R/ZINBI.R

In gamlss.dist: Distributions for Generalized Additive Models for Location Scale and Shape

# 30/4/10corrected
# 28/2/17 the q function is corrected thanks to Prof. Cajo J.F. ter Braak 
# ---------------------------------------------------------------------------------------
# zero inflated negative binomial type I (with probability y=0 is nu) 01/03/10
# ---------------------------------------------------------------------------------------
ZINBI = function (mu.link = "log", sigma.link = "log", nu.link = "logit") 
{
  mstats <- checklink("mu.link", "ZINBI", substitute(mu.link), 
                      c("inverse", "log", "identity"))
  dstats <- checklink("sigma.link", "ZINBI", substitute(sigma.link), 
                      c("inverse", "log", "identity"))
  vstats <- checklink("nu.link", "ZINBI", substitute(nu.link), 
                      c("logit", "probit", "cloglog", "log", "own"))
  
  structure(list(family = c("ZINBI", "Zero inflated negative binomial type I"),
                 parameters = list(mu = TRUE, sigma = TRUE, nu = TRUE),
                 nopar = 3,
                 type = "Discrete",
                 mu.link = as.character(substitute(mu.link)),
                 sigma.link = as.character(substitute(sigma.link)), 
                 nu.link = as.character(substitute(nu.link)),
                 mu.linkfun = mstats$linkfun, 
                 sigma.linkfun = dstats$linkfun,
                 nu.linkfun = vstats$linkfun, 
                 mu.linkinv = mstats$linkinv,
                 sigma.linkinv = dstats$linkinv, 
                 nu.linkinv = vstats$linkinv,
                 mu.dr = mstats$mu.eta,
                 sigma.dr = dstats$mu.eta, 
                 nu.dr = vstats$mu.eta,
                 dldm = function(y,mu,sigma,nu) {dldm0 <- (1-nu)*((nu+(1-nu)*dNBI(0,mu,sigma))^(-1))*dNBI(0,mu,sigma)*NBI()$dldm(0,mu,sigma)
                 dldm <- ifelse(y==0, dldm0, NBI()$dldm(y,mu,sigma))
                 dldm}, 
                 d2ldm2 = function(y,mu,sigma,nu) {dldm0 <- (1-nu)*((nu+(1-nu)*dNBI(0,mu,sigma))^(-1))*dNBI(0,mu,sigma)*NBI()$dldm(0,mu,sigma)
                 dldm <- ifelse(y==0, dldm0, NBI()$dldm(y,mu,sigma))
                 d2ldm2 <- -dldm*dldm
                 d2ldm2 <- ifelse(d2ldm2 < -1e-15, d2ldm2,-1e-15)    
                 d2ldm2},
                 dldd = function(y,mu,sigma,nu) {dldd0 <- (1-nu)*((nu+(1-nu)*dNBI(0,mu,sigma))^(-1))*dNBI(0,mu,sigma)*NBI()$dldd(0,mu,sigma)
                 dldd <- ifelse(y==0, dldd0, NBI()$dldd(y,mu,sigma))
                 dldd}, 
                 d2ldd2 = function(y,mu,sigma,nu) {dldd0 <- (1-nu)*((nu+(1-nu)*dNBI(0,mu,sigma))^(-1))*dNBI(0,mu,sigma)*NBI()$dldd(0,mu,sigma)
                 dldd <- ifelse(y==0, dldd0, NBI()$dldd(y,mu,sigma))
                 d2ldd2 <- -dldd^2  
                 d2ldd2 <- ifelse(d2ldd2 < -1e-15, d2ldd2,-1e-15)  
                 d2ldd2}, 
                 dldv = function(y,mu,sigma,nu) {dldv0 <- ((nu+(1-nu)*dNBI(0,mu,sigma))^(-1))*(1-dNBI(0,mu,sigma))
                 dldv <- ifelse(y==0, dldv0, -1/(1-nu))
                 dldv}, 
                 d2ldv2 = function(y,mu,sigma,nu) {dldv0 <- ((nu+(1-nu)*dNBI(0,mu,sigma))^(-1))*(1-dNBI(0,mu,sigma))
                 dldv <- ifelse(y==0, dldv0, -1/(1-nu))      
                 d2ldv2 <- -dldv^2
                 d2ldv2 <- ifelse(d2ldv2 < -1e-15, d2ldv2,-1e-15)  
                 d2ldv2},
                 d2ldmdd = function(y,mu,sigma,nu) {dldm0 <- (1-nu)*((nu+(1-nu)*dNBI(0,mu,sigma))^(-1))*dNBI(0,mu,sigma)*NBI()$dldm(0,mu,sigma)
                 dldm <- ifelse(y==0, dldm0, NBI()$dldm(y,mu,sigma))
                 dldd0 <- (1-nu)*((nu+(1-nu)*dNBI(0,mu,sigma))^(-1))*dNBI(0,mu,sigma)*NBI()$dldd(0,mu,sigma)
                 dldd <- ifelse(y==0, dldd0, NBI()$dldd(y,mu,sigma))
                 d2ldm2<--dldm*dldd
                 d2ldm2}, 
                 d2ldmdv = function(y,mu,sigma,nu) {  #partial derivate of log-density respect to mu and alpha
                   dldm0 <- (1-nu)*((nu+(1-nu)*dNBI(0,mu,sigma))^(-1))*dNBI(0,mu,sigma)*NBI()$dldm(0,mu,sigma)
                   dldm <- ifelse(y==0, dldm0, NBI()$dldm(y,mu,sigma))
                   dldv0 <- ((nu+(1-nu)*dNBI(0,mu,sigma))^(-1))*(1-dNBI(0,mu,sigma))
                   dldv <- ifelse(y==0, dldv0, -1/(1-nu))          
                   d2ldmdv <- -dldm*dldv
                   d2ldmdv
                 },
                 
                 d2ldddv = function(y,mu,sigma,nu) {   #partial derivate of log-density respect to sigma and alpha
                   dldd0 <- (1-nu)*((nu+(1-nu)*dNBI(0,mu,sigma))^(-1))*dNBI(0,mu,sigma)*NBI()$dldd(0,mu,sigma)
                   dldd <- ifelse(y==0, dldd0, NBI()$dldd(y,mu,sigma))
                   dldv0 <- ((nu+(1-nu)*dNBI(0,mu,sigma))^(-1))*(1-dNBI(0,mu,sigma))
                   dldv <- ifelse(y==0, dldv0, -1/(1-nu))            
                   d2ldddv <- -dldd*dldv
                   d2ldddv
                 },        
                 G.dev.incr  = function(y,mu,sigma,nu,...) -2*dZINBI(y, mu = mu, sigma = sigma, nu=nu, log = TRUE), 
                 rqres = expression(
                   rqres(pfun="pZINBI", type="Discrete", ymin=0, y=y, mu=mu, sigma=sigma, nu=nu)
                 ), 
                 mu.initial = expression(mu <- (y + mean(y))/2),            
                 ##           mu.initial = expression(mu <-  y+0.5),
                 sigma.initial = expression(
                   sigma <- rep( max( ((var(y)-mean(y))/(mean(y)^2)),0.1),length(y))),
                 nu.initial = expression(nu <- rep(((sum(y==0)/length(y))+0.01)/2, length(y))),# max((sum(y==0)/length(y))-0.1,.01)
                 mu.valid = function(mu) all(mu > 0) , 
                 sigma.valid = function(sigma)  all(sigma > 0), 
                 nu.valid = function(nu) all(nu > 0 & nu < 1),           
                 y.valid = function(y)  all(y >= 0),
                 mean = function(mu, sigma, nu) (1- nu) * mu,
                 variance = function(mu, sigma, nu)  mu * (1- nu) + mu^2 * (1 - nu) * (sigma + nu)
  ),
  class = c("gamlss.family","family"))
}
#-------------------------------------------------------------------------------------------
dZINBI<-function(x, mu = 1, sigma = 1, nu = 0.3, log = FALSE)
{ 
  if (any(mu <= 0) )  stop(paste("mu must be greater than 0 ", "\n", "")) 
  if (any(sigma <= 0) )  stop(paste("sigma must be greater than 0 ", "\n", "")) 
  if (any(nu <= 0)|any(nu >= 1))  stop(paste("nu must be between 0 and 1 ", "\n", ""))
 # if (any(x < 0) )  stop(paste("x must be >=0", "\n", ""))  
  ly <- max(length(x),length(mu),length(sigma),length(nu)) 
  x <- rep(x, length = ly)      
  sigma <- rep(sigma, length = ly)
  mu <- rep(mu, length = ly)   
  nu <- rep(nu, length = ly) 
  fy <- dNBI(x, mu = mu, sigma=sigma, log = T)
  logfy <- rep(0, length(x))
  logfy <- ifelse((x==0), log(nu+(1-nu)*exp(fy)), (log(1-nu) + fy ))          
  if(log == FALSE) fy2 <- exp(logfy) else fy2 <- logfy
  fy2 <- ifelse(x < 0, 0, fy2) 
  fy2
}
#------------------------------------------------------------------------------------------
pZINBI <- function(q, mu = 1, sigma = 1, nu = 0.3, lower.tail = TRUE, log.p = FALSE)
{     
  if (any(mu <= 0) )  stop(paste("mu must be greater than 0 ", "\n", "")) 
  if (any(sigma <= 0) )  stop(paste("sigma must be greater than 0 ", "\n", "")) 
  if (any(nu <= 0)|any(nu >= 1))  #In this parametrization  nu = alpha
    stop(paste("nu must be between 0 and 1 ", "\n", ""))
#if (any(q < 0) )  stop(paste("y must be >=0", "\n", ""))
  ly <- max(length(q),length(mu),length(sigma),length(nu)) 
  q <- rep(q, length = ly)      
  sigma <- rep(sigma, length = ly)
  mu <- rep(mu, length = ly)   
  nu <- rep(nu, length = ly) 
  cdf <- pNBI(q, mu = mu, sigma=sigma)
  cdf <- nu + (1-nu)*cdf
  if(lower.tail == TRUE) cdf <- cdf else cdf <-1-cdf
  if(log.p==FALSE) cdf <- cdf else cdf <- log(cdf) 
  cdf <- ifelse(q < 0, 0, cdf) 
  cdf
}
#------------------------------------------------------------------------------------------
qZINBI <- function(p, mu = 1, sigma = 1, nu = 0.3, lower.tail = TRUE, log.p = FALSE)
{      
  if (any(mu <= 0) )  stop(paste("mu must be greater than 0 ", "\n", "")) 
  if (any(sigma <= 0) )  stop(paste("sigma must be greater than 0 ", "\n", ""))
  if (any(nu <= 0)|any(nu >= 1))  #In this parametrization  nu = alpha
    stop(paste("nu must be between 0 and 1 ", "\n", ""))
  if (any(p < 0) | any(p > 1))  stop(paste("p must be between 0 and 1", "\n", ""))    
  if (log.p == TRUE) p <- exp(p)   else p <- p
  if (lower.tail == TRUE)  p <- p  else p <- 1 - p
  ly <- max(length(p),length(mu),length(sigma),length(nu)) 
  p <- rep(p, length = ly)      
  sigma <- rep(sigma, length = ly)
  mu <- rep(mu, length = ly)   
  nu <- rep(nu, length = ly) 
  pnew <- (p-nu)/(1-nu)-(1e-7)# added 28-2-17
  pnew <- ifelse((pnew > 0 ),pnew, 0)
  q <- qNBI(pnew, mu = mu, sigma=sigma)           
  q
}
#------------------------------------------------------------------------------------------
rZINBI <- function(n, mu = 1, sigma = 1, nu = 0.3)
{ 
  if (any(mu <= 0) )  stop(paste("mu must be greater than 0 ", "\n", "")) 
  if (any(sigma <= 0) )  stop(paste("sigma must be greater than 0 ", "\n", "")) 
  if (any(nu <= 0)|any(nu >= 1))  #In this parametrization  nu = alpha
    stop(paste("nu must be between 0 and 1 ", "\n", ""))
  if (any(n <= 0))  stop(paste("n must be a positive integer", "\n", ""))  
  n <- ceiling(n)
  p <- runif(n)
  r <- qZINBI(p, mu=mu, sigma=sigma, nu=nu)
  as.integer(r)
}
#------------------------------------------------------------------------------------------