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 : 

• Spatial trend 
          Slaughterhouse effect

• Chronological trend 
          Genetic selection effect 
  

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

• Double regression

  • Double sampling

  • Use of an auxiliary covariate

  • Estimation procedure

  • Optimization of the sampling design

• Multivariate double­regression

  • Two phase sampling

  • Multiple phase sampling

• Calibration methods

  • Experimental constraints

  • Sampling design

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

• Z better predictor of Y than X

• Z cheaper than Y

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 

Optimal subsets :

J 
(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

• Global experimental costs 

• Possible trends 

  • Chronological trends 

  • Spatial trends 

  • ... 
    

Sampling procedure

Perspectives

Methodological proposals

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

Practical proposals

• Statistical handbook

• Statistical software including detection of outliers, optimization of the sampling design, statistical analysis,...