binom2.orUC: Bivariate Odds Ratio Model

In VGAM: Vector Generalized Linear and Additive Models

Bivariate Odds Ratio Model

Description

Density and random generation for a bivariate binary regression model using an odds ratio as the measure of dependency.

Usage

rbinom2.or(n, mu1,
    mu2 = if (exchangeable) mu1 else
    stop("argument 'mu2' not specified"),
    oratio = 1, exchangeable = FALSE, tol = 0.001,
    twoCols = TRUE, colnames = if (twoCols) c("y1","y2") else
    c("00", "01", "10", "11"),
    ErrorCheck = TRUE)
dbinom2.or(mu1, mu2 = if (exchangeable) mu1 else
    stop("'mu2' not specified"),
    oratio = 1, exchangeable = FALSE, tol = 0.001,
    colnames = c("00", "01", "10", "11"), ErrorCheck = TRUE)

Arguments

n	number of observations. Same as in runif. The arguments mu1, mu2, oratio are recycled to this value.
mu1, mu2	The marginal probabilities. Only mu1 is needed if exchangeable = TRUE. Values should be between 0 and 1.
oratio	Odds ratio. Must be numeric and positive. The default value of unity means the responses are statistically independent.
exchangeable	Logical. If TRUE, the two marginal probabilities are constrained to be equal.
twoCols	Logical. If TRUE, then a n \times 2 matrix of 1s and 0s is returned. If FALSE, then a n \times 4 matrix of 1s and 0s is returned.
colnames	The dimnames argument of matrix is assigned list(NULL, colnames).
tol	Tolerance for testing independence. Should be some small positive numerical value.
ErrorCheck	Logical. Do some error checking of the input parameters?

Details

The function rbinom2.or generates data coming from a bivariate binary response model. The data might be fitted with the VGAM family function binom2.or.

The function dbinom2.or does not really compute the density (because that does not make sense here) but rather returns the four joint probabilities.

Value

The function rbinom2.or returns either a 2 or 4 column matrix of 1s and 0s, depending on the argument twoCols.

The function dbinom2.or returns a 4 column matrix of joint probabilities; each row adds up to unity.

Author(s)

T. W. Yee

See Also

binom2.or.

Examples

nn <- 1000  # Example 1
ymat <- rbinom2.or(nn, mu1 = logitlink(1, inv = TRUE),
                   oratio = exp(2), exch = TRUE)
(mytab <- table(ymat[, 1], ymat[, 2], dnn = c("Y1", "Y2")))
(myor <- mytab["0","0"] * mytab["1","1"] / (mytab["1","0"] *
         mytab["0","1"]))
fit <- vglm(ymat ~ 1, binom2.or(exch = TRUE))
coef(fit, matrix = TRUE)

bdata <- data.frame(x2 = sort(runif(nn)))  # Example 2
bdata <- transform(bdata,
           mu1 = logitlink(-2 + 4 * x2, inverse = TRUE),
           mu2 = logitlink(-1 + 3 * x2, inverse = TRUE))
dmat <- with(bdata, dbinom2.or(mu1 = mu1, mu2 = mu2,
                               oratio = exp(2)))
ymat <- with(bdata, rbinom2.or(n = nn, mu1 = mu1, mu2 = mu2,
                               oratio = exp(2)))
fit2 <- vglm(ymat ~ x2, binom2.or, data = bdata)
coef(fit2, matrix = TRUE)
## Not run: 
matplot(with(bdata, x2), dmat, lty = 1:4, col = 1:4,
        main = "Joint probabilities", ylim = 0:1, type = "l",
        ylab = "Probabilities", xlab = "x2", las = 1)
legend("top", lty = 1:4, col = 1:4,
       legend = c("1 = (y1=0, y2=0)", "2 = (y1=0, y2=1)",
                  "3 = (y1=1, y2=0)", "4 = (y1=1, y2=1)"))

## End(Not run)

VGAM documentation built on Sept. 18, 2024, 9:09 a.m.