Logit link function (for estimation with maxlogL object)

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

Usage

logit_link()

Value

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

Details

logit_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(), log_link()

Author

Jaime Mosquera Gutiérrez, jmosquerag@unal.edu.co

Examples

#--------------------------------------------------------------------------------
# Estimation of proportion in binomial distribution with 'logit' function
# 10 trials, probability of success equals to 30%)
N <- rbinom(n = 100, size = 10, prob = 0.3)
phat <- maxlogL(x = N, dist = 'dbinom', fixed = list(size=10),
                link = list(over = "prob", fun = "logit_link"))
summary(phat)
#> _______________________________________________________________
#> Optimization routine: nlminb 
#> Standard Error calculation: Hessian from optim 
#> _______________________________________________________________
#>        AIC      BIC
#>   350.0497 350.0497
#> _______________________________________________________________
#>      Estimate  Std. Error Z value Pr(>|z|)    
#> prob   0.30500    0.01456   20.95   <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 <- logit_link()$name
print(fun)
#> [1] "logit"

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


# Inverse link function
ginv <- logit_link()$g_inv
curve(ginv(x), from = -10, to = 10)


#--------------------------------------------------------------------------------