Implement linear model variants

[p-gw]

This issue splits #5.

Separately implement linear variants of simple Rasch models:

TODO

• Linear Logistic Test Model
• Linear Rating Scale Model
• Linear Partial Credit Model

[p-gw]

For the construction of the item predictor matrix Q we need to pass the matrix to the appropriate models.

On the user side it might be more convenient to allow constructions from Tables.jl compatible sources as well. This could easily be done via StatsModels.jl

using DataFrames
using StatsModels

df = DataFrame(item = 1:5, a=[1,1,1,0,0], b=[0,0,1,1,1])
f = @formula(0 ~ a + b)
f = apply_schema(f, schema(f, df))
Q = modelmatrix(f, df)
5×2 Matrix{Int64}:
 1  0
 1  0
 1  1
 0  1
 0  1

[t-alfers]

I thought of something like this:

using DataStructures: OrderedDict

Q_input = OrderedDict(
    "a" => [1, 2, 3],
    "b" => [3, 4, 5]
)

handle_q = function(Q_input::OrderedDict, I::Int)
    C = length(Q_input)
    Q_matrix = zeros(Int, I, C)
    Q_values = values(Q_input)

    for (i, v) in enumerate(Q_values)
        Q_matrix[v, i] .+= 1        
    end

    return Q_matrix
end

handle_q(Q_input, 5)
5×2 Matrix{Int64}:
 1  0
 1  0
 1  1
 0  1
 0  1

Maybe we can allow for numerous ways for convenient Q-matrix inputs.