Solve a least square problem for a set of FixedEffects

solve_coefficients!(y, fes, w; method = :cpu, maxiter = 10000, double_precision = true, tol = 1e-8)

Returns $\beta = argmin_{b} \sum_i w_i(y_i - X_i'b)$ where X denotes the matrix of fixed effects fes.

Arguments

• y : A AbstractVector
• fes: A Vector{<:FixedEffect}
• w: A vector of weights, i.e. AbstractWeights
• method : A Symbol for the method. Default is :cpu. The option :gpu requires using CUDA (in this case, it is recommanded to use the option double_precision = false).
• double_precision::Bool: Should the demeaning operation use Float64 rather than Float32? Default to true.
• tol : Tolerance. Default to 1e-8 if double_precision = true, 1e-6 otherwise.
• maxiter : Maximum number of iterations
• nthreads : Number of threads

Returns

• $\beta$ : Solution of the least square problem
• iterations: Number of iterations
• converged: Did the algorithm converge?

Fixed effects are generally not unique. We standardize the solution in the following way: the mean of fixed effects within connected components is zero (except for the first). This gives the unique solution in the case of two fixed effects.

Examples

using  FixedEffects
p1 = repeat(1:5, inner = 2)
p2 = repeat(1:5, outer = 2)
x = rand(10)
solve_coefficients!(rand(10), [FixedEffect(p1), FixedEffect(p2)])

solve_residuals!(y, fes, w; method = :cpu, double_precision = true, tol = 1e-8, maxiter = 10000, )

Returns $y_i - X_i'\beta$ where $\beta = argmin_{b} \sum_i y_i - X_i'b$, where X denotes the matrix of fixed effects fes.

Arguments

• y : A AbstractVector or A AbstractMatrix
• fes: A Vector{<:FixedEffect}
• w: A vector of weights, i.e. AbstractWeights
• method : A Symbol for the method. Default is :cpu. The option :gpu requires using CUDA or using Metal' (in this case, it is recommanded to use the optiondouble_precision = false`).
• double_precision::Bool: Should the demeaning operation use Float64 rather than Float32? Default to true.
• tol : Tolerance. Default to 1e-8 if double_precision = true, 1e-6 otherwise.
• maxiter : Maximum number of iterations

Returns

• res : Residual of the least square problem
• iterations: Number of iterations
• converged: Did the algorithm converge?

Examples

using  FixedEffects
p1 = repeat(1:5, inner = 2)
p2 = repeat(1:5, outer = 2)
solve_residuals!(rand(10), [FixedEffect(p1), FixedEffect(p2)])