# binom2.rhoUC: Bivariate Probit Model In VGAM: Vector Generalized Linear and Additive Models

## Description

Density and random generation for a bivariate probit model. The correlation parameter rho is the measure of dependency.

## Usage

 ```1 2 3 4 5 6 7 8 9``` ```rbinom2.rho(n, mu1, mu2 = if (exchangeable) mu1 else stop("argument 'mu2' not specified"), rho = 0, exchangeable = FALSE, twoCols = TRUE, colnames = if (twoCols) c("y1","y2") else c("00", "01", "10", "11"), ErrorCheck = TRUE) dbinom2.rho(mu1, mu2 = if (exchangeable) mu1 else stop("'mu2' not specified"), rho = 0, exchangeable = FALSE, colnames = c("00", "01", "10", "11"), ErrorCheck = TRUE) ```

## Arguments

 `n` number of observations. Same as in `runif`. The arguments `mu1`, `mu2`, `rho` are recycled to this value. `mu1, mu2` The marginal probabilities. Only `mu1` is needed if `exchangeable = TRUE`. Values should be between 0 and 1. `rho` The correlation parameter. Must be numeric and lie between -1 and 1. The default value of zero means the responses are uncorrelated. `exchangeable` Logical. If `TRUE`, the two marginal probabilities are constrained to be equal. `twoCols` Logical. If `TRUE`, then a n * 2 matrix of 1s and 0s is returned. If `FALSE`, then a n * 4 matrix of 1s and 0s is returned. `colnames` The `dimnames` argument of `matrix` is assigned `list(NULL, colnames)`. `ErrorCheck` Logical. Do some error checking of the input parameters?

## Details

The function `rbinom2.rho` generates data coming from a bivariate probit model. The data might be fitted with the VGAM family function `binom2.rho`.

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

## Value

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

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

## Author(s)

T. W. Yee

`binom2.rho`.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20``` ```(myrho <- rhobitlink(2, inverse = TRUE)) # Example 1 ymat <- rbinom2.rho(nn <- 2000, mu1 = 0.8, rho = myrho, exch = TRUE) (mytab <- table(ymat[, 1], ymat[, 2], dnn = c("Y1", "Y2"))) fit <- vglm(ymat ~ 1, binom2.rho(exch = TRUE)) coef(fit, matrix = TRUE) bdata <- data.frame(x2 = sort(runif(nn))) # Example 2 bdata <- transform(bdata, mu1 = probitlink(-2+4*x2, inverse = TRUE), mu2 = probitlink(-1+3*x2, inverse = TRUE)) dmat <- with(bdata, dbinom2.rho(mu1, mu2, myrho)) ymat <- with(bdata, rbinom2.rho(nn, mu1, mu2, myrho)) fit2 <- vglm(ymat ~ x2, binom2.rho, data = bdata) coef(fit2, matrix = TRUE) ## Not run: matplot(with(bdata, x2), dmat, lty = 1:4, col = 1:4, type = "l", main = "Joint probabilities", ylim = 0:1, lwd = 2, ylab = "Probability") legend(x = 0.25, y = 0.9, lty = 1:4, col = 1:4, lwd = 2, 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) ```