Abstract
Structural equation modeling (SEM) is an important research tool, both for path-based model specification (common in the social sciences) and also for matrix-based models (in heavy use in behavior genetics). We developed umx to give more immediate access, relatively concise syntax and helpful defaults for users in these two broad disciplines. umx supports development, modification and comparison of models, as well as both graphical and tabular outputs. The second major focus of umx, behavior genetic models, is supported via functions implementing standard multigroup twin models. These functions support raw and covariance data, including joint ordinal data, and give solutions for ACE models, including support for covariates, common- and independent-pathway models, and gene × environment interaction models. A tutorial site and question forum are also available.
Highlights
Structural equation modeling (SEM; Jöreskog, 1969) enables modeling with latent and measured variables, and allows researchers to realize the power of causal modeling (Pearl, 2009)
Despite its utility, learning, implementing and interpreting, these techniques have remained a bottleneck for many researchers, especially for more complex multiple-group models common in advanced fields such as behavior genetics
OpenMx has developed a strong following among geneticists and twin researchers, reflected in several hundred citations in published projects, many of which rely on testing complex models, often with constraints, using data comprising mixtures of binary, ordinal and continuous data, with missingness, and wide-format data comprising multiple genetically related groups, with data nested in these family structures
Summary
Lavaan implements a similar string-based syntax for model description, comparable multigroup capability and a range of estimators including robust ML and variants of Weighted Least Squares (WLS) It outputs standard errors (SEs) including robust and bootstrap SEs, along with standard fit indices and statistics such as Satorra-Bentler, Satterthwaite and Bollen-Stine bootstrap. Lavaan can handle missing data via FIML estimation It allows the use of linear and nonlinear equality (and inequality) constraints via a string syntax; for example, to equate model parameters ‘a1’ and ‘a2’, the user includes the following in their model statement: ‘a1 = a2’. OpenMx provides a sophisticated kit of basic objects for building structural equation models, including modeling via arbitrary matrices, algebras, constraints and fit-functions It supports RAM (McArdle & Boker, 1990) and LISREL (Jöreskog, 1969) path-based models. OpenMx has developed a strong following among geneticists and twin researchers, reflected in several hundred citations in published projects, many of which rely on testing complex models, often with constraints, using data comprising mixtures of binary, ordinal and continuous data, with missingness, and wide-format data comprising multiple genetically related groups (in particular, identical and fraternal twins, siblings, parents, grand-parents, offspring and adoptive parents), with data nested in these family structures
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