# GLM.jl, error on Binomial distribution, fixed number of trials
**URL:** https://discourse.julialang.org/t/glm-jl-error-on-binomial-distribution-fixed-number-of-trials/10767
**Category:** Statistics
**Tags:** glm
**Created:** [May 7, 2018, 9:22pm UTC](https://discourse.julialang.org/t/glm-jl-error-on-binomial-distribution-fixed-number-of-trials/10767 "2018-05-07T21:22:18Z")
**Posts on this page:** 5
**Page:** 1
### Author:  [@hung-q-ngo](https://discourse.julialang.org/u/hung-q-ngo)
#### Post date: [May 7, 2018, 9:22pm UTC](https://discourse.julialang.org/t/glm-jl-error-on-binomial-distribution-fixed-number-of-trials/10767/1 "2018-05-07T21:22:18Z")
Hello: the following gives an error
```julia
data = DataFrame(Y = [0,3,1,7,1,0,7,5,1], X1 = [1,2,3,1,2,3,1,2,3], X2 = [1,1,1,2,2,2,3,3,3])
model = glm(@formula(Y ~ X1 + X2), data, Binomial(10))
```
Error msg:
```julia
ERROR: LoadError: DomainError:
log will only return a complex result if called with a complex argument. Try log(complex(x)).
Stacktrace:
[1] nan_dom_err at ./math.jl:300 [inlined]
[2] log at ./math.jl:419 [inlined]
[3] logit(::Float64) at /home/hungngo/.julia/v0.6/StatsFuns/src/basicfuns.jl:45
[4] macro expansion at /home/hungngo/repos/git/GLM.jl/src/glmfit.jl:241 [inlined]
[5] macro expansion at ./simdloop.jl:73 [inlined]
[6] initialeta!(::Distributions.Binomial{Float64}, ::GLM.LogitLink, ::Array{Float64,1}, ::Array{Float64,1}, ::Array{Float64,1}, ::Array{Float64,1}) at /home/hungngo/repos/git/GLM.jl/src/glmfit.jl:239
[7] #fit#16(::Bool, ::Array{Float64,1}, ::Array{Float64,1}, ::Array{Any,1}, ::Function, ::Type{GLM.GeneralizedLinearModel}, ::Array{Float64,2}, ::Array{Float64,1}, ::Distributions.Binomial{Float64}, ::GLM.LogitLink) at /home/hungngo/repos/git/GLM.jl/src/glmfit.jl:295
[8] #fit#17(::Array{Any,1}, ::Function, ::Type{GLM.GeneralizedLinearModel}, ::Array{Float64,2}, ::Array{Int64,1}, ::Distributions.Binomial{Float64}, ::GLM.LogitLink) at /home/hungngo/repos/git/GLM.jl/src/glmfit.jl:311
[9] fit(::Type{GLM.GeneralizedLinearModel}, ::Array{Float64,2}, ::Array{Int64,1}, ::Distributions.Binomial{Float64}) at /home/hungngo/repos/git/GLM.jl/src/glmfit.jl:311
[10] #fit#44(::Dict{Any,Any}, ::Array{Any,1}, ::Function, ::Type{GLM.GeneralizedLinearModel}, ::StatsModels.Formula, ::DataFrames.DataFrame, ::Distributions.Binomial{Float64}, ::Vararg{Distributions.Binomial{Float64},N} where N) at /home/hungngo/.julia/v0.6/StatsModels/src/statsmodel.jl:72
[11] fit(::Type{GLM.GeneralizedLinearModel}, ::StatsModels.Formula, ::DataFrames.DataFrame, ::Distributions.Binomial{Float64}) at /home/hungngo/.julia/v0.6/StatsModels/src/statsmodel.jl:66
[12] #glm#18(::Array{Any,1}, ::Function, ::StatsModels.Formula, ::DataFrames.DataFrame, ::Distributions.Binomial{Float64}, ::Vararg{Distributions.Binomial{Float64},N} where N) at /home/hungngo/repos/git/GLM.jl/src/glmfit.jl:314
[13] glm(::StatsModels.Formula, ::DataFrames.DataFrame, ::Distributions.Binomial{Float64}, ::Vararg{Distributions.Binomial{Float64},N} where N) at /home/hungngo/repos/git/GLM.jl/src/glmfit.jl:314
[14] include_string(::String, ::String) at ./loading.jl:522
[15] include_string(::Module, ::String, ::String) at /home/hungngo/.julia/v0.6/Compat/src/Compat.jl:71
[16] (::Atom.##112#116{String,String})() at /home/hungngo/.julia/v0.6/Atom/src/eval.jl:109
[17] withpath(::Atom.##112#116{String,String}, ::String) at /home/hungngo/.julia/v0.6/CodeTools/src/utils.jl:30
[18] withpath(::Function, ::String) at /home/hungngo/.julia/v0.6/Atom/src/eval.jl:38
[19] hideprompt(::Atom.##111#115{String,String}) at /home/hungngo/.julia/v0.6/Atom/src/repl.jl:67
[20] macro expansion at /home/hungngo/.julia/v0.6/Atom/src/eval.jl:106 [inlined]
[21] (::Atom.##110#114{Dict{String,Any}})() at ./task.jl:80
```
Was that expected, or did I do something stupid? Thanks!
---
### Author:  [@Nosferican](https://discourse.julialang.org/u/Nosferican)
#### Post date: [May 7, 2018, 10:51pm UTC](https://discourse.julialang.org/t/glm-jl-error-on-binomial-distribution-fixed-number-of-trials/10767/2 "2018-05-07T22:51:48Z")
Are you sure you want `Binomial` and `LogitLink` as the distribution/link for that model? Usually logistic regression takes on `true` and `false`. It seems the response vector might be counts which should probably use `Poisson`. If you want to model the rates (events given 10 trials), you can use the offset argument.
---
### Author:  [@hung-q-ngo](https://discourse.julialang.org/u/hung-q-ngo)
#### Post date: [May 7, 2018, 11:03pm UTC](https://discourse.julialang.org/t/glm-jl-error-on-binomial-distribution-fixed-number-of-trials/10767/3 "2018-05-07T23:03:40Z")
To get a feel for `GLM`, I wanted to model the situation when `y` counts the number of successes out of `10` trials, and the count is modeled with `Binomial(10, theta)` which is a special case of GLM, AFAIK. This model is different from Poisson, in part because the count is always bounded by `10`.
This test would also be a very special case of multinomial GLM (of which the multinomial logistic regression is a special case, as multinomial logistic regression is categorical GLM). Sorry for being pedantic, I wanted to make sure our terminologies are sync’ed up
---
### Author:  [@Nosferican](https://discourse.julialang.org/u/Nosferican)
#### Post date: [May 8, 2018, 12:01am UTC](https://discourse.julialang.org/t/glm-jl-error-on-binomial-distribution-fixed-number-of-trials/10767/4 "2018-05-08T00:01:15Z")
Logistic regression (`Bernoulli`, `Binomial`, `Multinomial`) can be framed as `Poisson` models by changing the data representation and will be equivalent except for the log-likelihood / deviance statistics (depending on the details the number of observations and degrees of freedom); depending on whether on uses off-set or weights, etc. It seems that in that particular case, GLM.jl is using a bad initial value. Best to open an issue there and I can take a look at it. Will probably end up being a quick PR to fix it.
---
### Author:  [@hung-q-ngo](https://discourse.julialang.org/u/hung-q-ngo)
#### Post date: [May 8, 2018, 12:03am UTC](https://discourse.julialang.org/t/glm-jl-error-on-binomial-distribution-fixed-number-of-trials/10767/5 "2018-05-08T00:03:12Z")
OK great. [Issue opened](https://github.com/JuliaStats/GLM.jl/issues/228). thanks for the prompt reply