Influence of Uninformative Prior Distributions for MCMC Method on Estimating Variance Components in Generalizability Theory

The Markov chain Monte Carlo (MCMC) method is more and more widely used to estimate variance components in generalizability theory (GT). However, as an essential part of MCMC method, uninformative priors haven’t been explored and different GT researches vary in the use of uninformative priors. This study focused on effect of the different uninformative priors on estimating variance components. Based on p × i × r design, eight uninformative prior distributions were chosen for simulation study and empirical study, including σ 2 ∼ i n v − g a m m a ( 0.001 , 0.001 ) [prior 1], σ 2 ∼ i n v − g a m m a ( 1 , 1 ) [prior 2], σ 2 ∼ u n i f o r m ( 0.001 , 1000 ) [ prior 3 ] , σ ∼ u n i f o r m ( 0 , 100 ) [prior 4], log ⁡ ( σ 2 ) ∼ u n i f o r m ( − 10 , 10 ) [prior 5], 1 σ 2 ∼ p a r e t o ( 1 , 0.001 ) [ prior 6 ] , σ 2 ( σ 2