R: Bivariate Probit Model

Binom2.rho {VGAM} | R Documentation

## Bivariate Probit Model

### Description

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

### Usage

    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

### See Also

`binom2.rho`.

### Examples

    (myrho <- rhobit(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 = probit(-2+4*x2, inverse = TRUE),
                              mu2 = probit(-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)

[Package VGAM version 1.0-3 Index]