Logarithmic link function (for estimation with maxlogL object)

log_link object provides a way to implement logarithmic link function that maxlogL needs to perform estimation. See documentation for maxlogL for further information on parameter estimation and implementation of link objects.

Usage

log_link()

Value

A list with logit link function, its inverse and its name.

Details

log_link is part of a family of generic functions with no input arguments that defines and returns a list with details of the link function:

1. name: a character string with the name of the link function.

2. g: implementation of the link function as a generic function in R.

3. g_inv: implementation of the inverse link function as a generic function in R.

There is a way to add new mapping functions. The user must specify the details aforesaid.

See also

maxlogL

Other link functions: NegInv_link(), logit_link()

Examples

# One parameters of normal distribution mapped with logarithmic function
x <- rnorm(n = 10000, mean = 50, sd = 4)
theta_2 <- maxlogL( x = x, link = list(over = "sd",
                                       fun = "log_link") )
summary(theta_2)
#> _______________________________________________________________
#> Optimization routine: nlminb 
#> Standard Error calculation: Hessian from optim 
#> _______________________________________________________________
#>        AIC      BIC
#>   56230.86 56245.28
#> _______________________________________________________________
#>      Estimate  Std. Error Z value Pr(>|z|)    
#> mean  49.95956    0.04025  1241.4   <2e-16 ***
#> sd     4.02451    0.02846   141.4   <2e-16 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> _______________________________________________________________
#> Note: p-values valid under asymptotic normality of estimators 
#> ---

# Link function name
fun <- log_link()$name
print(fun)
#> [1] "log"

# Link function
g <- log_link()$g
curve(g(x), from = 0, to = 1)


# Inverse link function
ginv <- log_link()$g_inv
curve(ginv(x), from = -5, to = 5)