With models and research designs ever increasing in complexity, the foundational question of model identification is more important than ever. The determination of whether or not a model can be fit at all or fit to some particular data set is the essence of model identification. In this article, we pull from previously published work on data-independent model identification applicable to a broad set of structural equation models, and extend it further to include extremely flexible exogenous covariate effects and also to include data-dependent empirical model identification. For illustrative purposes, we apply this model identification solution to several small examples for which the answer is already known, including a real data example from the National Longitudinal Survey of Youth; however, the method applies similarly to models that are far from simple to comprehend. The solution is implemented in the open-source OpenMx package in R.

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 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.

A growing number of social scientists have turned to differential equations as a tool for capturing the dynamic interdependence among a system of variables. Current tools for fitting differential equation models do not provide a straightforward mechanism for diagnosing evidence for qualitative shifts in dynamics, nor do they provide ways of identifying the timing and possible determinants of such shifts. In this paper, we discuss regime-switching differential equation models, a novel modeling framework for representing abrupt changes in a system of differential equation models. Estimation was performed by combining the Kim filter (Kim and Nelson State-space models with regime switching: classical and Gibbs-sampling approaches with applications, MIT Press, Cambridge, 1999) and a numerical differential equation solver that can handle both ordinary and stochastic differential equations. The proposed approach was motivated by the need to represent discrete shifts in the movement dynamics of $n=29$\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$n= 29$$\end{document} mother–infant dyads during the Strange Situation Procedure (SSP), a behavioral assessment where the infant is separated from and reunited with the mother twice. We illustrate the utility of a novel regime-switching differential equation model in representing children’s tendency to exhibit shifts between the goal of staying close to their mothers and intermittent interest in moving away from their mothers to explore the room during the SSP. Results from empirical model fitting were supplemented with a Monte Carlo simulation study to evaluate the use of information criterion measures to diagnose sudden shifts in dynamics.

With the advent of new data collection technologies, intensive longitudinal data (ILD) are collected more frequently than ever. Along with the increased prevalence of ILD, more methods are being developed to analyze these data. However, relatively few methods have yet been applied for making long- or even short-term predictions from ILD in behavioral settings. Applications of forecasting methods to behavioral ILD are still scant. We first establish a general framework for modeling ILD and then extend that frame to two previously existing forecasting methods: these methods are Kalman prediction and ensemble prediction. After implementing Kalman and ensemble forecasts in free and open-source software, we apply these methods to daily drug and alcohol use data. In doing so, we create a simple, but nonlinear dynamical system model of daily drug and alcohol use and illustrate important differences between the forecasting methods. We further compare the Kalman and ensemble forecasting methods to several simpler forecasts of daily drug and alcohol use. Ensemble forecasts may be more appropriate than Kalman forecasts for nonlinear dynamical systems models, but further forecasting evaluation methods must be put into practice.

Generalized orthogonal linear derivative (GOLD) estimates were proposed to correct a problem of correlated estimation errors in generalized local linear approximation (GLLA). This paper shows that GOLD estimates are related to GLLA estimates by the Gram–Schmidt orthogonalization process. Analytical work suggests that GLLA estimates are derivatives of an approximating polynomial and GOLD estimates are linear combinations of these derivatives. A series of simulation studies then further investigates and tests the analytical properties derived. The first study shows that when approximating or smoothing noisy data, GLLA outperforms GOLD, but when interpolating noisy data GOLD outperforms GLLA. The second study shows that when data are not noisy, GLLA always outperforms GOLD in terms of derivative estimation. Thus, when data can be smoothed or are not noisy, GLLA is preferred whereas when they cannot then GOLD is preferred. The last studies show situations where GOLD can produce biased estimates. In spite of these possible shortcomings of GOLD to produce accurate and unbiased estimates, GOLD may still provide adequate or improved model estimation because of its orthogonal error structure. However, GOLD should not be used purely for derivative estimation because the error covariance structure is irrelevant in this case. Future research should attempt to find orthogonal polynomial derivative estimators that produce accurate and unbiased derivatives with an orthogonal error structure.

Electroacoustic measurements at 1 MHz, using the Electro-Sonic Amplitude (ESA), on a kaolinite suspension provide a ready method for following the adsorption of hydrolyzable metal ions onto the clay surface. Co2+, Cd2+ and Cu2+ ions show similar behavior: The initially negative surface becomes less negative, approaches zero, and may become positive at pH values around neutral, depending on the initial metal concentration. At higher pH, electrokinetic potential goes through a maximum. If the surface has become positive, it becomes less so; and at still higher pH values it may become negative again, depending on the metal ion concentration. The behavior can be interpreted using the model proposed by James and Healy.