5 Common vs. Independent Pathway Genetic Models

As another example of multivariate analysis we consider four atopic symptoms reported by female twins in a mailed questionnaire study (Duffy et al., 1990; 1992). Twins reported whether they had ever (versus never) suffered from asthma, hayfever, dust allergy and eczema. Tetrachoric correlation matrices were calculated with PRELIS and are shown in the Mx script in Appendix  and in Table 10.10. Tetrachoric or polychoric matrices and their corresponding asymptotic covariance matrices are read in with the PMatrix and ACov statements. The script shows that asymptotic covariance matrices are stored in files named ahdemzf.acv and ahdedzf.acv respectively for MZ and DZ twins. Reading polychoric matrices flags Mx that the weighted least squares (WLS) fit function is required, rather than maximum likelihood. Maximum-likelihood estimation is not appropriate when there are glaring departures from normality; the dichotomous items used in this example are inevitably non-normal.

Table 10.10: Tetrachoric correlations for female MZ (above diagonal) and DZ (below diagonal) twins for asthma (A), hayfever (H), dust allergy (D), and eczema (E).

		Twin 1				Twin 2
		A	H	D	E	A	H	D	E
Twin 1	Asthma		.56	.57	.27	.59	.41	.43	.09
	Hayfever	.52		.76	.26	.37	.59	.42	.20
	Dust Allergy	.59	.75		.31	.40	.45	.52	.19
	Eczema	.29	.31	.28		.23	.15	.19	.59
Twin 2	Asthma	.26	.17	.04	.14		.55	.64	.15
	Hayfever	.13	.32	.26	.09	.40		.77	.12
	Dust Allergy	.08	.17	.21	.02	.68	.72		.22
	Eczema	.22	.11	.09	.31	.25	.22	.28