The MNSs Blood Group System

Estimates the three independent parameters of the the MNSs blood group system.

Usage

MNSs(link = "logitlink", imS = NULL, ims = NULL, inS = NULL)

Arguments

link

Link function applied to the three parameters. See Links for more choices.

imS, ims, inS

Optional initial value for mS, ms and nS respectively. A NULL means they are computed internally.

Details

There are three independent parameters: m_S, m_s, n_S, say, so that n_s = 1 - m_S - m_s - n_S. We let the eta vector (transposed) be (g(m_S), g(m_s), g(n_S)) where g is the link function.

Value

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

References

Elandt-Johnson, R. C. (1971). Probability Models and Statistical Methods in Genetics, New York: Wiley.

Author

T. W. Yee

Note

The input can be a 6-column matrix of counts, where the columns are MS, Ms, MNS, MNs, NS, Ns (in order). Alternatively, the input can be a 6-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

# Order matters only:
y <- cbind(MS = 295, Ms = 107, MNS = 379, MNs = 322, NS = 102, Ns = 214)
fit <- vglm(y ~ 1, MNSs("logitlink", .25, .28, .08), trace = TRUE)
#> Iteration 1: deviance = 1.752635
#> Iteration 2: deviance = 1.752591
#> Iteration 3: deviance = 1.75259
fit <- vglm(y ~ 1, MNSs(link = logitlink), trace = TRUE, crit = "coef")
#> Iteration 1: coefficients = 
#> -1.11324317, -0.92882439, -2.43891461
#> Iteration 2: coefficients = 
#> -1.11331541, -0.92938385, -2.43952450
#> Iteration 3: coefficients = 
#> -1.1133252, -0.9293749, -2.4394867
#> Iteration 4: coefficients = 
#> -1.11332484, -0.92937527, -2.43948828
#> Iteration 5: coefficients = 
#> -1.11332486, -0.92937526, -2.43948821
Coef(fit)
#>         mS         ms         nS 
#> 0.24725155 0.28305148 0.08021066 
rbind(y, sum(y)*fitted(fit))
#>         MS       Ms      MNS      MNs        NS       Ns
#>   295.0000 107.0000 379.0000 322.0000 102.00000 214.0000
#> 1 285.3654 113.6876 394.0196 312.8744  97.79132 215.2617
sqrt(diag(vcov(fit)))
#> (Intercept):1 (Intercept):2 (Intercept):3 
#>    0.05146917    0.04870453    0.09795120