Zero-one beta response family

zero_one_beta() defines a one-response distribution for continuous proportions on [0, 1] when exact zeroes or ones are structural outcomes rather than binomial denominator outcomes.

Usage

zero_one_beta()

Value

A drm_family object.

Details

The implemented fixed-effect contract is logit(mu) = eta_mu, log(sigma) = eta_sigma, logit(zoi) = eta_zoi, and logit(coi) = eta_coi. Here zoi is the probability that an observation is exactly 0 or 1, and coi is the conditional probability of an exact 1 given that the observation is on the boundary. Interior observations follow the same beta mean-scale contract as beta(), with internal precision phi = 1 / sigma^2.

fitted() returns the unconditional response mean (1 - zoi) * mu + zoi * coi. Ordinary unlabelled random intercepts and independent numeric slopes such as (1 | id) and (0 + x | id) may enter mu. Correlated or labelled mu slopes, sigma, zoi, or coi random effects, structured effects, covariance blocks, and denominator syntax remain unsupported.

Examples

zero_one_beta()
#> $name
#> [1] "zero_one_beta"
#> 
#> $family
#> [1] "zero_one_beta"
#> 
#> $n_response
#> [1] 1
#> 
#> $dpars
#> [1] "mu"    "sigma" "zoi"   "coi"  
#> 
#> $links
#>      mu   sigma     zoi     coi 
#> "logit"   "log" "logit" "logit" 
#> 
#> attr(,"class")
#> [1] "drm_family"