7 Testing the Equality of Means

`Means`

command:
Means 0.9087 0.8685Second, we declare a matrix for the means, e.g.

`M Full 1 2`

in
the matrices declaration section. Third, we can equate parameters for the first
and second twins by using a `Specify`

statement such as
Specify M 101 101where

`101`

is a parameter number that has not been used
elsewhere in the script. By using the same number for the two means,
they are constrained to be equal. Fourth, we include a model for the
means:
Means M;In the DZ group we also supply the observed means, and adjust the model for the means. We can then either (i) equate the mean for MZ twins to that for DZ twins by using the same matrix

`M`

, 'copied' from the MZ group or
equated to that of the MZ group as follows:
M Full 1 2 = M2where

`M2`

refers to matrix `M`

in group 2; to fit a Female | Male | ||||||||

Young | Older | Young | Older | ||||||

df | |||||||||

Model I | 6 | 7.84 | .25 | 5.74 | .57 | 12.81 | .05 | 5.69 | .58 |

Model II | 5 | 3.93 | .56 | 4.75 | .58 | 7.72 | .17 | 5.36 | .50 |

Model III | 3 | 3.71 | .29 | 2.38 | .67 | 7.28 | .06 | 5.03 | .17 |

Genetic Model | ADE | AE | ADE | AE | |||||

AE models have one more degree of freedom than shown in the df column |

to the like-sex twin pair data on BMI. In each analysis, we have considered only the best-fitting genetic model identified in the analyses ignoring means. Again we subtract the of a more general model from the of a more restricted model to get a likelihood ratio test of the difference in fit between the two. For the two older cohorts we find no evidence for mean differences either between zygosity groups or between first and second twins. That is, the model that assumes no heterogeneity of means (model 1) does not give a significantly worse fit than either (i) estimating separate MZ and DZ means (model 2), or (ii) estimating 4 means. For older females, likelihood-ratio chi-squares are and ; and for older males, and . Maximum-likelihood estimates of mean log BMI in the older cohort are, respectively, 21.87 and 22.26 for females and males; estimates of genetic and environmental parameters are unchanged from those obtained in the analyses ignoring means. In the younger cohorts, however, we do find significant mean differences between zygosity groups, both in females ( ) and in males ( ). In both sexes, mean log BMI values are lower in MZ pairs (21.35 for females, 21.63 for males) than for DZ pairs (21.45 for females, 21.79 for males). As these data are not age-corrected, it is possible that BMI values are still changing in this age-group, and that the zygosity difference reflects a slight mean difference in age. We shall return to this question in Section 6.2.9.