Issue with fitting Zero Inflated Poisson in R

Question

I have 755 rows of data and ~87% zeros. I'm having a hard time fitting a Zero Inflated Poisson or negative binomial (or any) regression to this data. I have attempted 4 different ways and cannot get it to work. I'm not even really sure if these are the regressions I should be using. Any help would be much appreciated. I'm also not very good at coding, which I'm sure will be obvious.

I know this is long but this is my actual data...

c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0.404749055585537, 0, 0.134916351861846, 
0, 0.149907057624273, 0, 0, 0, 0, 0, 0, 0, 0, 0.269832703723691, 
0.134916351861846, 0.134916351861846, 0, 0, 0.269832703723691, 
0, 0.269832703723691, 0, 0, 0, 0, 0, 0.134916351861846, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.112430293218205, 0, 0, 0, 
0, 0, 0, 0.367953686895943, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0.269832703723691, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0.122651228965314, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.337290879654614, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0.578212936550767, 0, 0, 0.404749055585537, 0, 0, 0, 0.269832703723691, 
0.269832703723691, 0, 0, 0.299814115248546, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0.404749055585537, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0.134916351861846, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.192737645516922, 
0.192737645516922, 0, 0, 0, 0.134916351861846, 0, 0.134916351861846, 
0, 0, 0, 0, 0, 0.404749055585537, 0.134916351861846, 0.134916351861846, 
0.337290879654614, 0, 0, 0, 0, 0.674581759309228, 0, 0.134916351861846, 
0, 0.299814115248546, 0.168645439827307, 0.449721172872819, 0, 
0, 0, 0.269832703723691, 0, 0, 0, 0, 0, 0, 0.134916351861846, 
0, 0, 0, 0.122651228965314, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.134916351861846, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0.134916351861846, 0, 0.134916351861846, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0.122651228965314, 0, 0, 0.134916351861846, 
0, 0, 0.149907057624273, 0, 0, 0, 0, 0.269832703723691, 0, 0, 
0, 0, 0, 0, 0, 0.134916351861846, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0.134916351861846, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0.134916351861846, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0.449721172872819, 0, 0, 0, 0, 0, 0, 0, 0.112430293218205, 
0, 0, 0.134916351861846, 0.539665407447383, 0.134916351861846, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0.134916351861846, 0, 0, 0.134916351861846, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0.134916351861846, 0.134916351861846, 0, 0, 0, 0, 0, 0.134916351861846, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0.269832703723691, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.134916351861846, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0.134916351861846, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.134916351861846, 
0, 0, 0, 0, 0, 0, 0, 0, 0.404749055585537, 0, 0, 0, 0.404749055585537, 
0, 0, 0.674581759309228, 0.269832703723691, 0, 0, 0, 0, 0, 0, 
0.134916351861846, 0.134916351861846, 0, 0, 0, 0, 0, 0, 0.269832703723691, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.404749055585537, 
0, 0, 0, 0, 0, 0, 0, 0.134916351861846, 0, 0, 0, 0.269832703723691, 
0.269832703723691, 0.134916351861846, 0, 0.404749055585537, 0.809498111171074, 
0, 0.134916351861846, 0.134916351861846, 1.07933081489477, 0.134916351861846, 
0, 0.269832703723691, 0, 0.94441446303292, 0.245302457930628, 
0, 0, 0, 0, 0, 0.245302457930628, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0.134916351861846, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)

These are the 4 methods I have tried today.

> hog.cpue <- hogA$hog.cpue
> fitg <- fitdist(hog.cpue, "ZIP")
Error in computing default starting values.
Error in manageparam(start.arg = start, fix.arg = fix.arg, obs = data,  : 
  Error in start.arg.default(obs, distname) : 
  Unknown starting values for distribution ZIP.

> fit_zip2 <- fitdist(hogA$hog.cpue, 'nbinom', start = list(mu = 0.293, size = 0.1)) 
<simpleError in optim(par = vstart, fn = fnobj, fix.arg = fix.arg, obs = data,     gr = gradient, ddistnam = ddistname, hessian = TRUE, method = meth,     lower = lower, upper = upper, ...): function cannot be evaluated at initial parameters>
Error in fitdist(hogA$hog.cpue, "nbinom", start = list(mu = 0.293, size = 0.1)) : 
  the function mle failed to estimate the parameters, 
                with the error code 100

> fitzip <- fitdist(hogA$hog.cpue, "ZIP", start = list(mu = 0.293, sigma = 0.1), discrete = TRUE,
+                   optim.method = "L-BFGS-B", lower = c(0, 0), upper = c(Inf, 1))
<simpleError in dZIP(c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.404749055585537, 0, 0.134916351861846, 0, 0.149907057624273, 0, 0, 0, 0, 0, 0, 0, 0, 0.269832703723691, 0.134916351861846, 0.134916351861846, 0, 0, 0.269832703723691, 0, 0.269832703723691, 0, 0, 0, 0, 0, 0.134916351861846, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.112430293218205, 0, 0, 0, 0, 0, 0, 0.367953686895943, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.269832703723691, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.122651228965314, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.337290879654614, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.578212936550767, 0, 0, 0.404749055585537, 0, 0, 0, 0.269832703723691, 0.269832703723691, 0, 0, 0.299814115248546, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.404749055585537, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.134916351861846, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.192737645516922, 0.192737645516922, 0, 0, 0, 0.134916351861846, 0, 0.134916351861846, 0, 0, 0, 0, 0, 0.404749055585537, 0.134916351861846, 0.134916351861846, 0.337290879654614, 0, 0, 0, 0, 0.674581759309228, 0, 0.134916351861846, 0, 0.299814115248546, 0.168645439827307, 0.449721172872819, 0, 0, 0, 0.269832703723691, 0, 0, 0, 0, 0, 0, 0.134916351861846, 0, 0, 0, 0.122651228965314, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.134916351861846, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.134916351861846, 0, 0.134916351861846, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.122651228965314, 0, 0, 0.134916351861846, 0, 0, 0.149907057624273, 0, 0, 0, 0, 0.269832703723691, 0, 0, 0, 0, 0, 0, 0, 0.134916351861846, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.134916351861846, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.134916351861846, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.449721172872819, 0, 0, 0, 0, 0, 0, 0, 0.112430293218205, 0, 0, 0.134916351861846, 0.539665407447383, 0.134916351861846, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.134916351861846, 0, 0, 0.134916351861846, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.134916351861846, 0.134916351861846, 0, 0, 0, 0, 0, 0.134916351861846, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.269832703723691, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.134916351861846, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.134916351861846, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.134916351861846, 0, 0, 0, 0, 0, 0, 0, 0, 0.404749055585537, 0, 0, 0, 0.404749055585537, 0, 0, 0.674581759309228, 0.269832703723691, 0, 0, 0, 0, 0, 0, 0.134916351861846, 0.134916351861846, 0, 0, 0, 0, 0, 0, 0.269832703723691, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.404749055585537, 0, 0, 0, 0, 0, 0, 0, 0.134916351861846, 0, 0, 0, 0.269832703723691, 0.269832703723691, 0.134916351861846, 0, 0.404749055585537, 0.809498111171074, 0, 0.134916351861846, 0.134916351861846, 1.07933081489477, 0.134916351861846, 0, 0.269832703723691, 0, 0.94441446303292, 0.245302457930628, 0, 0, 0, 0, 0, 0.245302457930628, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.134916351861846, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),     mu = 0, sigma = 1, log = TRUE): mu must be greater than 0 
 >
Error in fitdist(hogA$hog.cpue, "ZIP", start = list(mu = 0.293, sigma = 0.1),  : 
  the function mle failed to estimate the parameters, 
                with the error code 100
In addition: Warning messages:
1: In fitdist(hogA$hog.cpue, "ZIP", start = list(mu = 0.293, sigma = 0.1),  :
  The dZIP function should return a zero-length vector when input has length zero
2: In fitdist(hogA$hog.cpue, "ZIP", start = list(mu = 0.293, sigma = 0.1),  :
  The pZIP function should return a zero-length vector when input has length zero

> fpoisZI <- fitdist(hogA$hog.cpue, "ZIP", start=list(sigma=sum(hogA$hog.cpue == 0)/length(hogA$hog.cpue), mu=mean(hogA$hog.cpue)))
<simpleError in dZIP(c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.404749055585537, 0, 0.134916351861846, 0, 0.149907057624273, 0, 0, 0, 0, 0, 0, 0, 0, 0.269832703723691, 0.134916351861846, 0.134916351861846, 0, 0, 0.269832703723691, 0, 0.269832703723691, 0, 0, 0, 0, 0, 0.134916351861846, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.112430293218205, 0, 0, 0, 0, 0, 0, 0.367953686895943, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.269832703723691, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.122651228965314, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.337290879654614, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.578212936550767, 0, 0, 0.404749055585537, 0, 0, 0, 0.269832703723691, 0.269832703723691, 0, 0, 0.299814115248546, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.404749055585537, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.134916351861846, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.192737645516922, 0.192737645516922, 0, 0, 0, 0.134916351861846, 0, 0.134916351861846, 0, 0, 0, 0, 0, 0.404749055585537, 0.134916351861846, 0.134916351861846, 0.337290879654614, 0, 0, 0, 0, 0.674581759309228, 0, 0.134916351861846, 0, 0.299814115248546, 0.168645439827307, 0.449721172872819, 0, 0, 0, 0.269832703723691, 0, 0, 0, 0, 0, 0, 0.134916351861846, 0, 0, 0, 0.122651228965314, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.134916351861846, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.134916351861846, 0, 0.134916351861846, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.122651228965314, 0, 0, 0.134916351861846, 0, 0, 0.149907057624273, 0, 0, 0, 0, 0.269832703723691, 0, 0, 0, 0, 0, 0, 0, 0.134916351861846, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.134916351861846, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.134916351861846, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.449721172872819, 0, 0, 0, 0, 0, 0, 0, 0.112430293218205, 0, 0, 0.134916351861846, 0.539665407447383, 0.134916351861846, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.134916351861846, 0, 0, 0.134916351861846, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.134916351861846, 0.134916351861846, 0, 0, 0, 0, 0, 0.134916351861846, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.269832703723691, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.134916351861846, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.134916351861846, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.134916351861846, 0, 0, 0, 0, 0, 0, 0, 0, 0.404749055585537, 0, 0, 0, 0.404749055585537, 0, 0, 0.674581759309228, 0.269832703723691, 0, 0, 0, 0, 0, 0, 0.134916351861846, 0.134916351861846, 0, 0, 0, 0, 0, 0, 0.269832703723691, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.404749055585537, 0, 0, 0, 0, 0, 0, 0, 0.134916351861846, 0, 0, 0, 0.269832703723691, 0.269832703723691, 0.134916351861846, 0, 0.404749055585537, 0.809498111171074, 0, 0.134916351861846, 0.134916351861846, 1.07933081489477, 0.134916351861846, 0, 0.269832703723691, 0, 0.94441446303292, 0.245302457930628, 0, 0, 0, 0, 0, 0.245302457930628, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.134916351861846, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),     sigma = 0.426547699594046, mu = -0.020557328452897, log = TRUE): mu must be greater than 0 
 >
Error in fitdist(hogA$hog.cpue, "ZIP", start = list(sigma = sum(hogA$hog.cpue ==  : 
  the function mle failed to estimate the parameters, 
                with the error code 100
In addition: Warning messages:
1: In fitdist(hogA$hog.cpue, "ZIP", start = list(sigma = sum(hogA$hog.cpue ==  :
  The dZIP function should return a zero-length vector when input has length zero
2: In fitdist(hogA$hog.cpue, "ZIP", start = list(sigma = sum(hogA$hog.cpue ==  :
  The pZIP function should return a zero-length vector when input has length zero

Answer 1

For a poisson distribution, zero inflated or not, the values have to be positive and discrete, ie integers, no decimals.. I have no clue whether the value you have is intended.

Once you have sorted out the values, you can consider using a glm based method:

library(pscl)

x = rpois(1000,20)
x[sample(length(x),200)] = 0
# fits intercept only model
fit = zeroinfl(x ~ 1,dist="poisson")

estimated_mean = exp(coefficients(fit)["count_(Intercept)"])
count_(Intercept) 
         20.14875

estimated_missing = coefficients(fit)["zero_(Intercept)"]
# it's a logit you need to convert to prob
estimated_missing = exp(estimated_missing)/(1+exp(estimated_missing))
zero_(Intercept) 
             0.2 

If you have decimals because it's a rate, what you need is an offset , so assume an underlying average rate of 0.5, and a missing of 0.2:

n = rep(1000 * 1:5 , each=100)
x = rpois(length(n),0.5*n)
x[sample(length(x),0.2*length(n))] = 0
# fits intercept only model
fit = zeroinfl(x ~ 1,dist="poisson",offset=log(n))

And you repeat the above, and get back 0.5 as coefficient and 0.2 as rate of missing.