4 Application to Body Mass Index

The natural logarithm of BMI was then taken to normalize the data. Before calculating covariance matrices of log BMI, the data from the two cohorts were combined, and the effects of age, age squared, sample (AARP vs. Virginia), sex, and their interactions were removed. The resulting covariance matrices are provided in the Mx scripts in Appendices and , while the correlations and sample sizes appear in Table 9.1 below.

Zygosity Group | N | r |

MZF | 1802 | 0.744 |

DZF | 1142 | 0.352 |

MZM | 750 | 0.700 |

DZM | 553 | 0.309 |

DZO | 1341 | 0.251 |

We note that both like-sex MZ correlations are greater than twice the respective DZ correlations; thus, models with dominant genetic effects, rather than common environmental effects, were fit to the data. In Table 9.2, we provide selected results from fitting the following models: general sex-limitation (I); common effects sex-limitation (II-IV); and scalar sex-limitation (V). We first note that the general sex-limitation model provides a good fit to the data, with . The estimate of under this model is fairly small, and when set to zero in model II, found to be non-significant ( = 2.54, ). Thus, there is no evidence for sex-specific additive genetic effects, and the common effects sex-limitation model (model II) is favored over the general model. As an exercise, the reader may wish to verify that the same conclusion is reached if the general sex-limitation model with sex-specific dominant genetic effects is compared to the common effects model with removed. Note that under model II the dominant genetic parameter for females is quite small; thus, when this parameter is fixed to zero in model III, there is not a significant worsening of fit, and model III becomes the most favored model. In model IV, we consider whether the dominant genetic effect for males can also be fixed to zero. The goodness-of-fit statistics indicate that this model fits the data poorly () and provides a significantly worse fit than model III ( = 26.73, ). Model IV is therefore rejected and model III remains the favored one. Finally, we consider the scalar sex-limitation model. Since there is evidence for dominant genetic effects in males and not in females, it seems unlikely that this model, which constrains the variance components of females to be scalar multiples of the male variance components, will provide a good fit to the data, unless the additive genetic variance in females is also much smaller than the male additive genetic variance. The model-fitting results support this contention: the model provides a marginal fit to the data ( = 0.05), and is significantly worse than model II ( = 7.82, ). We thus conclude from Table 9.2 that III is the best fitting model. This conclusion would also be reached if AIC was used to assess goodness-of-fit.

MODEL | |||||

Parameter | I | II | III | IV | V |

0.449 | 0.454 | 0.454 | 0.454 | 0.346 | |

0.172 | 0.000 | - | - | 0.288 | |

0.264 | 0.265 | 0.265 | 0.267 | 0.267 | |

0.210 | 0.240 | 0.240 | 0.342 | - | |

0.184 | 0.245 | 0.245 | - | - | |

0.213 | 0.213 | 0.213 | 0.220 | - | |

0.198 | - | - | - | - | |

- | - | - | - | 0.778 | |

9.26 | 11.80 | 11.80 | 38.53 | 19.62 | |

8 | 9 | 10 | 11 | 11 | |

0.32 | 0.23 | 0.30 | 0.00 | 0.05 | |

-6.74 | -6.20 | -8.20 | 16.53 | -2.38 |

Using the parameter estimates under model III, the expected variance of log BMI (residuals) in males and females can be calculated. A little arithmetic reveals that the phenotypic variance of males is markedly lower than that of females (0.17 vs. 0.28). Inspection of the parameter estimates indicates that the sex difference in phenotypic variance is due to increased