# ABO: The ABO Blood Group System In VGAM: Vector Generalized Linear and Additive Models

 ABO R Documentation

## The ABO Blood Group System

### Description

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

### Usage

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

### Arguments

 `link.pA, link.pB` 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`.

### 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.

T. W. Yee

### References

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

`AA.Aa.aa`, `AB.Ab.aB.ab`, `A1A2A3`, `MNSs`.

### Examples

```ymat <- cbind(A = 725, B = 258, AB = 72, O = 1073)  # Order matters, not the name