Question

Explain this question about reduced model in factorial design:

a. what is reduced model?

b. what is the different between full model and reduced model?

c. Is there any pro (benefit) and cons for using either full or reduced model?

d. what is the purpose of reducing the full model?

Answer 1

a. what is reduced model?

A reduced model does not include all the possible terms.

b. what is the different between full model and reduced model?

A full model includes all of the possible terms. A reduced model does not include all the possible terms.

c. Is there any pro (benefit) and cons for using either full or reduced model?

If truthfully the observations are actually drawn from the reduced model---they are all generated by the same mean--then there should be no real difference between the error achieved with the estimates from the full and the estimates from the reduced model.

d. what is the purpose of reducing the full model?

You might reduce a model if terms are not significant or if you need additional error degrees of freedom and you can assume that certain terms are zero.