A General Procedure for Testing Inequality Constrained Hypotheses in SEM

Researchers in the social and behavioral sciences often have clear expectations about the order and/or the sign of the parameters in their statistical model. For example, a researcher might expect that regression coefficient beta(1) is larger than regression coefficients beta(2) and beta(3). To test such a constrained hypothesis special methods have been developed. However, the existing methods for structural equation models (SEM) are complex, computationally demanding, and a software routine is lacking. Therefore, in this paper we describe a general procedure for testing order/inequality constrained hypotheses in SEM using the R package lavaan. We use the likelihood ratio (LR) statistic to test constrained hypotheses and the resulting plug-in p value is computed by either parametric or Bollen-Stine bootstrapping. Since the obtained plug-in p value can be biased, a double bootstrap approach is available. The procedure is illustrated by a real-life example about the psychosocial functioning in patients with facial burn wounds.