How to Add Sum to Zero Constraint to Glm in Python

Constrained regression in Python with multiple constraints

I am still not sure which model you are running (posting a Minimal, Complete, and Verifiable example would certainly help), but the following should work for GLMs. From the docs, we have,

constraints (formula expression or tuple) – If it is a tuple, then the constraint needs to be given by two arrays (constraint_matrix, constraint_value), i.e. (R, q). Otherwise, the constraints can be given as strings or list of strings. see t_test for details.

This implies the function call should be along the following lines,

R = [[0, 0, 0, a, b, 0, 0],
     [0, c, d, 0, 0, 0, 0]]
q = [0, 0]

results = model.fit_constrained((R, q))

This should work, but since we do not have your model I do not know for sure if R * params = q, which must hold according to the documentation.

R: Force regression coefficients to add up to 1

1) CVXR We can compute the coefficients using CVXR directly by specifying the objective and constraint. We assume that D is the response, the coefficients of A and B must sum to 1, b[1] is the intercept and b[2], b[3] and b[4] are the coefficients of A, B and C respectively.

library(CVXR)

b <- Variable(4)
X <- cbind(1, as.matrix(data[-4]))
obj <- Minimize(sum((data$D - X %*% b)^2))
constraints <- list(b[2] + b[3] == 1)
problem <- Problem(obj, constraints)
soln <- solve(problem)

bval <- soln$getValue(b)
bval
##            [,1]
## [1,]  1.6428605
## [2,] -0.3571428
## [3,]  1.3571428
## [4,] -0.1428588

The objective is the residual sum of squares and it equals:

soln$value
## [1] 0.07142857

2) pracma We can also use the pracma package to compute the coefficients. We specify the X matrix, response vector, the constraint matrix (in this case the vector given as the third argument is regarded as a one row matrix) and the right hand side of the constraint.

library(pracma)

lsqlincon(X, data$D, Aeq = c(0, 1, 1, 0), beq = 1) # X is from above
## [1]  1.6428571 -0.3571429  1.3571429 -0.1428571

3) limSolve This package can also solve for the coefficients of regression problems with constraints. The arguments are the same as in (2).

library(limSolve)
lsei(X, data$D, c(0, 1, 1, 0), 1)

giving:

$X
                    A          B          C 
 1.6428571 -0.3571429  1.3571429 -0.1428571 

$residualNorm
[1] 0

$solutionNorm
[1] 0.07142857

$IsError
[1] FALSE

$type
[1] "lsei"

Check

We can double check the above by using the lm approach in the other answer:

lm(D ~ I(A-B) + C + offset(B), data)

giving:

Call:
lm(formula = D ~ I(A - B) + C + offset(B), data = data)

Coefficients:
(Intercept)     I(A - B)            C  
     1.6429      -0.3571      -0.1429  

The I(A-B) coefficient equals the coefficient of A in the original formulation and one minus it is the coefficient of C. We see that all approaches do lead to the same coefficients.

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