Table 1.

Probabilities Associated With the Gene-Environment Interaction Model (Polytomous Logistic)

Parents (MF)	Offspring (C)	Probability (Pr(C|M,F,E,D))
00	0	1
02	1	1
22	2	1
01	0	$\exp ({\mathrm{\beta }}_{0}e+{\mathrm{\alpha }}_{010})/\left[1+\exp ({\mathrm{\beta }}_{0}e+{\mathrm{\alpha }}_{010})\right]$
	1	$1/\left[1+\exp ({\mathrm{\beta }}_{0}e+{\mathrm{\alpha }}_{010})\right]$
11	0	$\exp ({\mathrm{\beta }}_{0}e+{\mathrm{\alpha }}_{110})/\left[1+\exp ({\mathrm{\beta }}_{0}e+{\mathrm{\alpha }}_{110})+\exp ({\mathrm{\beta }}_{2}e+{\mathrm{\alpha }}_{112})\right]$
	1	$1/\left[1+\exp ({\mathrm{\beta }}_{0}e+{\mathrm{\alpha }}_{110})+\exp ({\mathrm{\beta }}_{2}e+{\mathrm{\alpha }}_{112})\right]$
	2	$\exp ({\mathrm{\beta }}_{2}e+{\mathrm{\alpha }}_{112})/\left[1+\exp ({\mathrm{\beta }}_{0}e+{\mathrm{\alpha }}_{110})+\exp ({\mathrm{\beta }}_{2}e+{\mathrm{\alpha }}_{112})\right]$
12	1	$1/\left[1+\exp ({\mathrm{\beta }}_{2}e+{\mathrm{\alpha }}_{122})\right]$
	2	$\exp ({\mathrm{\beta }}_{2}e+{\mathrm{\alpha }}_{122})/\left[1+\exp ({\mathrm{\beta }}_{2}e+{\mathrm{\alpha }}_{122})\right]$