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.
Early Warning Signals (EWS) have generated much excitement for their potential to anticipate transitions in various systems, ranging from climate change in ecology to disease staging in medicine. EWS hold particular promise for bifurcations, a transition mechanism in which a smooth, gradual change in a control parameter of the system results in a rapid change in system dynamics. The predominant reason to expect EWS is because many bifurcations are preceded by Critical Slowing Down (CSD): if assuming the system is subject to continuous, small, Gaussian noise, the system is slower to recover from perturbations closer to the transition. However, this focus on warning signs generated by stochasticity has overshadowed warning signs which may already be found in deterministic dynamics. This is especially true for higher-dimensional systems, where more complex attractors with intrinsic dynamics such as oscillations not only become possible—they are increasingly more likely. The present study focuses on univariate and multivariate EWS in deterministic dynamics to anticipate complex critical transitions, including the period-doubling cascade to chaos, chaos-chaos transitions, and the extinction of a chaotic attractor. In a four-dimensional continuous-time Lotka–Volterra model, EWS perform well for most bifurcations, even with lower data quality. The present study highlights three reasons why EWS may still work in the absence of CSD: changing attractor morphology (size, shape, and location in phase space), shifting power spectra (amplitude and frequency), and chaotic transitional characteristics (density across attractor). More complex attractors call for different warning detection methods to utilise warning signs already contained within purely deterministic dynamics.
First, I thank Sijtsma, Clark, Kane, and Heiser for taking the time and effort to provide a commentary on my paper, and the Editor for allowing me to respond to them. In general, the commentators agree with the thesis that psychometrics and psychology are, to an extent that must be deemed problematic, disconnected. They further agree with the upshot of this diagnosis: Psychometricians need to work harder to make a difference in psychology, and psychologists need to develop a greater awareness of important psychometric developments. However, the commentators also raise several points of disagreement and criticism. I focus on four important topics that concern:
From the Department of Psychology, Faculty of Social and Behavioral Sciences, University of Amsterdam, Amsterdam, The Netherlands. Reprints: Denny Borsboom, Department of Psychology, Faculty of Social and Behavioral Sciences, University of Amsterdam, Roetersstraat 15, 1018 WB Amsterdam. E-mail: [email protected].
No abstract is provided for this article.
No abstract is provided for this article.
In recent years, network models have been proposed as an alternative representation of psychometric constructs such as depression. In such models, the covariance between observables (e.g., symptoms like depressed mood, feelings of worthlessness, and guilt) is explained in terms of a pattern of causal interactions between these observables, which contrasts with classical interpretations in which the observables are conceptualized as the effects of a reflective latent variable. However, few investigations have been directed at the question how these different models relate to each other. To shed light on this issue, the current paper explores the relation between one of the most important network models-the Ising model from physics-and one of the most important latent variable models-the Item Response Theory (IRT) model from psychometrics. The Ising model describes the interaction between states of particles that are connected in a network, whereas the IRT model describes the probability distribution associated with item responses in a psychometric test as a function of a latent variable. Despite the divergent backgrounds of the models, we show a broad equivalence between them and also illustrate several opportunities that arise from this connection.
