Recognize the Value of the Sum Score, Psychometrics' Greatest Accomplishment

The sum score on a psychological test is, and should continue to be, a tool central in psychometric practice. This position runs counter to several psychometricians' belief that the sum score represents a pre-scientific conception that must be abandoned from psychometrics in favor of latent variables. First, we reiterate that the sum score stochastically orders the latent variable in a wide variety of much-used item response models. In fact, item response theory provides a mathematically based justification for the ordinal use of the sum score. Second, because discussions about the sum score often involve its reliability and estimation methods as well, we show that, based on very general assumptions, classical test theory provides a family of lower bounds several of which are close to the true reliability under reasonable conditions. Finally, we argue that eventually sum scores derive their value from the degree to which they enable predicting practically relevant events and behaviors. None of our discussion is meant to discredit modern measurement models; they have their own merits unattainable for classical test theory, but the latter model provides impressive contributions to psychometrics based on very few assumptions that seem to have become obscured in the past few decades. Their generality and practical usefulness add to the accomplishments of more recent approaches.

The College Students' Sense of Responsibility for Innovation and Entrepreneurship

The purpose of this paper is to analyze the relationship between positive psychological quality and college students’ sense of responsibility for innovation and entrepreneurship from the perspective of positive psychology, to explore the cultivation model that can effectively improve college students’ sense of responsibility for innovation and entrepreneurship, and to promote their success in entrepreneurship. In this study, a total of 1,500 college students were selected for questionnaire survey. ANOVA was used to analyze the differences of innovation and entrepreneurship responsibilities in demographic variables; factor analysis models were used to explore the factors that influence college students’ sense of responsibility for innovation and entrepreneurship; and Spearman correlation and linear regression were used to analyze the relationship between college students’ positive quality and innovation and entrepreneurship. The results showed that the average scores of individual responsibility, team responsibility, and social responsibility were 3.290, 3.624, and 3.720, respectively; individual responsibility differed significantly at the grade level; group responsibilities and social responsibilities were significantly different at the grade and gender levels; the linear fitting between benevolence, super-excellence, bravery, restraint, and wisdom with team responsibilities all reached significant levels, among which the wisdom coefficient was the highest; the linear fitting between syngroup, excellence, bravery, modesty, and wisdom with social responsibility reached a significant level, among which the wisdom coefficient was the highest; the linear fitting between syngroup, excellence, bravery, modesty, and wisdom with personal responsibility reached a significant level, among which the coefficient of excellence was the highest. This indicated that positive psychological qualities such as syngroup, excellence, modesty, benevolence, super-excellence, bravery, restraint, and wisdom were the influencing factors of college students’ sense of responsibility for innovation and entrepreneurship. Among them, the role of wisdom is the most noteworthy in predicting social and group responsibilities, and super-excellent is the most significant predictor for individual responsibility.

Structural factor equation models for causal network construction via directed acyclic mixed graphs

Directed acyclic mixed graphs (DAMGs) provide a useful representation of network topology with both directed and undirected edges subject to the restriction of no directed cycles in the graph. This graphical framework may arise in many biomedical studies, for example, when a directed acyclic graph (DAG) of interest is contaminated with undirected edges induced by some unobserved confounding factors (eg, unmeasured environmental factors). Directed edges in a DAG are widely used to evaluate causal relationships among variables in a network, but detecting them is challenging when the underlying causality is obscured by some shared latent factors. The objective of this paper is to develop an effective structural equation model (SEM) method to extract reliable causal relationships from a DAMG. The proposed approach, termed structural factor equation model (SFEM), uses the SEM to capture the network topology of the DAG while accounting for the undirected edges in the graph with a factor analysis model. The latent factors in the SFEM enable the identification and removal of undirected edges, leading to a simpler and more interpretable causal network. The proposed method is evaluated and compared to existing methods through extensive simulation studies, and illustrated through the construction of gene regulatory networks related to breast cancer.

A Penalized Likelihood Method for Structural Equation Modeling

A penalized likelihood (PL) method for structural equation modeling (SEM) was proposed as a methodology for exploring the underlying relations among both observed and latent variables. Compared to the usual likelihood method, PL includes a penalty term to control the complexity of the hypothesized model. When the penalty level is appropriately chosen, the PL can yield an SEM model that balances the model goodness-of-fit and model complexity. In addition, the PL results in a sparse estimate that enhances the interpretability of the final model. The proposed method is especially useful when limited substantive knowledge is available for model specifications. The PL method can be also understood as a methodology that links the traditional SEM to the exploratory SEM (Asparouhov & Muthén in Struct Equ Model Multidiscipl J 16:397-438, 2009). An expectation-conditional maximization algorithm was developed to maximize the PL criterion. The asymptotic properties of the proposed PL were also derived. The performance of PL was evaluated through a numerical experiment, and two real data illustrations were presented to demonstrate its utility in psychological research.

A latent factor linear mixed model for high-dimensional longitudinal data analysis

High-dimensional longitudinal data involving latent variables such as depression and anxiety that cannot be quantified directly are often encountered in biomedical and social sciences. Multiple responses are used to characterize these latent quantities, and repeated measures are collected to capture their trends over time. Furthermore, substantive research questions may concern issues such as interrelated trends among latent variables that can only be addressed by modeling them jointly. Although statistical analysis of univariate longitudinal data has been well developed, methods for modeling multivariate high-dimensional longitudinal data are still under development. In this paper, we propose a latent factor linear mixed model (LFLMM) for analyzing this type of data. This model is a combination of the factor analysis and multivariate linear mixed models. Under this modeling framework, we reduced the high-dimensional responses to low-dimensional latent factors by the factor analysis model, and then we used the multivariate linear mixed model to study the longitudinal trends of these latent factors. We developed an expectation-maximization algorithm to estimate the model. We used simulation studies to investigate the computational properties of the expectation-maximization algorithm and compare the LFLMM model with other approaches for high-dimensional longitudinal data analysis. We used a real data example to illustrate the practical usefulness of the model.