Add Linear and logistic regression: OLS, binomial and multinomial logit with the matrix functions, and where a nested logit fits
The matrix functions matr_mul, matr_var and matr_inv had reference pages but
nothing that showed what they are for. The new page builds three estimators
from them and explains the layout tricks that make it work: a union_data of
the regressors is the transposed data matrix, a lookup with swapped
coordinates transposes it, and a vector and a one-column matrix are relabels
of each other. Newton-Raphson steps for the two logit models run in an
iterate loop with a template whose currValue/nextValue are the coefficient
attribute.
The page ends with the nested logit: the probability computation as a
runnable fragment (nest domain, inclusive value, two-level probabilities),
and the two estimation routes, sequential and full-information with the
BHHH matrix as matr_var of the score matrix. Mixed logit, elasticities and
the specification variations (choice sets per actor, sampling of
alternatives, aggregate counts, alternative-specific coefficients) are
placed as remarks.
Linked from Matrix functions, Logit regression (whose example section was a
stub), Configuration examples, and the see-also of the three matr_ pages.
Verified: all four code blocks were extracted from the page as written and
run with GeoDmsRun (build of GeoDMS 20.19); the coefficients, standard
errors, R2, log-likelihoods and shares in the tables agree with a numpy
reference to all printed digits, the nested probabilities sum to one per
actor and equal the multinomial ones at lambda = 1.
Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>