CAR: A MATLAB Package to Compute Correspondence Analysis with Rotations

Correspondence analysis (CA) is a popular method that can be used to analyse relationships between categorical variables. Like principal component analysis, CA solutions can be rotated both orthogonally and obliquely to simple structure without affecting the total amount of explained inertia. We describe a MATLAB package for computing CA. The package includes orthogonal and oblique rotation of axes. It is designed not only for advanced users of MATLAB but also for beginners. Analysis can be done using a user-friendly interface, or by using command lines. We illustrate the use of CAR with one example.

Bootstrap confidence intervals for principal covariates regression

Principal covariate regression (PCOVR) is a method for regressing a set of criterion variables with respect to a set of predictor variables when the latter are many in number and/or collinear. This is done by extracting a limited number of components that simultaneously synthesize the predictor variables and predict the criterion ones. So far, no procedure has been offered for estimating statistical uncertainties of the obtained PCOVR parameter estimates. The present paper shows how this goal can be achieved, conditionally on the model specification, by means of the bootstrap approach. Four strategies for estimating bootstrap confidence intervals are derived and their statistical behaviour in terms of coverage is assessed by means of a simulation experiment. Such strategies are distinguished by the use of the varimax and quartimin procedures and by the use of Procrustes rotations of bootstrap solutions towards the sample solution. In general, the four strategies showed appropriate statistical behaviour, with coverage tending to the desired level for increasing sample sizes. The main exception involved strategies based on the quartimin procedure in cases characterized by complex underlying structures of the components. The appropriateness of the statistical behaviour was higher when the proper number of components were extracted

Candecomp/Parafac with zero constraints at arbitrary positions in a loading matrix

When one interprets Candecomp/Parafac (CP) solutions for analyzing three-way data, small loadings are often ignored, that is, considered to be zero. Rather than just considering them zero, it seems better to actually model such values as zero. This can be done by successive modeling approaches as well as by a simultaneous modeling approach. This paper offers algorithms for three such approaches, and compares them on the basis of empirical data and a simulation study. The conclusion of the latter was that, under realistic circumstances, all approaches recovered the underlying structure well, when the number of values to constrain to zero was given. Whereas the simultaneous modeling approach seemed to perform slightly better, differences were very small and not substantial. Given that the simultaneous approach is far more time consuming than the successive approaches, the present study suggests that for practical purposes successive approaches for modeling zeros in the CP model seem to be indicated

On the white, the black, and the many shades of gray in between:Our reply to Van Ravenzwaaij and Wagenmakers (2021)

In 2019 we wrote an article (Tendeiro & Kiers, 2019) in Psychological Methods over null hypothesis Bayesian testing and its working horse, the Bayes factor. Recently, van Ravenzwaaij and Wagenmakers (2021) offered a response to our piece, also in this journal. Although we do welcome their contribution with thought-provoking remarks on our article, we ended up concluding that there were too many "issues" in van Ravenzwaaij and Wagenmakers (2021) that warrant a rebuttal. In this article we both defend the main premises of our original article and we put the contribution of van Ravenzwaaij and Wagenmakers (2021) under critical appraisal. Our hope is that this exchange between scholars decisively contributes toward a better understanding among psychologists of null hypothesis Bayesian testing in general and of the Bayes factor in particular. (PsycInfo Database Record (c) 2022 APA, all rights reserved)

Are Assumptions of Well-Known Statistical Techniques Checked, and Why (Not)?

A valid interpretation of most statistical techniques requires that one or more assumptions be met. In published articles, however, little information tends to be reported on whether the data satisfy the assumptions underlying the statistical techniques used. This could be due to self-selection: Only manuscripts with data fulfilling the assumptions are submitted. Another explanation could be that violations of assumptions are rarely checked for in the first place. We studied whether and how 30 researchers checked fictitious data for violations of assumptions in their own working environment. Participants were asked to analyze the data as they would their own data, for which often used and well-known techniques such as the t-procedure, ANOVA and regression (or non-parametric alternatives) were required. It was found that the assumptions of the techniques were rarely checked, and that if they were, it was regularly by means of a statistical test. Interviews afterward revealed a general lack of knowledge about assumptions, the robustness of the techniques with regards to the assumptions, and how (or whether) assumptions should be checked. These data suggest that checking for violations of assumptions is not a well-considered choice, and that the use of statistics can be described as opportunistic

Flavour-conserving oscillations of Dirac-Majorana neutrinos

We analyze both chirality-changing and chirality-preserving transitions of Dirac-Majorana neutrinos. In vacuum, the first ones are suppressed with respect to the others due to helicity conservation and the interactions with a (``normal'') medium practically does not affect the expressions of the probabilities for these transitions, even if the amplitudes of oscillations slightly change. For usual situations involving relativistic neutrinos we find no resonant enhancement for all flavour-conserving transitions. However, for very light neutrinos propagating in superdense media, the pattern of oscillations $\nu_L \to \nu^C_L$ is dramatically altered with respect to the vacuum case, the transition probability practically vanishing. An application of this result is envisaged.Comment: 14 pages, latex 2E, no figure

Onset of an outline map to get a hold on the wildwood of clustering methods

The domain of cluster analysis is a meeting point for a very rich multidisciplinary encounter, with cluster-analytic methods being studied and developed in discrete mathematics, numerical analysis, statistics, data analysis and data science, and computer science (including machine learning, data mining, and knowledge discovery), to name but a few. The other side of the coin, however, is that the domain suffers from a major accessibility problem as well as from the fact that it is rife with division across many pretty isolated islands. As a way out, the present paper offers an outline map for the clustering domain as a whole, which takes the form of an overarching conceptual framework and a common language. With this framework we wish to contribute to structuring the domain, to characterizing methods that have often been developed and studied in quite different contexts, to identifying links between them, and to introducing a frame of reference for optimally setting up cluster analyses in data-analytic practice.Comment: 33 pages, 4 figure

Worked-out examples of the adequacy of Bayesian optional stopping

The practice of sequentially testing a null hypothesis as data are collected until the null hypothesis is rejected is known as optional stopping. It is well known that optional stopping is problematic in the context of p value-based null hypothesis significance testing: The false-positive rates quickly overcome the single test's significance level. However, the state of affairs under null hypothesis Bayesian testing, where p values are replaced by Bayes factors, has perhaps surprisingly been much less consensual. Rouder (2014) used simulations to defend the use of optional stopping under null hypothesis Bayesian testing. The idea behind these simulations is closely related to the idea of sampling from prior predictive distributions. Deng et al. (2016) and Hendriksen et al. (2020) have provided mathematical evidence to the effect that optional stopping under null hypothesis Bayesian testing does hold under some conditions. These papers are, however, exceedingly technical for most researchers in the applied social sciences. In this paper, we provide some mathematical derivations concerning Rouder's approximate simulation results for the two Bayesian hypothesis tests that he considered. The key idea is to consider the probability distribution of the Bayes factor, which is regarded as being a random variable across repeated sampling. This paper therefore offers an intuitive perspective to the literature and we believe it is a valid contribution towards understanding the practice of optional stopping in the context of Bayesian hypothesis testing