lslx is a package for fitting semi-confirmatory structural equation modeling (SEM) via penalized likelihood (PL) with elastic-net or minimax concave penalty (MCP) developed by Huang, Chen, and Weng (2017). In this semi-confirmatory method, an SEM model is distinguished into two parts: a confirmatory part and an exploratory part. The confirmatory part includes all of the freely estimated parameters and fixed parameters that are allowed for theory testing. The exploratory part is composed by a set of penalized parameters describing relationships that cannot be clearly determined by available substantive theory. By implementing a sparsity-inducing penalty and choosing an optimal penalty level, the relationships in the exploratory part can be efficiently determined by the sparsity pattern of these penalized parameters.

lslx can be also seen as a package for conducting usual SEM with several state-of-art inference methods, including sandwich standard error formula, mean-adjusted likelihood ratio test, and two-stage method with auxiliary variables for missing data. lslx also supports multi-group analysis for evaluating group heterogeneity and penalized least squares for SEM with ordianl data under delta parameterization. For now, the major limitations of lslx are that (1) it cannot impose linear or non-linear constraints for coefficients; (2) it cannot make valid inference under clustered or dependent data.

To learn more about lslx, please see its JSS paper doi:10.18637/jss.v093.i07.