Description Usage Arguments Details Value Note Author(s) See Also Examples

Computes the `inv.chisqMlink`

transformation, its inverse and
the first two derivatives.

1 2 |

`theta` |
Numeric or character. This is |

`bvalue, inverse, deriv, short, tag` |
See |

This link functions models the mean of the
inverse chi–squared distribution,
`inv.chisqff`

.

It is defined as

* η = -log(df - 2)*

where *df* denotes the (non–negative) degrees of freedom, as in
`inv.chisqff`

.

Notice, however, that *df > 2* is required for the mean of
this distribution to be real. Consequently, the domain set for
`df`

for this link function is *(2, ∞)*.

Numerical values of *df* out of range will
result in `NA`

or `NaN`

.

For `deriv = 0`

, the `inv.chisqMlink`

transformation of
`theta`

when `inverse = FALSE`

.
If `inverse = TRUE`

, then the inverse `exp(-theta) + 2`

.

For `deriv = 1`

,
*d* `eta`

/ *d* `theta`

when `inverse = FALSE`

.
If `inverse = TRUE`

, then
*d* `theta`

/ *d* `eta`

as a function of
`theta`

.

When `deriv = 2`

, the second derivatives in
terms of `theta`

are returned.

Numerical instability may occur for values `theta`

too large or
possibly, too close to 2. Use argument `bvalue`

to replace them
before computing the link.

If `theta`

is character, then arguments `inverse`

and
`deriv`

are ignored. See `Links`

for further details.

V. Miranda and Thomas W. Yee.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 | ```
## E1. Modelling the mean of the exponential distribution ##
set.seed(17010502)
dof <- 2.5
isq.data <- data.frame(x2 = runif(100, 0, 1))
isq.data <- transform(isq.data, y = rinv.chisq(n = 100, df = dof + x2))
hist(isq.data$y)
fit.inv <- vglm(y ~ x2, family = inv.chisqff(link = "inv.chisqMlink"),
data = isq.data, trace = TRUE )
coef(fit.inv, matrix = TRUE)
summary(fit.inv)
## E3. Special values in a matrix ##
(theta <- matrix(c(Inf, -Inf, NA, NaN, 1 , 2, 3, 4), ncol = 4, nrow = 2))
inv.chisqMlink(theta = theta) ## NaNs for df = theta <= 2
## E2. inv.chisqMlink() and its inverse ##
theta <- 0.1 + 1:5 # dof = df
my.diff <- theta - inv.chisqMlink(inv.chisqMlink(theta = theta), inverse =TRUE)
summary(my.diff) # Zero
``` |

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