# Predict values using multinomial logistic regression?

**URL:** <https://discourse.julialang.org/t/predict-values-using-multinomial-logistic-regression/128621>\
**Category:** Statistics\
**Tags:** question, glm, econometrics\
**Created:** [May 2, 2025, 10:38am UTC](https://discourse.julialang.org/t/predict-values-using-multinomial-logistic-regression/128621 "2025-05-02T10:38:36Z")\
**Posts on this page:** 2\
**Page:** 1

<div class="post-metadata">

**Author:** ![Paulogcd](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/paulogcd/32/215821_2.png) [@Paulogcd](https://discourse.julialang.org/u/Paulogcd)\
**Post date:** [May 2, 2025, 10:38am UTC](https://discourse.julialang.org/t/predict-values-using-multinomial-logistic-regression/128621/1 "2025-05-02T10:38:36Z")

</div>

Dear Julia community 🙂,

I have been trying to run a Multinomial logistic regression and to get the estimated results from a certain set of values.

I managed to run the regression, but fail to get the estimated results for a certain set of covariate values.

In a model managed by the GLM package, I would have done:

```julia
# Packages:
begin 
    using GLM
    using Plots
    using DataFrames
end

# Data: 
begin 
    Y = Float64.(rand(Binomial(), 100))
    X1 = rand(100)
    data = DataFrame(Y = Y, X1 = X1)
    new_data = DataFrame(X1 = rand(100))
end

# Regression:
begin 
    logistic_model = GLM.glm(@formula(Y ~ X1), data, Bernoulli(), LogitLink())
    predicted_values = GLM.predict(logistic_model, new_data)
    Plots.plot(X1, predicted_values)
end

```

Now, if I am trying to run a multinomial logistic regression, how could I manage to get results similar to those obtained through the `GLM.predict() function?

First, trying with Econometrics.jl:

```julia
# Package: 
begin 
    using Econometrics
end

# Data: 
begin 
    Y = rand(1:5, 100)
    X1 = rand(1:5,100)
    data = DataFrame(Y = Y, X1 = X1)
    new_data = DataFrame(X1 = rand(1:5,100)) 
end

# Regression:
begin 
    multinomial_logistic = Econometrics.fit(EconometricModel,
                                    @formula(Y ~ X1 ),
                                    data)
    Econometrics.predict(multinomial_logistic) # Yields the estimated vaues for the exact vector of values on which the regression was performed.
    # Econometrics.predict(multinomial_logistic, new_data) # Method error 
end

```

Trying with OrdinalMultinomialModels.jl, I run:

```julia
begin 
    using OrdinalMultinomialModels

    model = polr(@formula(Y ~ X1), data, LogitLink())

    # predict(model) # Method error

    # OrdinalMultinomialModels.predict(model, new_data) # Method error too
    # predict function ?
end

```

My problem here is that I do not find a function similar to the `GLM.predict()` one.

When looking up different methods for predict functions, I get results for all the mentioned

```julia
methods(predict)

# 13 methods for generic function "predict" from StatsAPI:
  [1] predict(mm::StatsModels.TableRegressionModel{T, S}, data; kwargs...) where {T<:OrdinalMultinomialModel, S<:(Matrix)}
     @ OrdinalMultinomialModels ~/.julia/packages/OrdinalMultinomialModels/axgiL/src/ordmnfit.jl:183
  [2] predict(m::StatsModels.TableRegressionModel, new_x::AbstractMatrix; kwargs...)
     @ StatsModels ~/.julia/packages/StatsModels/mPD8T/src/statsmodel.jl:137
  [3] predict(mm::StatsModels.TableRegressionModel, data; kwargs...)
     @ StatsModels ~/.julia/packages/StatsModels/mPD8T/src/statsmodel.jl:172
  [4] predict(a::StatsModels.TableRegressionModel, args...; kwargs...)
     @ StatsModels ~/.julia/packages/StatsModels/mPD8T/src/statsmodel.jl:28
  [5] predict(mm::LinearModel, newx::AbstractMatrix, interval::Symbol, level::Real)
     @ GLM deprecated.jl:103
  [6] predict(mm::LinearModel, newx::AbstractMatrix; interval, level)
     @ GLM ~/.julia/packages/GLM/vM20T/src/lm.jl:250
  [7] predict(mm::LinearModel, newx::AbstractMatrix, interval::Symbol)
     @ GLM deprecated.jl:103
  [8] predict(mm::GLM.LinPredModel)
     @ GLM ~/.julia/packages/GLM/vM20T/src/linpred.jl:265
  [9] predict(mm::GLM.AbstractGLM, newX::AbstractMatrix; offset, interval, level, interval_method)
     @ GLM ~/.julia/packages/GLM/vM20T/src/glmfit.jl:650
 [10] predict(obj::EconometricModel{<:Econometrics.NominalResponse})
     @ Econometrics ~/.julia/packages/Econometrics/yAppe/src/statsbase.jl:176
 [11] predict(obj::EconometricModel{<:Econometrics.OrdinalResponse})
     @ Econometrics ~/.julia/packages/Econometrics/yAppe/src/statsbase.jl:178
 [12] predict(obj::EconometricModel)
     @ Econometrics ~/.julia/packages/Econometrics/yAppe/src/statsbase.jl:175
 [13] predict(m::OrdinalMultinomialModel, newX::Matrix{T}; kind) where T<:Union{Float32, Float64}
     @ OrdinalMultinomialModels ~/.julia/packages/OrdinalMultinomialModels/axgiL/src/ordmnfit.jl:144

```

Going to the source of OrdinalMultinomialModels.jl, I find that the following function exists:

```julia
predict(m::OrdinalMultinomialModel, newX::Matrix{T}; kind::Symbol=:class) 

```

But the type of my model when running `model = polr(@formula(Y ~ X1), data, LogitLink())` is:

`StatsModels.TableRegressionModel{OrdinalMultinomialModel{Int64, Float64, LogitLink}, Matrix{Float64}}`.

I am quite sure I am missing the function I want, given the number of methods existing for `predict()` in both package. I am sorry if my question is not relevant. Having the equivalent of the `GLM.predict()` would be of great help.

Maybe I am missing something else?

Does anyone know if such function exists for multinomial logistic regression? Any hint would be greatly appreciated .

Thank you.

---

<div class="post-metadata">

**Author:** ![nilshg](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/nilshg/32/2283_2.png) [@nilshg](https://discourse.julialang.org/u/nilshg)\
**Post date:** [May 2, 2025, 11:39am UTC](https://discourse.julialang.org/t/predict-values-using-multinomial-logistic-regression/128621/2 "2025-05-02T11:39:16Z")

</div>

Might be good to add docs for `predict` to the packages, but from the test of OrdinalMultinomialModels.jl you can get:

```julia
julia> using OrdinalMultinomialModels, RDatasets

julia> housing = dataset("MASS", "housing");

julia> houseplr1 = polr(@formula(Sat ~ Infl + Type + Cont), housing,
                   LogitLink(), wts = housing[!, :Freq])
StatsModels.TableRegressionModel{OrdinalMultinomialModel{Int64, Float64, LogitLink}, Matrix{Float64}}

Sat ~ Infl + Type + Cont

Coefficients:
───────────────────────────────────────────────────────────────
                        Estimate Std.Error t value Pr(>|t|)
───────────────────────────────────────────────────────────────
intercept Low|Medium -0.496141 0.124541 -3.98376 0.0002
intercept Medium|High 0.690706 0.125212 5.51628 <1e-06
Infl: Medium 0.566392 0.104963 5.39611 <1e-05
Infl: High 1.28881 0.126705 10.1718 <1e-14
Type: Apartment -0.572352 0.118747 -4.81991 <1e-05
Type: Atrium -0.366182 0.156766 -2.33586 0.0226
Type: Terrace -1.09101 0.151514 -7.20075 <1e-09
Cont: High 0.360284 0.0953574 3.77825 0.0003
───────────────────────────────────────────────────────────────

julia> predict(houseplr1, housing,kind=:probs)
72×3 DataFrame
 Row │ Low Medium High
     │ Float64? Float64? Float64?
─────┼──────────────────────────────
   1 │ 0.378448 0.287676 0.333876
   2 │ 0.378448 0.287676 0.333876
   3 │ 0.378448 0.287676 0.333876
(...)

```