Why is betareg() giving "invalid dependent variable" error?

Question

I am trying to run a beta regression using the betareg package and I am using the following script:

require(betareg)



betareg(response ~ predictor
                    ,na.action = na.omit
                    ,weights = sqrt(total)
                    , data = ex.dat.new) 

And R returns this error:

Error in betareg(response ~ predictor, na.action = na.omit, weights = sqrt(total),  : 
  invalid dependent variable, all observations must be in (0, 1)

However, the dependent variable (named "response" here) IS constrained between 0 and 1.

Why is R returning this error and how can I correct it?

Data:

    dput(ex.dat.new)
    structure(list(predictor = structure(c(2L, 2L, 2L, 2L, 2L, 2L, 
    3L, 3L, 3L, 3L, 3L, 3L, 4L, 4L, 4L, 4L, 4L, 4L, 5L, 5L, 5L, 5L, 
    5L, 5L, 6L, 6L, 6L, 6L, 6L, 6L, 7L, 7L, 7L, 7L, 7L, 7L, 8L, 8L, 
    8L, 8L, 8L, 8L, 9L, 9L, 9L, 9L, 9L, 9L, 10L, 10L, 10L, 10L, 10L, 
   10L, 1L, 1L, 1L, 1L, 1L, 1L, 11L, 11L, 11L, 11L, 11L, 11L, 12L, 
   12L, 12L, 12L, 12L, 12L), .Label = c("Asoca", "bida", "coma", 
   "cyro", "melo", "oeno", "pano", "sena", "sida", "soam", "soda", 
   "verb"), class = "factor"), response = c(1, 1, 0.981270985, 1, 
   0.911258698, 1, 0.249252611, 0.671639842, 0.575247687, 0.943358751, 
   0.470602887, 0.875696109, 1, 1, 1, 1, 1, 1, 1, 0.131273134, 0.479774791, 
   0.497419936, 0.54108693, 0.838144234, 1, 1, 1, 1, 0.868294819, 
   1, 1, 1, 1, 1, 1, 1, 0.305218209, 1, 1, 1, 1, 0.095933078, 1, 
   1, 1, 1, 1, 1, 0.217037264, 0.410118055, 0.173707357, 0.200733967, 
   0.469833694, 0.208464348, 0.407013896, 0.846212651, 0.299872736, 
   0.965380984, 0.251676335, 0.806683955, 1, 1, 1, 1, 1, 1, 0.934555905, 
   0.564142452, 1, NA, 1, 0.029682211), total = c(109.98, 46.834, 
   293.662, 197.144, 59.927, 7.33, 70.579, 222.125, 201.767, 43.802, 
   417.541, 143.117, 70.658, 167.073, 666.542, 49.872, 258.847, 
   93.83, 56.036, 116.17, 378.5276, 12.209, 163.58, 182.329, 209.913, 
   411.1590278, 1003.223, 29.3499744, 95.896, 160.8383437, 124.437, 
   52.017, 187.045, 132.032, 67.188, 86.12, 171.189, 21.27, 29.69, 
   106.1, 77.14, 56.185, 68.97225736, 17.475, 539.401, 5.9, 49.256, 
   12.854, 342.015, 250.562, 2177.605021, 748.1001011, 1035.573167, 
   275.414, 660.717, 323.102, 1273.727, 285.97, 212.368, 140.366, 
   420.044, 54.295, 802.118, 150.612, 157.469, 85.275, 368.131, 
   35.998, 349.624, 0, 13.207, 191.731)), class = "data.frame", row.names = c(NA, 
  -72L))

Answer 1

The error message posted by R tells you what the problem is:

invalid dependent variable, all observations must be in (0,1)

In other words, your dependent variable should take values that are strictly greater than 0 and strictly less than 1; they cannot be equal to 0 or equal to 1.

In your case, you have several response values that are equal to 1, so R throws the invalid response variable message.

Beta regression would work for response values in (0,1); because you have response values in (0,1] (with a fair number of these values equal to 1), you will need to consider one-inflated beta regression. If your response had values in [0,1) (with a fair number of these values equal to 0), you could consider a zero-inflated beta regression if that made sense for your data - based on Dr. Zeileis response to your question, you might not be able to consider this type of model for your data. See the 2012 article A general class of zero-or-one inflated beta regression models by Ospina and Ferrari for further details on these types of models.

You can fit a one inflated regression model in R using the gamlss and gamlss.dist packages, for example. The latter includes a BEOI() function which defines the one-inflated beta distribution, a three parameter distribution, for a gamlss.family object to be used in GAMLSS fitting using the function gamlss(). (It also includes a BEZI() function for a zero-inflated beta distribution.). Your most complete regression model would be specified like this:

library(gamlss)

library(gamlss.dist)

model <- gamlss(response ~ 1 + predictor, 
                sigma.formula = ~ 1 + predictor, 
                nu.formula = ~ 1 + predictor, 
                family=BEOI, 
                data=yourdata)

See http://www.gamlss.com/wp-content/uploads/2018/01/InflatedDistributioninR.pdf.

Answer 2

As the error message tells you betareg() requires responses to be greater than $0$ and less than $1$, i.e., the open interval $(0, 1)$. That is the support of the beta distribution which is modeled by beta regression. Your data has a very high share of $1$ observations (40 out of 71, excluding the NA) and consequently does not seem to be suitable for beta regression.

Some authors suggest to use a 1-inflated beta regression in such scenarios but I doubt that this is the right model in your case. If you look at the data:

plot(response ~ predictor, data = ex.dat.new)

Then you see that many groups have no variation at all in the response (cyro, pano, sida, soda) and others have very little variation in the response (bida, oeno). First, modeling something as stochastic that has no variation at all is challenging without further assumptions. Second, you need to consider carefully what exactly you want to model. The details will depend on your specific setup and what these data mean etc.