Sometimes one needs to classify individuals into groups, but there is no available grouping information due to social desirability bias in reporting behavior like unethical or dishonest intentions or unlawful actions. Assessing hard-to-detect behaviors is useful; however it is methodologically difficult because people are unlikely to self-disclose bad actions. This paper presents an unsupervised classification methodology utilizing ordinal categorical predictor variables. It allows for classification, individual respondent ranking, and grouping without access to a dependent group indicator variable. The methodology also measures predictor variable worth (for determining target behavior group membership) at a predictor variable category-by-category level, so different variable response categories can contain different amounts of information about classification. It is asymmetric in that a “0” on a binary predictor does not have a similar impact toward signaling “membership in the target group” as a “1” has for signaling “membership in the non-target group.” The methodology is illustrated by identifying Spanish consumers filing fraudulent insurance claims. A second illustration classifies Portuguese high school student’s propensity to alcohol abuse. Results show the methodology is useful when it is difficult to get dependent variable information, and is useful for deciding which predictor variables and categorical response options are most important.

When comparing multilevel models (MLMs) differing in fixed and/or random effects, researchers have had continuing interest in using R-squared differences to communicate effect size and importance of included terms. However, there has been longstanding confusion regarding which R-squared difference measures should be used for which kind of MLM comparisons. Furthermore, several limitations of recent studies on R-squared differences in MLM have led to misleading or incomplete recommendations for practice. These limitations include computing measures that are by definition incapable of detecting a particular type of added term, considering only a subset of the broader class of available R-squared difference measures, and incorrectly defining what a given R-squared difference measure quantifies. The purpose of this paper is to elucidate and resolve these issues. To do so, we define a more general set of total, within-cluster, and between-cluster R-squared difference measures than previously considered in MLM comparisons and give researchers concrete step-by-step procedures for identifying which measure is relevant to which model comparison. We supply simulated and analytic demonstrations of limitations of previous MLM studies on R-squared differences and show how application of our step-by-step procedures and general set of measures overcomes each. Additionally, we provide and illustrate graphical tools and software allowing researchers to automatically compute and visualize our set of measures in an integrated manner. We conclude with recommendations, as well as extensions involving (a) how our framework relates to and can be used to obtain pseudo-R-squareds, and (b) how our framework can accommodate both simultaneous and hierarchical model-building approaches.

A commentary by Thoemmes on Wiedermann and Sebastian’s introductory article on Direction Dependence Analysis (DDA) is responded to in the interest of elaborating and extending direction dependence principles to evaluate causal effect directionality. Considering Thoemmes’ observation that some DDA principles are already well-established in machine learning, we argue that several other connections between DDA and research lines in theoretical statistics, econometrics, and quantitative psychology exist, suggesting that DDA is best conceptualized as a framework that summarizes and extends existing knowledge on properties of linear models under non-normality. Further, Thoemmes articulates concerns about assumptions of error distributions used in our main article and presents an artificial data example in which some DDA tests have suboptimal statistical power. We present extensions of DDA to entirely relax distributional assumptions about errors and describe two sensitivity analysis approaches to critically evaluate DDA results. Both sensitivity approaches are illustrated using Thoemmes’ artificial data example. Incorporating DDA sensitivity results yields correct causal conclusions. Thus, overall, we stay with our initial conclusion that the use of higher moments in causal inference constitutes an exciting open research area.

Studies have used the latent differential equation (LDE) model to estimate the parameters of damped oscillation in various phenomena, but it has been shown that correct, non-zero parameter estimates are only obtained when the latent series exhibits little or no process noise. Consequently, LDEs are limited to modeling deterministic processes with measurement error rather than those with random behavior in the true latent state. The reasons for these limitations are considered, and a piecewise deterministic approximation (PDA) algorithm is proposed to treat process noise outliers as functional discontinuities and obtain correct estimates of the damping parameter. Comprehensive, random-effects simulations were used to compare results with those obtained using a state-space model (SSM) based on the Kalman filter. The LDE with the PDA algorithm (LDEPDA) successfully recovered the simulated damping parameter under a variety of conditions when process noise was present in the latent state. The LDEPDA had greater precision and accuracy than the SSM when estimating parameters from data with sparse jump discontinuities, but worse performance for diffusion processes overall. All three methods were applied to a sample of postural sway data. The basic LDE estimated zero damping, while the LDEPDA and SSM estimated moderate to high damping. The SSM estimated the smallest standard errors for both frequency and damping parameter estimates.

Recently, researchers in clinical psychology have endeavored to create network models of the relationships between symptoms, both within and across mental disorders. Symptoms that connect two mental disorders are called "bridge symptoms." Unfortunately, no formal quantitative methods for identifying these bridge symptoms exist. Accordingly, we developed four network statistics to identify bridge symptoms: bridge strength, bridge betweenness, bridge closeness, and bridge expected influence. These statistics are nonspecific to the type of network estimated, making them potentially useful in individual-level psychometric networks, group-level psychometric networks, and networks outside the field of psychopathology such as social networks. We first tested the fidelity of our statistics in predicting bridge nodes in a series of simulations. Averaged across all conditions, the statistics achieved a sensitivity of 92.7% and a specificity of 84.9%. By simulating datasets of varying sample sizes, we tested the robustness of our statistics, confirming their suitability for network psychometrics. Furthermore, we simulated the contagion of one mental disorder to another, showing that deactivating bridge nodes prevents the spread of comorbidity (i.e., one disorder activating another). Eliminating nodes based on bridge statistics was more effective than eliminating nodes high on traditional centrality statistics in preventing comorbidity. Finally, we applied our algorithms to 18 group-level empirical comorbidity networks from published studies and discussed the implications of this analysis.

Factor rotation is usually performed for a p-variables -factors loading matrix so that the resulting rotated matrix has a simple structure. This simple structure was originally defined by Thurstone (1947) by specifying how zero elements are arranged in the loading matrix. In this article, we propose a new rotation technique, which is directly based on Thurstone’s definition. It can give a p-variables -factors target matrix of zero and nonzero elements, which stands for the properties to be possessed by the rotated loading matrix. However, it is unknown how the rows of the target matrix are associated with those of the loading matrix. In the proposed procedure, a loading matrix is rotated simultaneously with a permutation of the rows of the target matrix, so that the rotated loading matrix is optimally matched to the permuted target matrix in a least squares sense. Its novel feature is the use of permutation, thus we call the technique Permutimin. Its algorithm is presented, with Thurstone’s definition of simple structure modified so as to specify the target matrix uniquely. Permutimin is illustrated with real data examples. Finally, we discuss the relationships between Permutimin and Procrustes rotation.

Structural equation modeling is a common technique to assess change in longitudinal designs. However, these models can become of unmanageable size with many measurement occasions. One solution is the imposition of Kronecker product restrictions to model the multivariate longitudinal structure of the data. The resulting longitudinal three-mode models (L3MMs) are very parsimonious and have attractive interpretation. This paper provides an instructive description of L3MMs. The models are applied to health-related quality of life (HRQL) data obtained from 682 patients with painful bone metastasis, with eight measurements at 13 occasions; before and every week after treatment with radiotherapy. We explain (1) how the imposition of Kronecker product restrictions can be used to model the multivariate longitudinal structure of the data, (2) how to interpret the Kronecker product restrictions and the resulting L3MM parameters, and (3) how to test substantive hypotheses in L3MMs. In addition, we discuss the challenges for the evaluation of (differences in) fit of these complex and parsimonious models. The L3MM restrictions lead to parsimonious models and provide insight in the change patterns of relationships between variables in addition to the general patterns of change. The L3MM thus provides a convenient model for multivariate longitudinal data, as it not only facilitates the analysis of complex longitudinal data but also the substantive interpretation of the dynamics of change.

"Advancing Multiple Imputation for Latent Profile Analysis." Multivariate Behavioral Research, 54(1), pp. 157–158

The Flynn effect (FE; e.g., Flynn, 1984) is the longitudinal increase in measured IQ. IQ tests must be regularly renormed to have consistent meaning in the presence of the FE. Understudied, however...

In this paper, Multidimensional Cross-Recurrence Quantification Analysis (MdCRQA) is introduced. It is an extension of Multidimensional Recurrence Quantification Analysis (MdRQA), which allows to quantify the (auto-)recurrence properties of a single multidimensional time-series. MdCRQA extends MdRQA to bi-variate cases to allow for the quantification of the co-evolution of two multidimensional time-series. Moreover, it is shown how a Diagonal Cross-Recurrence Profile (DCRP) can be computed from the MdCRQA output that allows to capture time-lagged coupling between two multidimensional time-series. The core concepts of these analyses are described, as well as practical aspects of their application. In the supplementary materials to this paper, implementations of MdCRQA and the DCRP as MatLab- and R-functions are provided.