# AB.Ab.aB.ab: The AB-Ab-aB-ab Blood Group System In VGAM: Vector Generalized Linear and Additive Models

## Description

Estimates the parameter of the AB-Ab-aB-ab blood group system.

## Usage

 `1` ```AB.Ab.aB.ab(link = "logitlink", init.p = NULL) ```

## Arguments

 `link` Link function applied to `p`. See `Links` for more choices. `init.p` Optional initial value for `p`.

## Details

This one parameter model involves a probability called `p`.

## 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 AB, Ab, aB and ab (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`, `ABO`, `A1A2A3`, `MNSs`.
 ```1 2 3 4 5 6 7 8``` ```ymat <- cbind(AB=1997, Ab=906, aB=904, ab=32) # Data from Fisher (1925) fit <- vglm(ymat ~ 1, AB.Ab.aB.ab(link = "identitylink"), trace = TRUE) fit <- vglm(ymat ~ 1, AB.Ab.aB.ab, trace = TRUE) rbind(ymat, sum(ymat)*fitted(fit)) Coef(fit) # Estimated p p <- sqrt(4*(fitted(fit)[, 4])) p*p summary(fit) ```