A study of the non-full rank design model

• Main Author: Binsol, Antonina A.
• Format: text
• Language: English
• Published: Animo Repository 1990
• Subjects: Geometrical models; Experimental design; Statistical design
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/15940
• Institution: De La Salle University

The study of the non-full rank design model focuses on the large possibilities of carrying put solutions and derivations similar to the full rank model. A matrix that is non-full rank has no unique inverse and therefore solutions that appear in the full rank case are not applicable. There is a matrix designed as an inverse for this non-full rank matrix and this inverse is called a conditional inverse. With this inverse, similar solutions and derivations can be performed as in the full rank case. In this study, aside from using matrix notations, another technique used to show B solutions is through projections on subspaces in geometry. To carry out tests of hypotheses, there must exist estimable functions of B. Estimable functions are sets of linear combinations of B and there exist unbiased estimates of estimable functions which are linear combinations of the observation variable. The non-full rank design model can be transformed into a full rank model by using the approach which is known as reparameterization. In this transformation, the former values of the estimable functions are preserved.