Intrablock, Interblock and Combined Estimates in Incomplete Block Designs: A Numerical Study

Open Access
Altinisik, Yasin
Graduate Program:
Master of Science
Document Type:
Master Thesis
Date of Defense:
Committee Members:
  • James Landis Rosenberger, Thesis Advisor
  • Balanced Incomplete Block Designs
  • Intrablock Estimates
  • Interblock Estimates
  • Combined Estimates
  • Precision Increase
Intrablock analysis and interblock analysis are used to estimate true treatment means in block designs. The estimates after using these analyses are called intrablock estimates and interblock estimates respectively. These estimates are unbiased and they are independent from each other. However, a linear combination of these estimates, which are called combined estimates, can also be used to estimate true treatment means. Combined estimates are also unbiased and have better precision estimating treatment contrasts. The SAS PROC MIXED procedure uses matrix notation to obtain combined estimates. First we focus on understanding the matrix notation that SAS PROC MIXED uses in complete and incomplete block designs. We show that the LMER function in R uses the same matrix notation as SAS PROC MIXED, and obtains exactly the same results that SAS PROC MIXED gives with respect to covariance parameter estimates, treatment mean estimates and treatment mean standard error estimates. Second, we focus on a multiple imputation method to deal with missing values in incomplete block designs to make the data complete. An R package called Amelia2 is used for this purpose. Treatment mean estimates are also obtained with SAS PROC MIXED after using the Amelia2 procedure. Afterwards, combined and amelia treatment mean estimates of true treatment means are compared in some balanced incomplete block designs by using a simulation study.