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This article presents the authors' response which consists of three main parts. The first involves recapping the general thrust of their focus article. The second part consists of some general points that they hope will clarify issues raised by the commentators that were not made as clearly as they should have been in the focus article. The third part consists of more targeted rejoinders to particular aspects of the individual commentaries. (Contains 1 footnote.)

It seems that just when we are about to lay P-technique factor analysis finally to rest as obsolete because of newer, more sophisticated multivariate time-series models using latent variables--dynamic factor models--it rears its head to inform us that an obituary may be premature. We present the results of some simulations demonstrating that even though it does not explicitly model lagged information, P-technique's ability to recover the parameters of underlying dynamic processes involving lagged relations among the manifest variables is apparently robust and accurate. An empirical example is presented using 103 days of affective mood self-ratings from a young pregnant woman. Implications of the simulation and empirical findings are briefly discussed. (Contains 6 tables and 1 footnote.)

Four methods for estimating a dynamic factor model, the direct autoregressive factor score (DAFS) model, are evaluated and compared. The first method estimates the DAFS model using a Kalman filter algorithm based on its state space model representation. The second one employs the maximum likelihood estimation method based on the construction of a block-Toeplitz covariance matrix in the structural equation modeling framework. The third method is built in the Bayesian framework and implemented using Gibbs sampling. The fourth is the least squares method, which also employs the block-Toeplitz matrix. All 4 methods are implemented in currently available software. The simulation study shows that all 4 methods reach appropriate parameter estimates with comparable precision. Differences among the 4 estimation methods and related software are discussed. (Contains 1 figure, 5 tables and 7 footnotes.)

Dynamic factor models have been used to analyze continuous time series behavioral data. We extend 2 main dynamic factor model variations--the direct autoregressive factor score (DAFS) model and the white noise factor score (WNFS) model--to categorical DAFS and WNFS models in the framework of the underlying variable method and illustrate them with a categorical time series data set from an emotion study. To estimate the categorical dynamic factor models, a Bayesian method via Gibbs sampling is used. The results show that today's affect directly influences tomorrow's affect. The results are then validated by means of simulation studies. Differences between continuous and categorical dynamic factor models are examined. (Contains 3 figures, 6 tables and 2 footnotes.)

Ideally, the unit of analysis in psychology is the individual. However, many psychological methods do not cope well, either at the level of construct definition or at the level of measurement, with individuality in behavior. There is little leeway for constructs to be both idiosyncratically tailored to the individual, and still identified as having the same core meaning between individuals. Generally accepted ways to aggregate data in the course of empirically studying relationships simply ignore idiosyncrasy-but do so at some as yet undetermined costs. We identify, and illustrate with empirical data, the main features of an individually-oriented approach to general construct definition and measurement that seem to challenge the established concepts and norms of "good" measurement practice in behavioral research yet, at the same time, can be reconciled with them. (Contains 7 footnotes, 7 tables and 3 figures.)

In the past several decades, methodologies used to estimate nonlinear relationships among latent variables have been developed almost exclusively to fit cross-sectional models. We present a relatively new estimation approach, the unscented Kalman filter (UKF), and illustrate its potential as a tool for fitting nonlinear dynamic models in two ways: (1) as a building block for approximating the log-likelihood of nonlinear state-space models and (2) to fit time-varying dynamic models wherein parameters are represented and estimated online as other latent variables. Furthermore, the substantive utility of the UKF is demonstrated using simulated examples of (1) the classical predator-prey model with time series and multiple-subject data, (2) the chaotic Lorenz system and (3) an empirical example of dyadic interaction.

Bayesian methods for analyzing longitudinal data in social and behavioral research are recommended for their ability to incorporate prior information in estimating simple and complex models. We first summarize the basics of Bayesian methods before presenting an empirical example in which we fit a latent basis growth curve model to achievement data from the National Longitudinal Survey of Youth. This step-by-step example illustrates how to analyze data using both noninformative and informative priors. The results show that in addition to being an alternative to the maximum likelihood estimation (MLE) method, Bayesian methods also have unique strengths, such as the systematic incorporation of prior information from previous studies. These methods are more plausible ways to analyze small sample data compared with the MLE method. (Contains 3 figures, 3 tables and 7 footnotes.)

With few exceptions, the dynamics underlying the mood structures of individuals with Parkinson's Disease have consistently been overlooked. Based on 12 participants' daily self-reports over 72 days, we identified 10 participants whose covariance matrices for positive and negative affect were similar enough to warrant pooling. Dynamic factor models that included factor autoregression and cross-regressions were fitted to the pooled, lagged covariance matrix representing approximately 700 occasions of measurement. Although results from the pooled data indicated that both positive and negative affect had a strong lag-1 autoregressive impact on current positive and negative affect, most individuals showed stronger autoregressive effects for positive than negative affect when examined individually. There was also a weak cross-regression effect of positive affect on negative affect, but the reverse was not true. Through model fitting, we demonstrated that failure to incorporate lagged relations among factors could lead to an overestimation of concurrent correlations among latent factors. Implications of the findings in relation to the orthogonality of positive and negative affect are discussed.

Makes the case that the value of methods of differential psychology have been constrained as much by the phenomena to which they are applied as by the underlying flaws that render them inferior to classical experimental methods. Examines some applications of differential methods to alternative phenomena. (SLD)

Examined two methods for fitting models of intrinsic dynamics to intraindividual variability data by testing these techniques' behavior in equations through simulation studies. Among the main results is the demonstration that a local linear approximation of derivatives can accurately recover the parameters of a simulated linear oscillator, with restrictive assumptions as noted. Discusses other findings related to recovering the parameters of a process from a limited amount of data. (SLD)

Proposes a special rotation procedure for the exploratory dynamic factor model for stationary multivariate time series. The rotation procedure applies separately to each univariate component series of a q-variate latent factor series and transforms such a component, initially represented as white noise, into a univariate moving-average. (Author/SLD)

Pseudo-Maximum Likelihood (p-ML) and Asymptotically Distribution Free (ADF) estimation methods for estimating dynamic factor model parameters within a covariance structure framework were compared through a Monte Carlo simulation. Both methods appear to give consistent model parameter estimates, but only ADF gives standard errors and chi-square statistics that appear consistent. (SLD)