc G.; Davidian, Marie.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

TY - CHAP

T1 - Linear mixed effects models with flexible generalized skew-elliptical random effects

AU - Ma, Yanyuan

AU - Genton, Marc G.

AU - Davidian, Marie

PY - 2004/1/1

Y1 - 2004/1/1

N2 - The linear mixed effects model is a popular framework for analysis of continuous longitudinal responses from a sample of individuals in biomedical, agricultural, environmental, and social science applications. Inter-individual heterogeneity in features of the longitudinal profiles, such as (error-free) baseline response or rate of change, is represented explicitly by individualspecific random effects, so that inference on questions involving population or individual characteristics is possible. A standard assumption is that the random effects and within-individual errors are normally distributed, and software such as SAS proc mixed (Littell, Milliken, Stroup, and Wolfinger, 1996) or Splus lme() (Pinheiro and Bates, 2000) incorporates this assumption. Although normality of within-individual deviations may be a reasonable model for many continuous measurements, perhaps on a transformed scale, normality of the random effects implies a belief about inter-individual heterogeneity that may be unrealistic. For example, a common feature in biological contexts is skewness or heavy-tailedness of features underlying individual profiles.

AB - The linear mixed effects model is a popular framework for analysis of continuous longitudinal responses from a sample of individuals in biomedical, agricultural, environmental, and social science applications. Inter-individual heterogeneity in features of the longitudinal profiles, such as (error-free) baseline response or rate of change, is represented explicitly by individualspecific random effects, so that inference on questions involving population or individual characteristics is possible. A standard assumption is that the random effects and within-individual errors are normally distributed, and software such as SAS proc mixed (Littell, Milliken, Stroup, and Wolfinger, 1996) or Splus lme() (Pinheiro and Bates, 2000) incorporates this assumption. Although normality of within-individual deviations may be a reasonable model for many continuous measurements, perhaps on a transformed scale, normality of the random effects implies a belief about inter-individual heterogeneity that may be unrealistic. For example, a common feature in biological contexts is skewness or heavy-tailedness of features underlying individual profiles.

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UR - http://www.scopus.com/inward/citedby.url?scp=78650411654&partnerID=8YFLogxK

M3 - Chapter

AN - SCOPUS:78650411654

SN - 9781584884316

SP - 339

EP - 358

BT - Skew-Elliptical Distributions and Their Applications

PB - CRC Press

ER -