Identity test for regression models

Authors

  • Adair José Regazzi

DOI:

https://doi.org/10.1590/S1678-3921.pab1996.v31.4446

Keywords:

identity of models, least square, applied statistics

Abstract

It is considered in this paper the adjustment of H regression equations in the case of juxtaposition of r polynomial submodels of k degree. The points of intersection of the submodels are supposed to be known. Appropriate restrictions are imposed in such a way that the polynomial submodels are concordant in the points of intersection. The linear model for the hth equation is Yh = Xh βh+εh , h = 1,2,..., H, where Yh is an nh × 1 vector of observations, Xh is an nh × p matrix of known constants, βh is an p×1 vector of unknown parameters and εh is an nh×1 vector of errors that is distributed NID (εh:ϕσ2 I). In the parameters estimation, the Least Square Method was used. A statistic test was derived for the hypothesis that H regression models in the case of juxtapositon of r polynomial submodels of k degree were identical. The hypothesis in consideration is: H0:β1 = β2 =…= βH (H models are identical) vs. Hα:βi ≠ βj for at least one i j (the H models are not all identical). This method is applied to a set of H = two regression equations in the case of juxtaposition of r two polynomial submodels of first degree.

Published

1996-01-01

How to Cite

Regazzi, A. J. (1996). Identity test for regression models. Pesquisa Agropecuaria Brasileira, 31(1), 1–17. https://doi.org/10.1590/S1678-3921.pab1996.v31.4446

Issue

Section

STATISTICS