Title
USING ISOTONIC REGRESSION TO IMPROVE ESTIMATION IN FACTORIAL EXPERIMENTS WITH ORDERED FACTOR LEVELS
Abstract
In many designed experiments in agriculture and the life sciences, a researcher can anticipate the direction that responses will take when treatments are varied. For example, in a 2-way factorial, a researcher may know that increasing the levels of nitrogen and phosphorus will increase yields of a crop. Classical analysis of variance does not take into account a known ordering among population means. However, it can be shown that by restricting the estimates of means to have the same ordering as the anticipated ordering of population means, a reduction in mean-squared errors of estimators will likely occur, often by more than 50%. A procedure used to create such estimates is called isotonic regression.
In this article, a recently proposed method of isotonic regression for lattice-ordered means will be presented after first reviewing well-established methods. The newer method will be illustrated using data from an entomology experiment. In addition, standard errors of the estimators will be approximated using a bootstrap procedure.
Keywords
lattice order; parametric bootstrap procedure
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.
Recommended Citation
Strand, Matt and Higgins, Jim
(1999).
"USING ISOTONIC REGRESSION TO IMPROVE ESTIMATION IN FACTORIAL EXPERIMENTS WITH ORDERED FACTOR LEVELS,"
Conference on Applied Statistics in Agriculture.
https://doi.org/10.4148/2475-7772.1262
USING ISOTONIC REGRESSION TO IMPROVE ESTIMATION IN FACTORIAL EXPERIMENTS WITH ORDERED FACTOR LEVELS
In many designed experiments in agriculture and the life sciences, a researcher can anticipate the direction that responses will take when treatments are varied. For example, in a 2-way factorial, a researcher may know that increasing the levels of nitrogen and phosphorus will increase yields of a crop. Classical analysis of variance does not take into account a known ordering among population means. However, it can be shown that by restricting the estimates of means to have the same ordering as the anticipated ordering of population means, a reduction in mean-squared errors of estimators will likely occur, often by more than 50%. A procedure used to create such estimates is called isotonic regression.
In this article, a recently proposed method of isotonic regression for lattice-ordered means will be presented after first reviewing well-established methods. The newer method will be illustrated using data from an entomology experiment. In addition, standard errors of the estimators will be approximated using a bootstrap procedure.
