Comparative Study of Covariance Structures in Repeated Measures Experimental Design

Abstract

This paper intends to compare different covariance structures in repeated measures 
experimental design. Multiple responses taken in sequence from same experimental 
area at different occasions over a specific period of time are referred as Repeated 
Measurement. Weight of 90 chickens (broilers) for six class of different sector were 
collected and analyzed. Ten variance-covariance structures was used for 
comparison (UN, UNC, TOEP, TOEPH, ANTE (1), AR (1), ARH (1), CS, CSH and HF) 
using five goodness of fit criteria: AIC, AICC, BIC, HQIC, CAIC. The result indicates that 
Mauchly sphericity assumptions was violated, which shows that the best variance is 
covariance structure was heterogeneous first-order auto-regressive, followed by 
first-order ante-dependence, then heterogeneous teoplitz, while the least structure 
in this study was heterogeneous compound symmetry. Also, on the ground of 
goodness of fit criteria selection Hannan Quinn information criteria was the best 
information criteria, followed by Akaike information criteria, then Burhamn 
Handerson information criteria, then Bozdogan information criteria, while Bayesian 
Information criteria was the least one in this study paper. When comparing many 
variance covariance structures with large number of observations, then Hannan 
Quinn information criteria will be the best selected criteria, as the number of 
parameters increases, the selection criteria will definitely change.