ABO {VGAM} | R Documentation

## The ABO Blood Group System

### Description

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

### Usage

    ABO(link = "logit", earg=list(), ipA = NULL, ipO = NULL)

### Arguments

`link` | Link function applied to `pA` and `pB`. See `Links` for more choices.
`earg` | List. Extra argument applied to each of the links. See `earg` in `Links` for general information.
`ipA, ipO` | Optional initial value for `pA` and `pO`. A `NULL` value means values are computed internally.

### 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`.

### 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.

### Author(s)

T. W. Yee

### References

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

### See Also

`AA.Aa.aa`, `AB.Ab.aB.ab`, `AB.Ab.aB.ab2`, `G1G2G3`, `MNSs`.

### Examples

    y = cbind(A=725, B=258, AB=72, O=1073) # Order matters, not the name
    fit = vglm(y ~ 1, ABO(link=logit), trace=TRUE, cri="coef")
    fit = vglm(y ~ 1, ABO(link=identity), trace=TRUE, cri="coef")
    coef(fit, matrix=TRUE)
    Coef(fit) # Estimated pA and pB
    rbind(y, sum(y)*fitted(fit))
    sqrt(diag(vcov(fit)))

[Package VGAM version 0.7-9 Index]