### Abstract

This note shows three cases in which a considerable loss of efficiency can result from assuming a parametric distribution for a random effect that is substantially different from the true distribution. For two simple models for binary response data, we studied the effects of assuming normality or of using a nonparametric fitting procedure for random effects, when the true distribution is potentially far from normal. Although usually the choice of random effects distribution has little effect on efficiency of predicting outcome probabilities, the normal approach suffered when the true distribution was a two-point mixture with a large variance component. Likewise, for a simple survival model, assuming a gamma distribution for the frailty distribution when the true one was a two-point mixture resulted in considerable loss of efficiency in predicting the frailties. The paper concludes with a discussion of possible ways of addressing the problem of potential efficiency loss, and makes suggestions for future research.

Original language | English (US) |
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Pages (from-to) | 639-653 |

Number of pages | 15 |

Journal | Computational Statistics and Data Analysis |

Volume | 47 |

Issue number | 3 |

DOIs | |

State | Published - Oct 1 2004 |

### Keywords

- Binomial
- Frailty model
- Gamma distribution
- Logit model
- Nonparametric
- Odds ratio

### ASJC Scopus subject areas

- Statistics and Probability
- Computational Mathematics
- Computational Theory and Mathematics
- Applied Mathematics

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## Cite this

*Computational Statistics and Data Analysis*,

*47*(3), 639-653. https://doi.org/10.1016/j.csda.2003.12.009