Reducing costs in linear regression 
experiments
 

David Causeur & Thierry Dhorne 
Laboratory of Applied Statistics (SABRES) 
University of South Brittany 
Rue Yves Mainguy, Tohannic 
F­56000 Vannes, France 
email : causeur@iu­vannes.fr 
thierry.dhorne@univ­ubs.fr 

Methodological aspects of grading

 

Experimental constraints

Experimental costs :

Multiplicity of grading systems : 

 

Main references

Reduction of experimental costs :

 

Double sampling : 


Connioee, D. and Moran, M.A. (1972)

Double sampling with regression in comparative studies of carcass composition.

Biometrics 28, 1011­ 1023. 

Cook, G.L., Jones, D.W. and Kempster, A.J. (1983)

A note on a simple criterion for choosing among sample joints for use in double sampling.

Animal Production 36, 493­495. 

Engel B. and Walstra P. (1991) Increasing precision or reducing expense in regression by using information from a concomitant variable. 
Biometrics 47, 13­20. 

Refinements : 

Causeur, D. and Dhorne, T. (1998)

Finite­sample properties of a multivariate extension of double­regression.

Biometrics. 54 (4), 299­309. 

Causeur, D. (1998)

Plan d'échantillonnage  á plusieurs phases pour la réduction des coûts expérimentaux en régression linéaire.

Revue de Statistique Appliquée. XLVI (4), 59­73. 

Multiplicity of grading systems :

Causeur, D. and Dhorne, T. (2000)

Using surrogate predictors in linear regression models.

Submitted to Biometrika

Main parts of the talk

 

 

Experimental costs in linear regression experiments

 
Sampling design for linear regression experiments


Double sampling for reduction of costs


Naïve sampling design 

 

Auxiliary covariate

 

Double sampling design 

 

 

Practical properties of Z

 

Double sampling procedure

 

Random sub sampling or selection

 

Estimation procedure

 

 

 

 

 

Double sampling properties


    Unbiased procedure

 

        Efficiency of the procedure

           

        Comparison with OLS efficiency 

 

           

        Therefore

 

           

 

Optimization of the double sampling design 


E.C. protocol : ''120 carcasses'' constraint 

           

Objective function to be optimized

           

Example

Multiple auxiliary covariates

Multiple phase sampling plan


Objective


    To take into account the different costs of the auxiliary covariates


Monotone sampling design

      

Multiple phase sampling plan : example


Number of auxiliary covariates : 7 

Nr of covariates Optimal plan  Cost Reduction (%)
0 120 45600 0
1 (76,245) 34795 23.70
2 (69,216,398) 32275 29.22
3 (64,195,195,377) 31125 31.74
4 (53,134,209,209,209) 29155 36.06
5 (48,153,178,178,178,241) 27575 39.53
6 (47,141,157,157,157,217,337) 26570 41.73
7 (46,61,140,155,155,155,215,333)  26430 42.04

 



Optimal subsets :


(J,F) 
(J,Ld,F) 
(E,J,Ld,Lc) 
(E,J,Ld,Lc,D) 
(E,J,Ld,Lc,D,F) 
(P,E,J,Ld,Lc,D,F) 

 

Experimental constraints


Multiplicity of new grading systems 

Multiplicity of prediction formulae

 
Multiplicity of linear regression experiments with measurements of Y


Main practical problems

Sampling procedure

Perspectives


Methodological proposals


    How do these methods interact with PLS, PCR, ... ?


Practical proposals