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 β1 is larger than β2 and β3. 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 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.

Vanbrabant, L., Van de Schoot, R., Van Loey, N., & Rosseel, Y. (2017). A General procedure for Testing Inequality Constrained Hypotheses in SEM. Methodology, 13(2), 61-70. https://doi.org/10.1027/1614-2241/a000123

Leonard Vanbrabant
PhD Student

The topic of my PhD project is sample-size reduction by order constraints. Many researchers are familiar with the power gain in the context of the one-sided t-test.

 
Nancy van Loey
Program leader Psychosocial & behavioral research (ADBC)
Nancy is related to the departement of Clinical and Health Psychology and program leader at Association of Dutch Burn Centres.
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Yves Rosseel
Professor of Data Analysis and developer of Lavaan
Yves is the author of lavaan, an R-package for latent variable analysis. In 2013, Rens and Yves supervised a research master student, Leonard Vanbrabant, to add constrained statistical inference to the package lavaan. After this successful collaboration Leonard was hired as PhD-student, and they obtained funding from the Belgium Reseach Institute to continue working on the project which resulted in the R package Restriktor.
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