How can I project level curves onto the axis planes in 3d?

General Usage
1

I’m interested in plotting the level curves of a surface onto the xy plane. Here is an example of what I want to achieve

image
image1066×900 93.9 KB

I’ve got some code to make the surface and plot it already. How can I modify my code to get my desired result?

using Plots
using LinearAlgebra
using Distributions
pyplot()

function expit(x)
    1.0 / (1.0 + exp(-x))
end

function make_data()
    N,p = 1000, 2
    μ = zeros(p)

    X = rand(Normal(), N)
    X = [ones(N) X]
    β = [-0.8, 0.2]
    η = X*β;

    θ = expit.(η)
    dgp = Binomial.(1,θ)
    y = rand.(dgp);
    X,y
end

X, y = make_data();

function LL(b0, b1, X, y)
    
    density = Binomial.(1, expit.(X*[b0,b1]))
    
    sum(loglikelihood.(density, y))
    
end

b1 = -8:0.1:8
b0 = -8:0.1:8
z = [LL(i,j,X,y) for i in b0, j in b1];

plot(b0, b1, z, st = :surface, camera = (-30, 15))
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