A Note on the Conversion of Item Parameters Standard Errors

The relations among alternative parameterizations of the binary factor analysis (FA) model and two-parameter logistic (2PL) item response theory (IRT) model have been thoroughly discussed in literature. However, the conversion formulas widely available are mainly for transforming parameter estimates from one parameterization to another. There is a lack of discussion about the standard error (SE) conversion among different parameterizations, when SEs of IRT model parameters are often of immediate interest to practitioners. This article provides general formulas for computing the SEs of transformed parameter values, when these parameters are transformed from FA to IRT models. These formulas are suitable for unidimensional 2PL, multidimensional 2PL, and bi-factor 2PL models. A simulation study is conducted to verify the formula by providing empirical evidence. A real data example is given in the end for an illustration.     

Replies to comments on "Which method delivers greater signal-to-noise ratio: Structural equation modelling or regression analysis with weighted composites?" by Yuan and Fang (2023)

Observational data typically contain measurement errors. Covariance-based structural equation modelling (CB-SEM) is capable of modelling measurement errors and yields consistent parameter estimates. In contrast, methods of regression analysis using weighted composites as well as a partial least squares approach to SEM facilitate the prediction and diagnosis of individuals/participants. But regression analysis with weighted composites has been known to yield attenuated regression coefficients when predictors contain errors. Contrary to the common belief that CB-SEM is the preferred method for the analysis of observational data, this article shows that regression analysis via weighted composites yields parameter estimates with much smaller standard errors, and thus corresponds to greater values of the signal-to-noise ratio (SNR). In particular, the SNR for the regression coefficient via the least squares (LS) method with equally weighted composites is mathematically greater than that by CB-SEM if the items for each factor are parallel, even when the SEM model is correctly specified and estimated by an efficient method. Analytical, numerical and empirical results also show that LS regression using weighted composites performs as well as or better than the normal maximum likelihood method for CB-SEM under many conditions even when the population distribution is multivariate normal. Results also show that the LS regression coefficients become more efficient when considering the sampling errors in the weights of composites than those that are conditional on weights.     

Measuring inaccuracy of uncertain doxastic states in many-valued logical systems

I will propose an alternative philosophical approach to the representation of uncertain doxastic states. I will argue that the current account of measuring inaccuracy of uncertain doxastic states is inadequate for Belnap's four-valued logic. Specifically, a situation can be found in which either an inaccuracy measure returns a completely wrong result or an agent's inaccuracy score is inadequate relative to the mistake in her doxastic attitude. This will motivate an alternative representation of uncertain doxastic states based on ordered pairs. I will describe a possible inaccuracy measure that is suitable for ordered pairs, and I will show that it has all the qualities that are required for an inaccuracy measure to be legitimate. Finally, I will introduce conditions of rationality for uncertain doxastic states represented by ordered pairs.     

Exploration of anomalous perceptual experiences in migraine between attacks using the Cardiff Anomalous Perceptions Scale

Distortions in sensory experiences that precede a migraine attack have been extensively documented, the most well-known being the visual aura. Distortions in the experience of other senses are also reported as part of an aura, albeit less frequently, together with changes in the perception or ownership of the body or body parts. There are many examples of differences in aspects of visual perception between migraine and control groups, between attacks, but not as much on unusual experiences involving other senses, the sense of the body or the experience of the environment. Seventy-seven migraine (33 with aura) and 74 control participants took part. Anomalous perceptions were experienced by both migraine and control groups, but more with migraine experienced them and rated them as more distressing, intrusive and frequent. Associations with reports of visual triggers of migraine and visual discomfort are presented. This study is the first to show relationships between these factors.     

Constitutivism and the virtues

In Self-Constitution, I argue that the principles governing action are “constitutive standards” of agency, standards that arise from the nature of agency itself. To be an agent is to be autonomously efficacious, and the categorical and hypothetical imperatives arise from those two attributes. These principles are also “constitutive” of agency in two more specific ways. First, they meet the “constitution requirement”: the object must meet the standard in question, at least to some extent, in order to be the kind of object that it is. Second, they meet the “self-constitution requirement”: the object makes itself into the kind of object that it is by conforming to the standard. That is, the agent makes herself into an agent, and into the particular agent who she is, by conforming to those standards. Some neo-Aristotelians believe that Aristotelian virtues are constitutive standards. In this paper, I first ask why moral philosophers should focus on the virtues at all, considering the views of David Hume, Philippa Foot, and Aristotle. I then ask whether Aristotelian virtues meet the constitution requirement, and suggest that there are grounds for this view in the Nicomachean Ethics. But Aristotelian virtues do not meet the self-constitution requirement, which leaves Aristotle unable to explain moral responsibility. I end by examining the role that Aristotelian virtues could play in a Kantian ethic.     

Estimating Age-Based Developmental Trajectories Using Latent Change Score Models Based on Measurement Occasion

Abstract

Accelerated longitudinal designs (ALDs) are designs in which participants from different cohorts provide repeated measures covering a fraction of the time range of the study. ALDs allow researchers to study developmental processes spanning long periods within a relatively shorter time framework. The common trajectory is studied by aggregating the information provided by the different cohorts. Latent change score (LCS) models provide a powerful analytical framework to analyze data from ALDs. With developmental data, LCS models can be specified using measurement occasion as the time metric. This provides a number of benefits, but has an important limitation: It makes it not possible to characterize the longitudinal changes as a function of a developmental process such as age or biological maturation. To overcome this limitation, we propose an extension of an occasion-based LCS model that includes age differences at the first measurement occasion. We conducted a Monte Carlo study and compared the results of including different transformations of the age variable. Our results indicate that some of the proposed transformations resulted in accurate expectations for the studied process across all the ages in the study, and excellent model fit. We discuss these results and provide the R code for our analysis.