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.

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.
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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