Combinatorial data analysis: Association and partial association

A combinatorial data analysis strategy is reviewed that is designed to compare two arbitrary measures of proximity defined between the objects from some set. Based on a particular cross-product definition of correspondence between these two numerically specified notions of proximity (typically represented in the form of matrices), extensions are then pursued to indices of partial association that relate the observed pattern of correspondence between the first two proximity measures to a third. The attendant issues of index normalization and significance testing are discussed; the latter is approached through a simple randomization model implemented either through a Monte Carlo procedure or distributional approximations based on the first three moments. Applications of the original comparison strategy and its extensions to partial association may be developed for a variety of methodological and substantive tasks. Besides rank correlation, we emphasize the topics of spatial autocorrelation for one variable and spatial association between two and mention the connection to the usual randomization approach for one-way analysis-of-variance.     

Comparing the effects of two correction procedures on human acquisition of sequential behavior patterns

Thirty-one college undergraduates learned to touch abstract stimuli on a computer screen in arbitrarily designated “correct” sequential orders. Four sets of seven stimuli were used; the stimuli were arrayed horizontally on the screen in random sequences. A correct response (i.e., touching first the stimulus designated as first) resulted in that stimulus appearing near the top of the screen in its correct sequential position (left to right), and remaining there until the end of the trial. Incorrect responses (i.e., touching a stimulus out of sequence) terminated the trial. New trials displayed either the same sequence as the one on which an error had occurred (same-order correction procedure), or a new random sequence (new-order correction procedure). Whenever all responses occurred in the correct sequence, the next trial displayed a new random sequence. Each phase ended when five consecutive correct response sequences occurred. Initially, the same-order correction procedure increased control by the position as well as by the shape of the stimuli; also, it produced more errors, more total trials, more trials to mastery, and more individual patterns of reacquisition than were produced by the new-order procedure.     

Premature conclusions about the signal-to-noise ratio in structural equation modeling research: A commentary on Yuan and Fang (2023)

In a recent article published in this journal, Yuan and Fang (British Journal of Mathematical and Statistical Psychology, 2023) suggest comparing structural equation modeling (SEM), also known as covariance-based SEM (CB-SEM), estimated by normal-distribution-based maximum likelihood (NML), to regression analysis with (weighted) composites estimated by least squares (LS) in terms of their signal-to-noise ratio (SNR). They summarize their findings in the statement that “[c]ontrary 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 [SNR].” In our commentary, we show that Yuan and Fang have made several incorrect assumptions and claims. Consequently, we recommend that empirical researchers not base their methodological choice regarding CB-SEM and regression analysis with composites on the findings of Yuan and Fang as these findings are premature and require further research.     

Interpreting canonical correlation analysis through biplots of structure correlations and weights

This paper extends the biplot technique to canonical correlation analysis and redundancy analysis. The plot of structure correlations is shown to the optimal for displaying the pairwise correlations between the variables of the one set and those of the second. The link between multivariate regression and canonical correlation analysis/redundancy analysis is exploited for producing an optimal biplot that displays a matrix of regression coefficients. This plot can be made from the canonical weights of the predictors and the structure correlations of the criterion variables. An example is used to show how the proposed biplots may be interpreted.     

Stochastic ordering using the latent trait and the sum score in polytomous IRT models

In a restricted class of item response theory (IRT) models for polytomous items the unweighted total score has monotone likelihood ratio (MLR) in the latent trait. MLR implies two stochastic ordering (SO) properties, denoted SOM and SOL, which are both weaker than MLR, but very useful for measurement with IRT models. Therefore, these SO properties are investigated for a broader class of IRT models for which the MLR property does not hold.In this study, first a taxonomy is given for nonparametric and parametric models for polytomous items based on the hierarchical relationship between the models. Next, it is investigated which models have the MLR property and which have the SO properties. It is shown that all models in the taxonomy possess the SOM property. However, counterexamples illustrate that many models do not, in general, possess the even more useful SOL property.Hemker's research was supported by the Netherlands Research Council, Grant 575-67-034. Junker's research was supported in part by the National Institutes of Health, Grant CA54852, and by the National Science Foundation, Grant DMS-94.04438.     

The logics of orthoalgebras

The notion of unsharp orthoalgebra is introduced and it is proved that the category of unsharp orthoalgebras is isomorphic to the category of D-posets. A completeness theorem for some partial logics based on unsharp orthoalgebras, orthoalgebras and orthomodular posets is proved.     

Naturalistic Partial Sleep Deprivation Leads to Greater Next-Day Anxiety: The Moderating Role of Baseline Anxiety and Depression

The detrimental effects of insufficient sleep on emotional functioning have been well established. Total sleep deprivation usually leads to increased anxiety and depressive symptoms the following day. However, no study has yet examined the relationships between unmanipulated partial sleep deprivation and next-day symptoms of anxiety and depression in everyday life, which this study sought to characterize. Participants (N = 94) completed daily diary surveys twice per day for 2 weeks without instructions to alter their sleep in any way. Nights of spontaneous, naturally occurring partial sleep deprivation were followed by increased levels of self-reported symptoms of anxious arousal the next day, but were unrelated to next-day symptoms of anhedonic depression or general distress. The relationship between partial sleep deprivation and next-day anxious arousal was found to be moderated by both baseline depressive symptoms and anxiety such that individuals reporting higher levels of depression or anxiety at baseline showed relatively greater increases in symptoms of anxiety following partial sleep deprivation. These results suggest that partial sleep deprivation occurring in everyday life can lead to higher next-day levels of anxious arousal, a relationship that is particularly deleterious for individuals with higher overall levels of anxiety or depressive symptoms.     

Flexible moral theories: Complexity,domination, and indeterminacy

In this article we identify three previously unnoticed problems with flexible moral theories, i.e., theories according to which different moral rules apply when there is full compliance and when there is partial compliance. The first problem is that flexible theories are necessarily very complex, which undermines their ability to motivate and guide action. The second problem is that flexible theories allow for a troubling kind of (moral) domination: the duties an agent has depend on other agents' willingness to comply. Finally, flexible theories introduce indeterminacy: it is sometimes impossible to determine which moral rules apply. When agents stand at the threshold—i.e., when a different rule would apply if a single additional act of noncompliance took place—it is impossible to determine which rule should apply.