Software packages BIEMS and bain: Bayes factors for testing equality (=) and order (<, >) constraints on means and regression coefficients (Mulder, Hoijtink, & De Leeuw, 2012; Gu, Hoitink, Mulder, & Rosseel, 2019). Examples:
- Bayesian (multivariate) t test, e.g.,
H0: mu = 0 vs H1: mu < 0 vs H2: mu>0.
- Linear regression, e.g.,
H0: beta1 > beta2 > beta3 > 0 vs H1: beta1 = beta2 = beta3 = 0 vs H2: neither H0 nor H1.
- Repeated measurement means:
H1: mean1 > mean2 > mean3 > mean4 vs H2: complement of H0.
H1: mean1 > mean2 > mean3 > mean4 vs H0: mean1 = mean2 = mean3 = mean4.
Software packages BOCOR and BCT: Bayes factors for testing equality and order constraints on bivariate, partial, polychoric correlations (Mulder, 2016; Mulder & Gelissen, 2019), such as
- Exploratory testing of correlations:
H0: corr(2,1)=0 vs H1: corr(2,1)<0 vs H2: corr(2,1)>0.
- Equality/order constrained testing of correlations:
H1: corr(2,1)=corr(3,1)=corr(4,1) vs H2: corr(2,1)>corr(3,1)>corr(4,1) vs H3: complement
Feel free to email at j[dot]mulder[dot]3[at]tilburguniversity[dot]edu. I am always interested in extending these methods to new and challenging testing problems involving equality or order constraints.