OpenMx is free, full–featured, open source, structural equation modeling (SEM) software. OpenMx runs within the R statistical programming environment on Windows, Mac OS–X, and Linux computers. The rationale for developing OpenMx is discussed along with the philosophy behind the user interface. The OpenMx data structures are introduced — these novel structures define the user interface framework and provide new opportunities for model specification. Two short example scripts for the specification and fitting of a confirmatory factor model are next presented. We end with an abbreviated list of modeling applications available in OpenMx 1.0 and a discussion of directions for future development.

The new software package OpenMx 2.0 for structural equation and other statistical modeling is introduced and its features are described. OpenMx is evolving in a modular direction and now allows a mix-and-match computational approach that separates model expectations from fit functions and optimizers. Major backend architectural improvements include a move to swappable open-source optimizers such as the newly-written CSOLNP. Entire new methodologies such as Item Factor analysis (IRT) and State-space modeling have been implemented. New model expectation functions including support for the expression of models in LISREL syntax and a simplified multigroup expectation function are available. Ease-of-use improvements include helper functions to standardize model parameters and compute their Jacobian-based standard errors, access to model components through standard R $ mechanisms, and improved tab completion from within the R Graphical User Interface.

This article considers the identification conditions of confirmatory factor analysis (CFA) models for ordered categorical outcomes with invariance of different types of parameters across groups. The current practice of invariance testing is to first identify a model with only configural invariance and then test the invariance of parameters based on this identified baseline model. This approach is not optimal because different identification conditions on this baseline model identify the scales of latent continuous responses in different ways. Once an invariance condition is imposed on a parameter, these identification conditions may become restrictions and define statistically non-equivalent models, leading to different conclusions. By analyzing the transformation that leaves the model-implied probabilities of response patterns unchanged, we give identification conditions for models with invariance of different types of parameters without referring to a specific parametrization of the baseline model. Tests based on this approach have the advantage that they do not depend on the specific identification condition chosen for the baseline model.

Objective The importance of dimensional approaches is widely recognized, but an empirical base for clinical application is lacking. This is particularly true for irritability, a dimensional phenotype that cuts across many areas of psychopathology and manifests early in life. We examine longitudinal, dimensional patterns of irritability and their clinical import in early childhood. Method Irritability was assessed longitudinally over an average of 16 months in a clinically enriched diverse community sample of preschoolers (N=497; M=4.2 years; SD=0.8). Using the Temper Loss scale of the Multidimensional Assessment Profile of Disruptive Behavior (MAP-DB) as a developmentally sensitive indicator of early childhood irritability, we examined its convergent/divergent, clinical and incremental predictive validity, and modeled its linear and nonlinear associations with clinical risk. Results The Temper Loss scale demonstrated convergent and divergent validity to child and maternal factors. In multivariate analyses, Temper Loss predicted mood (separation anxiety disorder [SAD], generalized anxiety disorder [GAD], and depression/dysthymia) and disruptive (oppositional defiant disorder [ODD], attention-deficit/hyperactivity disorder [ADHD], and conduct disorder [CD]) symptoms. Preschoolers with even mildly elevated Temper Loss scale scores showed substantially increased risk of symptoms and disorders. For ODD, GAD, SAD, and depression, increases in Temper Loss scale scores at the higher end of the dimension had a greater impact on symptoms relative to increases at the lower end. Temper Loss scale scores also showed incremental validity over DSM-IV disorders in predicting subsequent impairment. Finally, accounting for the substantial heterogeneity in longitudinal patterns of Temper Loss significantly improved prediction of mood and disruptive symptoms. Conclusion Dimensional, longitudinal characterization of irritability informs clinical prediction. A vital next step will be empirically generating parameters for incorporation of dimensional information into clinical decision-making with reasonable certainty.

Longitudinal data spanning 22 years, obtained from deceased participants of the German Socio-Economic Panel Study (SOEP; N = 1,637; 70 to 100 year olds), were used to examine if and how life satisfaction exhibits terminal decline at the end of life. Changes in life satisfaction were more strongly associated with distance to death than with distance from birth (chronological age). Multi-phase growth models were used to identify a transition point roughly four years prior to death wherein the prototypical rate of decline in life satisfaction tripled from –0.64 to –1.94 T-score units per year. Further individual-level analyses suggest that individuals dying at older ages spend more years in the terminal periods of life satisfaction decline than individuals dying at earlier ages. Overall, the evidence suggests that late-life changes in aspects of well-being are driven by mortality-related mechanisms and characterized by terminal decline.