I am doing a Bayesian ANOVA as follows:
BIC0 = -2 * logLik0 + k0 * log(N) # null hypothesis BIC BIC1 = -2 * logLik1 + k1 * log(N) # alternate hypothesis BIC
This is robust ANOVA, so model I use a non-central t-distribution as the likelihood function for different levels of the categorical variable. see: Estimating parameters of Student's t-distribution
What should be the value of k in BIC0 or BIC1?
For the alternate hypothesis, suppose x has three levels A, B, C. I am estimating mu,sigma and also latent variable w (one for each data point) for every level of x. So should k = (2 + N) * 3 ?