ANOVA for generated parameter with three subscripts

My question: Is there ANOVA for three subscripts posterior samples (not data) to show that such samples differ for the first subscripts?


Let m,r,c be integers m=1,2,...M,r=1,2,..,R,c=1,2,...,C indicating categories.

Let f(y_{m,r,c}|\theta) be a likelihood, where subscripts of y_{m,r,c} representing heterogeneity and model parameter \theta has form \theta = (\theta_{m},\theta_{t},\theta_{c}, \theta_{m,r,c},..)

From this, I estimate some characteristics A_{m,r,c}=A_{m,r,c}(\theta) as a funtion of \theta described in generated parameter block of stan file.
So estimates of A_{m,r,c} are indeterminate, i.e., posterior samples.

And I want to test the null hypothesis that the characteristic A_{m,r,c} is significantly different among the first subscript m.

I quietly do not know whether such ANOVA exists or not.

So, this ANOVA is associated with posterior samples A_{m,r,c}, not with data y_{m,r,c}.

Please let me know any book or PDF or paper which explain this.