It appears the reference level is selected as the first unique element of the categorical value. However, in my case, the reference is P (and not A).
ols_all= lm( @formula( value ~ Treatment ), s_treat) gives
value ~ 1 + Treatment Coefficients: ──────────────────────────────────────────────────────────────────────── Coef. Std. Error t Pr(>|t|) Lower 95% Upper 95% ──────────────────────────────────────────────────────────────────────── (Intercept) 19.0845 0.531803 35.89 <1e-99 18.039 20.13 Treatment: P 5.5775 0.752082 7.42 <1e-12 4.09895 7.05605 What I really want is Treatment: A (P is the placebo or the control group). Granted I could rename the values of the variables. But in SAS and R it is possible to select the reference, hence I am hoping there is a way to do it with Julia GLM as well.
2 Answers
GLM.jl does not take the first unique element of CategoricalVector, but the first level in this column as a refrence. Therefore if you reorder levels you can change the reference and also the order of appearance of levels in the output. Here is an example:
julia> using CategoricalArrays julia> using DataFrames julia> using GLM julia> y = rand(10) 10-element Vector{Float64}: 0.6680787249599323 0.4405942175942186 0.012595806803754828 0.21742822324104805 0.4588945549282415 0.05463125900208077 0.5889309471773907 0.014531957298235865 0.8444514228200215 0.13148010370633267 julia> x = categorical(rand(["a", "b", "c"], 10)) 10-element CategoricalArray{String,1,UInt32}: "b" "b" "a" "a" "c" "a" "c" "c" "a" "b" julia> df = DataFrame(x=x, y=y) 10×2 DataFrame Row │ x y │ Cat… Float64 ─────┼───────────────── 1 │ b 0.668079 2 │ b 0.440594 3 │ a 0.0125958 4 │ a 0.217428 5 │ c 0.458895 6 │ a 0.0546313 7 │ c 0.588931 8 │ c 0.014532 9 │ a 0.844451 10 │ b 0.13148 julia> lm(@formula(y~x), df) StatsModels.TableRegressionModel{LinearModel{GLM.LmResp{Vector{Float64}}, GLM.DensePredChol{Float64, LinearAlgebra.CholeskyPivoted{Float64, Matrix{Float64}}}}, Matrix{Float64}} y ~ 1 + x Coefficients: ──────────────────────────────────────────────────────────────────────── Coef. Std. Error t Pr(>|t|) Lower 95% Upper 95% ──────────────────────────────────────────────────────────────────────── (Intercept) 0.282277 0.165972 1.70 0.1328 -0.110185 0.674739 x: b 0.131108 0.253527 0.52 0.6210 -0.468388 0.730603 x: c 0.0718425 0.253527 0.28 0.7851 -0.527653 0.671338 ──────────────────────────────────────────────────────────────────────── julia> levels(df.x) 3-element Vector{String}: "a" "b" "c" julia> levels!(df.x, ["c", "b", "a"]) 10-element CategoricalArray{String,1,UInt32}: "b" "b" "a" "a" "c" "a" "c" "c" "a" "b" julia> lm(@formula(y~x), df) StatsModels.TableRegressionModel{LinearModel{GLM.LmResp{Vector{Float64}}, GLM.DensePredChol{Float64, LinearAlgebra.CholeskyPivoted{Float64, Matrix{Float64}}}}, Matrix{Float64}} y ~ 1 + x Coefficients: ─────────────────────────────────────────────────────────────────────────── Coef. Std. Error t Pr(>|t|) Lower 95% Upper 95% ─────────────────────────────────────────────────────────────────────────── (Intercept) 0.354119 0.191648 1.85 0.1071 -0.0990568 0.807295 x: b 0.0592652 0.271031 0.22 0.8331 -0.581622 0.700153 x: a -0.0718425 0.253527 -0.28 0.7851 -0.671338 0.527653 ─────────────────────────────────────────────────────────────────────────── More advanced strategies are described here: .
Using the contrasts documentation .
There is another way to set the reference for the categorical variable as such:
ols_all= lm(@formula(value ~ Treatment), s_treat, contrasts= Dict(:Treatment => DummyCoding(base="P"))) The advantage is when there is a relatively long list of levels that could be tedious to reorder. So I thought it would be helpful to have both options in the answers.
