  The Schwarz or Bayesian information criterion (BIC) is one of the most widely
used tools for model comparison in social science research. The BIC however is
not suitable for evaluating models with order constraints on the parameters of
interest. This paper explores two extensions of the BIC for evaluating order
constrained models, one where a truncated unit information prior is used under
the order-constrained model, and the other where a truncated local unit
information prior is used. The first prior is centered around the maximum
likelihood estimate and the latter prior is centered around a null value.
Several analyses show that the order-constrained BIC based on the local unit
information prior works better as an Occam's razor for evaluating
order-constrained models and results in lower error probabilities. The
methodology based on the local unit information prior is implemented in the R
package `BICpack' which allows researchers to easily apply the method for
order-constrained model selection. The usefulness of the methodology is
illustrated using data from the European Values Study.
