### Abstract

For mixed models generally, it is well known that modeling data with few clusters will result in biased estimates, particularly of the variance components and fixed effect standard errors. In linear mixed models, small sample bias is typically addressed through restricted maximum likelihood estimation (REML) and a Kenward-Roger correction. Yet with binary outcomes, there is no direct analog of either procedure. With a larger number of clusters, estimation methods for binary outcomes that approximate the likelihood to circumvent the lack of a closed form solution such as adaptive Gaussian quadrature and the Laplace approximation have been shown to yield less-biased estimates than linearization estimation methods that instead linearly approximate the model. However, adaptive Gaussian quadrature and the Laplace approximation are approximating the full likelihood rather than the restricted likelihood; the full likelihood is known to yield biased estimates with few clusters. On the other hand, linearization methods linearly approximate the model, which allows for restricted maximum likelihood and the Kenward-Roger correction to be applied. Thus, the following question arises: Which is preferable, a better approximation of a biased function or a worse approximation of an unbiased function? We address this question with a simulation and an illustrative empirical analysis.

Original language | English (US) |
---|---|

Pages (from-to) | 790-804 |

Number of pages | 15 |

Journal | Multivariate Behavioral Research |

Volume | 51 |

Issue number | 6 |

DOIs | |

State | Published - Nov 1 2016 |

Externally published | Yes |

### Fingerprint

### Keywords

- hierarchical generalized linear model
- Mutilevel logistic regression
- small sample

### ASJC Scopus subject areas

- Statistics and Probability
- Experimental and Cognitive Psychology
- Arts and Humanities (miscellaneous)

### Cite this

**Estimation Methods for Mixed Logistic Models with Few Clusters.** / McNeish, Daniel.

Research output: Contribution to journal › Article

*Multivariate Behavioral Research*, vol. 51, no. 6, pp. 790-804. https://doi.org/10.1080/00273171.2016.1236237

}

TY - JOUR

T1 - Estimation Methods for Mixed Logistic Models with Few Clusters

AU - McNeish, Daniel

PY - 2016/11/1

Y1 - 2016/11/1

N2 - For mixed models generally, it is well known that modeling data with few clusters will result in biased estimates, particularly of the variance components and fixed effect standard errors. In linear mixed models, small sample bias is typically addressed through restricted maximum likelihood estimation (REML) and a Kenward-Roger correction. Yet with binary outcomes, there is no direct analog of either procedure. With a larger number of clusters, estimation methods for binary outcomes that approximate the likelihood to circumvent the lack of a closed form solution such as adaptive Gaussian quadrature and the Laplace approximation have been shown to yield less-biased estimates than linearization estimation methods that instead linearly approximate the model. However, adaptive Gaussian quadrature and the Laplace approximation are approximating the full likelihood rather than the restricted likelihood; the full likelihood is known to yield biased estimates with few clusters. On the other hand, linearization methods linearly approximate the model, which allows for restricted maximum likelihood and the Kenward-Roger correction to be applied. Thus, the following question arises: Which is preferable, a better approximation of a biased function or a worse approximation of an unbiased function? We address this question with a simulation and an illustrative empirical analysis.

AB - For mixed models generally, it is well known that modeling data with few clusters will result in biased estimates, particularly of the variance components and fixed effect standard errors. In linear mixed models, small sample bias is typically addressed through restricted maximum likelihood estimation (REML) and a Kenward-Roger correction. Yet with binary outcomes, there is no direct analog of either procedure. With a larger number of clusters, estimation methods for binary outcomes that approximate the likelihood to circumvent the lack of a closed form solution such as adaptive Gaussian quadrature and the Laplace approximation have been shown to yield less-biased estimates than linearization estimation methods that instead linearly approximate the model. However, adaptive Gaussian quadrature and the Laplace approximation are approximating the full likelihood rather than the restricted likelihood; the full likelihood is known to yield biased estimates with few clusters. On the other hand, linearization methods linearly approximate the model, which allows for restricted maximum likelihood and the Kenward-Roger correction to be applied. Thus, the following question arises: Which is preferable, a better approximation of a biased function or a worse approximation of an unbiased function? We address this question with a simulation and an illustrative empirical analysis.

KW - hierarchical generalized linear model

KW - Mutilevel logistic regression

KW - small sample

UR - http://www.scopus.com/inward/record.url?scp=84994173157&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84994173157&partnerID=8YFLogxK

U2 - 10.1080/00273171.2016.1236237

DO - 10.1080/00273171.2016.1236237

M3 - Article

VL - 51

SP - 790

EP - 804

JO - Multivariate Behavioral Research

JF - Multivariate Behavioral Research

SN - 0027-3171

IS - 6

ER -