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rbinaryglmpoisson

Error when running poisson regression with a binary outcome

I am trying to run a poisson regression to predict a common binary outcome.

This is my first attempt at using dput - if I have used it inappropriately, please let me know so I can correct it.

Example data:

df <- structure(list(id = 1:30, sex = structure(c(1L, 2L, 2L, 2L, 2L, 
2L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 
2L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 1L), .Label = c("Female", "Male"
), class = "factor"), migStat = structure(c(1L, 2L, 1L, 1L, 1L, 
1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 
1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L), .Label = c("Australian-born", 
"Migrant"), class = "factor"), mhAreaBi = structure(c(1L, 1L, 
1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 2L, 
1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L), .Label = c("Metropolitan", 
"Regional"), class = "factor"), empStatBi = structure(c(2L, 2L, 
1L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 2L, 1L, 
2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L), .Label = c("Student / employed", 
"Unemployed"), class = "factor"), pensBenBi = structure(c(1L, 
2L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 2L, 
1L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 1L, 2L), .Label = c("No benefit", 
"In receipt of pension benefit"), class = "factor"), maritStatBi = structure(c(2L, 
2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 
2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L), .Label = c("Married (including de facto)", 
"Not married"), class = "factor"), cto = structure(c(1L, 2L, 
2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 
2L, 1L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 2L, 2L), .Label = c("No", 
"Yes"), class = "factor")), .Names = c("id", "sex", "migStat", 
"mhAreaBi", "empStatBi", "pensBenBi", "maritStatBi", "cto"), row.names = c(NA, 
-30L), class = "data.frame")

When running the regression using glm in R, I receive an error:

fit <- glm(cto ~ sex + migStat + mhAreaBi + empStatBi + pensBenBi + maritStatBi, df, family = poisson)

Error in if (any(y < 0)) stop("negative values not allowed for the 'Poisson' family") : 
  missing value where TRUE/FALSE needed
In addition: Warning message:
In Ops.factor(y, 0) : ‘<’ not meaningful for factors

The same error has been explained briefly in this thread:

Because the "<" operator is not defined for factors the result that is passed to if is of length 0. Setting the factor variable on the RHS and using the integer values on hte LHS succeeds.

The error does not appear when I convert the outcome to an integer; however, this:

  1. seems to defeat the purpose of predicting a binary outcome (unless a numeric variable with range 0-1 is treated the same as a factor variable with two levels); and
  2. does not seem necessary (at least according to this post, which uses geeglm from geepack to predict a binary outcome [unfortunately, I receive the same error when I adapt the code to my own dataset])

Questions:

Could I receive further explanation of the error?

If I convert my outcome to an integer with range 0-1, will glm treat it the same as a binary variable? If not, is there an approach better suited to running a regression for a common binary outcome?

Solution

  • I think the best option here is:

    df$cto_binary <- as.numeric(df$cto == "Yes")
fit <- glm(cto_binary ~ sex + migStat + mhAreaBi + empStatBi + pensBenBi + maritStatBi, 
           df, family = poisson)

    As this way you explicitly show in your code what will be a 1/success in your binary outcome and don't get tripped up by things like the ordering of factor levels. Note that in R as.numeric(c(FALSE, TRUE)) gives c(0, 1), so you always know what you're going to get from a logical comparison.