The ABO Blood Group System

Estimates the two independent parameters of the the ABO blood group system.

ABO(link.pA = "logitlink", link.pB = "logitlink", ipA = NULL, ipB = NULL,
    ipO = NULL, zero = NULL)

Arguments

Link functions applied to pA and pB. See Links for more choices.

ipA, ipB, ipO

Optional initial value for pA and pB and pO. A NULL value means values are computed internally.

zero

Details at CommonVGAMffArguments.

Details

The parameters pA and pB are probabilities, so that pO=1-pA-pB is the third probability. The probabilities pA and pB correspond to A and B respectively, so that pO is the probability for O. It is easier to make use of initial values for pO than for pB. In documentation elsewhere I sometimes use pA=p, pB=q, pO=r.

Value

An object of class "vglmff" (see vglmff-class). The object is used by modelling functions such as vglm and vgam.

References

Lange, K. (2002). Mathematical and Statistical Methods for Genetic Analysis, 2nd ed. New York: Springer-Verlag.

Author

T. W. Yee

Note

The input can be a 4-column matrix of counts, where the columns are A, B, AB, O (in order). Alternatively, the input can be a 4-column matrix of proportions (so each row adds to 1) and the weights argument is used to specify the total number of counts for each row.

Examples

ymat <- cbind(A = 725, B = 258, AB = 72, O = 1073)  # Order matters, not the name
fit <- vglm(ymat ~ 1, ABO(link.pA = "identitylink",
                          link.pB = "identitylink"), trace = TRUE,
            crit = "coef")
#> Iteration 1: coefficients = 0.209130654, 0.080801008
#> Iteration 2: coefficients = 0.209130655, 0.080801008
coef(fit, matrix = TRUE)
#>                    pA         pB
#> (Intercept) 0.2091307 0.08080101
Coef(fit)  # Estimated pA and pB
#>         pA         pB 
#> 0.20913065 0.08080101 
rbind(ymat, sum(ymat) * fitted(fit))
#>          A       B       AB        O
#>   725.0000 258.000 72.00000 1073.000
#> 1 725.0729 258.078 71.91775 1072.931
sqrt(diag(vcov(fit)))
#> (Intercept):1 (Intercept):2 
#>   0.006628726   0.004267233