# binom2.orUC: Bivariate Odds Ratio Model In VGAM: Vector Generalized Linear and Additive Models

 Binom2.or R Documentation

## 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

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. 19, 2023, 9:06 a.m.