### Abstract

A number of articles have discussed the way lower order polynomial and interaction terms should be handled in linear regression models. Only if all lower order terms are included in the model will the regression model be invariant with respect to coding transformations of the variables. If lower order terms are omitted, the regression model will not be well formulated. In this paper, we extend this work to examine the implications of the ordering of variables in the linear mixed-effects model. We demonstrate how linear transformations of the variables affect the model and tests of significance of fixed effects in the model. We show how the transformations modify the random effects in the model, as well as their covariance matrix and the value of the restricted log-likelihood. We suggest a variable selection strategy for the linear mixed-effects model.

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

Pages (from-to) | 338-343 |

Number of pages | 6 |

Journal | American Statistician |

Volume | 51 |

Issue number | 4 |

State | Published - Nov 1997 |

Externally published | Yes |

### Fingerprint

### Keywords

- Hierarchical linear models
- Hierarchical ordering
- Random coefficient models
- Variable selection
- Well-formulated models

### ASJC Scopus subject areas

- Mathematics(all)
- Statistics and Probability

### Cite this

*American Statistician*,

*51*(4), 338-343.

**Linear Transformations of Linear Mixed-Effects Models.** / Morrell, Christopher H.; Pearson, Jay D.; Brant, Larry J.

Research output: Contribution to journal › Article

*American Statistician*, vol. 51, no. 4, pp. 338-343.

}

TY - JOUR

T1 - Linear Transformations of Linear Mixed-Effects Models

AU - Morrell, Christopher H.

AU - Pearson, Jay D.

AU - Brant, Larry J.

PY - 1997/11

Y1 - 1997/11

N2 - A number of articles have discussed the way lower order polynomial and interaction terms should be handled in linear regression models. Only if all lower order terms are included in the model will the regression model be invariant with respect to coding transformations of the variables. If lower order terms are omitted, the regression model will not be well formulated. In this paper, we extend this work to examine the implications of the ordering of variables in the linear mixed-effects model. We demonstrate how linear transformations of the variables affect the model and tests of significance of fixed effects in the model. We show how the transformations modify the random effects in the model, as well as their covariance matrix and the value of the restricted log-likelihood. We suggest a variable selection strategy for the linear mixed-effects model.

AB - A number of articles have discussed the way lower order polynomial and interaction terms should be handled in linear regression models. Only if all lower order terms are included in the model will the regression model be invariant with respect to coding transformations of the variables. If lower order terms are omitted, the regression model will not be well formulated. In this paper, we extend this work to examine the implications of the ordering of variables in the linear mixed-effects model. We demonstrate how linear transformations of the variables affect the model and tests of significance of fixed effects in the model. We show how the transformations modify the random effects in the model, as well as their covariance matrix and the value of the restricted log-likelihood. We suggest a variable selection strategy for the linear mixed-effects model.

KW - Hierarchical linear models

KW - Hierarchical ordering

KW - Random coefficient models

KW - Variable selection

KW - Well-formulated models

UR - http://www.scopus.com/inward/record.url?scp=0031489758&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031489758&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0031489758

VL - 51

SP - 338

EP - 343

JO - American Statistician

JF - American Statistician

SN - 0003-1305

IS - 4

ER -