PCovR2: A flexible principal covariates regression approach to parsimoniously handle multiple criterion variables.

Principal covariates regression (PCovR) allows one to deal with the interpretational and technical problems associated with running ordinary regression using many predictor variables. In PCovR, the predictor variables are reduced to a limited number of components, and simultaneously, criterion variables are regressed on these components. By means of a weighting parameter, users can flexibly choose how much they want to emphasize reconstruction and prediction. However, when datasets contain many criterion variables, PCovR users face new interpretational problems, because many regression weights will be obtained and because some criteria might be unrelated to the predictors. We therefore propose PCovR2, which extends PCovR by also reducing the criteria to a few components. These criterion components are predicted based on the predictor components. The PCovR2 weighting parameter can again be flexibly used to focus on the reconstruction of the predictors and criteria, or on filtering out relevant predictor components and predictable criterion components. We compare PCovR2 to two other approaches, based on partial least squares (PLS) and principal components regression (PCR), that also reduce the criteria and are therefore called PLS2 and PCR2. By means of a simulated example, we show that PCovR2 outperforms PLS2 and PCR2 when one aims to recover all relevant predictor components and predictable criterion components. Moreover, we conduct a simulation study to evaluate how well PCovR2, PLS2 and PCR2 succeed in finding (1) all underlying components and (2) the subset of relevant predictor and predictable criterion components. Finally, we illustrate the use of PCovR2 by means of empirical data.

iTOP: inferring the topology of omics data.

Motivation: In biology, we are often faced with multiple datasets recorded on the same set of objects, such as multi-omics and phenotypic data of the same tumors. These datasets are typically not independent from each other. For example, methylation may influence gene expression, which may, in turn, influence drug response. Such relationships can strongly affect analyses performed on the data, as we have previously shown for the identification of biomarkers of drug response. Therefore, it is important to be able to chart the relationships between datasets. Results: We present iTOP, a methodology to infer a topology of relationships between datasets. We base this methodology on the RV coefficient, a measure of matrix correlation, which can be used to determine how much information is shared between two datasets. We extended the RV coefficient for partial matrix correlations, which allows the use of graph reconstruction algorithms, such as the PC algorithm, to infer the topologies. In addition, since multi-omics data often contain binary data (e.g. mutations), we also extended the RV coefficient for binary data. Applying iTOP to pharmacogenomics data, we found that gene expression acts as a mediator between most other datasets and drug response: only proteomics clearly shares information with drug response that is not present in gene expression. Based on this result, we used TANDEM, a method for drug response prediction, to identify which variables predictive of drug response were distinct to either gene expression or proteomics. Availability and implementation: An implementation of our methodology is available in the R package iTOP on CRAN. Additionally, an R Markdown document with code to reproduce all figures is provided as Supplementary Material. Supplementary information: Supplementary data are available at Bioinformatics online.

A review of tensor-based methods and their application to hospital care data.

In many situations, a researcher is interested in the analysis of the scores of a set of observation units on a set of variables. However, in medicine, it is very frequent that the information is replicated at different occasions. The occasions can be time-varying or refer to different conditions. In such cases, the data can be stored in a 3-way array or tensor. The Candecomp/Parafac and Tucker3 methods represent the most common methods for analyzing 3-way tensors. In this work, a review of these methods is provided, and then this class of methods is applied to a 3-way data set concerning hospital care data for a hospital in Rome (Italy) during 15 years distinguished in 3 groups of consecutive years (1892-1896, 1940-1944, 1968-1972). The analysis reveals some peculiar aspects about the use of health services and its evolution along the time.

MultiLevel simultaneous component analysis: A computational shortcut and software package.

MultiLevel Simultaneous Component Analysis (MLSCA) is a data-analytical technique for multivariate two-level data. MLSCA sheds light on the associations between the variables at both levels by specifying separate submodels for each level. Each submodel consists of a component model. Although MLSCA has already been successfully applied in diverse areas within and outside the behavioral sciences, its use is hampered by two issues. First, as MLSCA solutions are fitted by means of iterative algorithms, analyzing large data sets (i.e., data sets with many level one units) may take a lot of computation time. Second, easily accessible software for estimating MLSCA models is lacking so far. In this paper, we address both issues. Specifically, we discuss a computational shortcut for MLSCA fitting. Moreover, we present the MLSCA package, which was built in MATLAB, but is also available in a version that can be used on any Windows computer, without having MATLAB installed.

Penalized optimal scaling for ordinal variables with an application to international classification of functioning core sets.

Ordinal data occur frequently in the social sciences. When applying principal component analysis (PCA), however, those data are often treated as numeric, implying linear relationships between the variables at hand; alternatively, non-linear PCA is applied where the obtained quantifications are sometimes hard to interpret. Non-linear PCA for categorical data, also called optimal scoring/scaling, constructs new variables by assigning numerical values to categories such that the proportion of variance in those new variables that is explained by a predefined number of principal components (PCs) is maximized. We propose a penalized version of non-linear PCA for ordinal variables that is a smoothed intermediate between standard PCA on category labels and non-linear PCA as used so far. The new approach is by no means limited to monotonic effects and offers both better interpretability of the non-linear transformation of the category labels and better performance on validation data than unpenalized non-linear PCA and/or standard linear PCA. In particular, an application of penalized optimal scaling to ordinal data as given with the International Classification of Functioning, Disability and Health (ICF) is provided.

With Bayesian estimation one can get all that Bayes factors offer, and more.

In classical statistics, there is a close link between null hypothesis significance testing (NHST) and parameter estimation via confidence intervals. However, for the Bayesian counterpart, a link between null hypothesis Bayesian testing (NHBT) and Bayesian estimation via a posterior distribution is less straightforward, but does exist, and has recently been reiterated by Rouder, Haaf, and Vandekerckhove (2018). It hinges on a combination of a point mass probability and a probability density function as prior (denoted as the spike-and-slab prior). In the present paper, it is first carefully explained how the spike-and-slab prior is defined, and how results can be derived for which proofs were not given in Rouder, Haaf, and Vandekerckhove (2018). Next, it is shown that this spike-and-slab prior can be approximated by a pure probability density function with a rectangular peak around the center towering highly above the remainder of the density function. Finally, we will indicate how this 'hill-and-chimney' prior may in turn be approximated by fully continuous priors. In this way, it is shown that NHBT results can be approximated well by results from estimation using a strongly peaked prior, and it is noted that the estimation itself offers more than merely the posterior odds on which NHBT is based. Thus, it complies with the strong APA requirement of not just mentioning testing results but also offering effect size information. It also offers a transparent perspective on the NHBT approach employing a prior with a strong peak around the chosen point null hypothesis value.

A review of applications of the Bayes factor in psychological research.

The last 25 years have shown a steady increase in attention for the Bayes factor as a tool for hypothesis evaluation and model selection. The present review highlights the potential of the Bayes factor in psychological research. We discuss six types of applications: Bayesian evaluation of point null, interval, and informative hypotheses, Bayesian evidence synthesis, Bayesian variable selection and model averaging, and Bayesian evaluation of cognitive models. We elaborate what each application entails, give illustrative examples, and provide an overview of key references and software with links to other applications. The article is concluded with a discussion of the opportunities and pitfalls of Bayes factor applications and a sketch of corresponding future research lines. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

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).

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.

A New Opinion Polarization Index Developed by Integrating Expert Judgments.

Opinion polarization is increasingly becoming an issue in today's society, producing both unrest at the societal level, and conflict within small scale communications between people of opposite opinion. Often, opinion polarization is conceptualized as the direct opposite of agreement and consequently operationalized as an index of dispersion. However, in doing so, researchers fail to account for the bimodality that is characteristic of a polarized opinion distribution. A valid measurement of opinion polarization would enable us to predict when, and on what issues conflict may arise. The current study is aimed at developing and validating a new index of opinion polarization. The weights of this index were derived from utilizing the knowledge of 58 international experts on polarization through an expert survey. The resulting Opinion Polarization Index predicted expert polarization scores in opinion distributions better than common measures of polarization, such as the standard deviation, Van der Eijk's polarization measure and Esteban and Ray's polarization index. We reflect on the use of expert ratings for the development of measurements in this case, and more in general.

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.

The effect of preregistration on trust in empirical research findings: results of a registered report.

The crisis of confidence has undermined the trust that researchers place in the findings of their peers. In order to increase trust in research, initiatives such as preregistration have been suggested, which aim to prevent various questionable research practices. As it stands, however, no empirical evidence exists that preregistration does increase perceptions of trust. The picture may be complicated by a researcher's familiarity with the author of the study, regardless of the preregistration status of the research. This registered report presents an empirical assessment of the extent to which preregistration increases the trust of 209 active academics in the reported outcomes, and how familiarity with another researcher influences that trust. Contrary to our expectations, we report ambiguous Bayes factors and conclude that we do not have strong evidence towards answering our research questions. Our findings are presented along with evidence that our manipulations were ineffective for many participants, leading to the exclusion of 68% of complete datasets, and an underpowered design as a consequence. We discuss other limitations and confounds which may explain why the findings of the study deviate from a previously conducted pilot study. We reflect on the benefits of using the registered report submission format in light of our results. The OSF page for this registered report and its pilot can be found here: http://dx.doi.org/10.17605/OSF.IO/B3K75.

A structured overview of simultaneous component based data integration.

BACKGROUND: Data integration is currently one of the main challenges in the biomedical sciences. Often different pieces of information are gathered on the same set of entities (e.g., tissues, culture samples, biomolecules) with the different pieces stemming, for example, from different measurement techniques. This implies that more and more data appear that consist of two or more data arrays that have a shared mode. An integrative analysis of such coupled data should be based on a simultaneous analysis of all data arrays. In this respect, the family of simultaneous component methods (e.g., SUM-PCA, unrestricted PCovR, MFA, STATIS, and SCA-P) is a natural choice. Yet, different simultaneous component methods may lead to quite different results. RESULTS: We offer a structured overview of simultaneous component methods that frames them in a principal components setting such that both the common core of the methods and the specific elements with regard to which they differ are highlighted. An overview of principles is given that may guide the data analyst in choosing an appropriate simultaneous component method. Several theoretical and practical issues are illustrated with an empirical example on metabolomics data for Escherichia coli as obtained with different analytical chemical measurement methods. CONCLUSION: Of the aspects in which the simultaneous component methods differ, pre-processing and weighting are consequential. Especially, the type of weighting of the different matrices is essential for simultaneous component analysis. These types are shown to be linked to different specifications of the idea of a fair integration of the different coupled arrays.

Integrating functional genomics data using maximum likelihood based simultaneous component analysis.

BACKGROUND: In contemporary biology, complex biological processes are increasingly studied by collecting and analyzing measurements of the same entities that are collected with different analytical platforms. Such data comprise a number of data blocks that are coupled via a common mode. The goal of collecting this type of data is to discover biological mechanisms that underlie the behavior of the variables in the different data blocks. The simultaneous component analysis (SCA) family of data analysis methods is suited for this task. However, a SCA may be hampered by the data blocks being subjected to different amounts of measurement error, or noise. To unveil the true mechanisms underlying the data, it could be fruitful to take noise heterogeneity into consideration in the data analysis. Maximum likelihood based SCA (MxLSCA-P) was developed for this purpose. In a previous simulation study it outperformed normal SCA-P. This previous study, however, did not mimic in many respects typical functional genomics data sets, such as, data blocks coupled via the experimental mode, more variables than experimental units, and medium to high correlations between variables. Here, we present a new simulation study in which the usefulness of MxLSCA-P compared to ordinary SCA-P is evaluated within a typical functional genomics setting. Subsequently, the performance of the two methods is evaluated by analysis of a real life Escherichia coli metabolomics data set. RESULTS: In the simulation study, MxLSCA-P outperforms SCA-P in terms of recovery of the true underlying scores of the common mode and of the true values underlying the data entries. MxLSCA-P further performed especially better when the simulated data blocks were subject to different noise levels. In the analysis of an E. coli metabolomics data set, MxLSCA-P provided a slightly better and more consistent interpretation. CONCLUSION: MxLSCA-P is a promising addition to the SCA family. The analysis of coupled functional genomics data blocks could benefit from its ability to take different noise levels per data block into consideration and improve the recovery of the true patterns underlying the data. Moreover, the maximum likelihood based approach underlying MxLSCA-P could be extended to custom-made solutions to specific problems encountered.

Discriminating between strong and weak structures in three-mode principal component analysis.

Recently, a number of model selection heuristics (i.e. DIFFIT, CORCONDIA, the numerical convex hull based heuristic) have been proposed for choosing among Parafac and/or Tucker3 solutions of different complexity for a given three-way three-mode data set. Such heuristics are often validated by means of extensive simulation studies. However, these simulation studies are unrealistic in that it is assumed that the variance in real three-way data can be split into two parts: structural variance, due to a true underlying Parafac or Tucker3 model of low complexity, and random noise. In this paper, we start from the much more reasonable assumption that the variance in any real three-way data set is due to three different sources: (1) a strong Parafac or Tucker3 structure of low complexity, accounting for a considerable amount of variance, (2) a weak Tucker3 structure, capturing less prominent data aspects, and (3) random noise. As such, Parafac and Tucker3 simulation studies are run in which the data are generated by adding a weak Tucker3 structure to a strong Parafac or Tucker3 one and perturbing the resulting data with random noise. The design of these studies is based on the reanalysis of real data sets. In these studies, the performance of the numerical convex hull based model selection method is evaluated with respect to its capability of discriminating strong from weak underlying structures. The results show that in about two-thirds of the simulated cases, the hull heuristic yields a model of the same complexity as the strong underlying structure and thus succeeds in disentangling strong and weak underlying structures. In the vast majority of the remaining third, this heuristic selects a solution that combines the strong structure and (part of) the weak structure.

Bootstrap confidence intervals in multi-level simultaneous component analysis.

Multi-level simultaneous component analysis (MLSCA) was designed for the exploratory analysis of hierarchically ordered data. MLSCA specifies a component model for each level in the data, where appropriate constraints express possible similarities between groups of objects at a certain level, yielding four MLSCA variants. The present paper discusses different bootstrap strategies for estimating confidence intervals (CIs) on the individual parameters. In selecting a proper strategy, the main issues to address are the resampling scheme and the non-uniqueness of the parameters. The resampling scheme depends on which level(s) in the hierarchy are considered random, and which fixed. The degree of non-uniqueness depends on the MLSCA variant, and, in two variants, the extent to which the user exploits the transformational freedom. A comparative simulation study examines the quality of bootstrap CIs of different MLSCA parameters. Generally, the quality of bootstrap CIs appears to be good, provided the sample sizes are sufficient at each level that is considered to be random. The latter implies that if more than a single level is considered random, the total number of observations necessary to obtain reliable inferential information increases dramatically. An empirical example illustrates the use of bootstrap CIs in MLSCA.

Oblique rotation in correspondence analysis: a step forward in the search for the simplest interpretation.

Correspondence analysis (CA) is a popular method that can be used to analyse relationships between categorical variables. It is closely related to several popular multivariate analysis methods such as canonical correlation analysis and principal component analysis. Like principal component analysis, CA solutions can be rotated orthogonally as well as obliquely into a simple structure without affecting the total amount of explained inertia. However, some specific aspects of CA prevent standard rotation procedures from being applied in a straightforward fashion. In particular, the role played by weights assigned to points and dimensions and the duality of CA solutions are unique to CA. For orthogonal simple structure rotation, procedures recently have been proposed. In this paper, we construct oblique rotation methods for CA that take into account these specific difficulties. We illustrate the benefits of our oblique rotation procedure by means of two illustrative examples.

The LMPCA program: a graphical user interface for fitting the linked-mode PARAFAC-PCA model to coupled real-valued data.

In behavioral research, PARAFAC analysis, a three-mode generalization of standard principal component analysis (PCA), is often used to disclose the structure of three-way three-mode data. To get insight into the underlying mechanisms, one often wants to relate the component matrices resulting from such a PARAFAC analysis to external (two-way two-mode) information, regarding one of the modes of the three-way data. To this end, linked-mode PARAFAC-PCA analysis can be used, in which the three-way and the two-way data set, which have one mode in common, are simultaneously analyzed. More specifically, a PARAFAC and a PCA model are fitted to the three-way and the two-way data, respectively, restricting the component matrix for the common mode to be equal in both models. Until now, however, no software program has been publicly available to perform such an analysis. Therefore, in this article, the LMPCA program, a free and easy-to-use MATLAB graphical user interface, is presented to perform a linked-mode PARAFAC-PCA analysis. The LMPCA software can be obtained from the authors at http://ppw.kuleuven.be/okp/software/LMPCA. For users who do not have access to MATLAB, a stand-alone version is provided.

A review of issues about null hypothesis Bayesian testing.

Null hypothesis significance testing (NHST) has been under scrutiny for decades. The literature shows overwhelming evidence of a large range of problems affecting NHST. One of the proposed alternatives to NHST is using Bayes factors instead of p values. Here we denote the method of using Bayes factors to test point null models as "null hypothesis Bayesian testing" (NHBT). In this article we offer a wide overview of potential issues (limitations or sources of misinterpretation) with NHBT which is currently missing in the literature. We illustrate many of the shortcomings of NHBT by means of reproducible examples. The article concludes with a discussion of NHBT in particular and testing in general. In particular, we argue that posterior model probabilities should be given more emphasis than Bayes factors, because only the former provide direct answers to the most common research questions under consideration. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

Assessing the application of latent class and latent profile analysis for evaluating the construct validity of complex posttraumatic stress disorder: cautions and limitations.

Background: The diagnosis of complex posttraumatic stress disorder (CPTSD) has been suggested for inclusion in the 11th version of the International Classification of Diseases (ICD-11), with support for its construct validity coming from studies employing Latent Class Analysis (LCA) and Latent Profile Analysis (LPA). Objective: The current study aimed to critically evaluate the application of the techniques LCA and LPA as applied in previous studies to substantiate the construct validity of CPTSD. Method: Both LCA and LPA were applied systematically in one sample (n = 245), replicating the setup of previous studies as closely as possible. The interpretation of classes was augmented with the use of graphical visualization. Results: The LCA and LPA analyses indicated divergent results in the same dataset. LCA and LPA partially supported the existence of classes of patients endorsing different PTSD and CPTSD symptom patterns. However, further inspection of the results with scatterplots did not support a clear distinction between PTSD and CPTSD, but rather suggested that there is much greater variability in clinical presentations amongst adult PTSD patients than can be fully accounted for by either PTSD or CPTSD. Discussion: We argue that LCA and LPA may not be sufficient methods to decide on the construct validity of CPTSD, as different subgroups of patients are identified, depending on the statistical exact method used and the interpretation of the fit of different models. Additional methods, including graphical inspection should be employed in future studies.

Antecedentes: El diagnóstico de Trastorno por Estrés Postraumático Complejo (TEPTC) ha sido sugerido para su inclusión en la 11ª versión de la Clasificación Internacional de Enfermedades (CIE-11), con el respaldo de su validez de constructo proveniente de estudios que emplean Análisis de Clases Latentes (LCA) y Análisis de Perfil Latente (APL).Objetivo: El presente estudio tuvo como objetivo evaluar críticamente la aplicación de las técnicas LCA y APL, utilizadas en estudios anteriores, para corroborar la validez de constructo del TEPTC.Método: Se aplicaron sistemáticamente, tanto la técnica LCA como la técnica APL, en una muestra (n = 245), que buscó replicar lo más fielmente posible las configuraciones empleadas en estudios previos. La interpretación de las clases se potenció con el uso de visualización gráfica.Resultados: Los análisis LCA y APL indicaron resultados divergentes en el mismo conjunto de datos. LCA y APL apoyaron parcialmente la existencia de clases de pacientes que validan diferentes patrones de síntomas para el TEPT y el TEPTC. Sin embargo, una mayor inspección de los resultados con diagramas de dispersión no respaldó una distinción clara entre el TEPT y el TEPTC, sino que sugirieron que existe una variabilidad mucho mayor en las presentaciones clínicas entre los pacientes adultos con TEPT de lo que pueda explicarse ya sea por el TEPT o el TEPTC.Discusión: Proponemos que los análisis LCA y APL pueden ser métodos insuficientes para decidir sobre la validez de constructo del TEPTC, ya que se identifican diferentes subgrupos de pacientes, que depende del método estadístico utilizado y la interpretación del ajuste de diferentes modelos. En futuros estudios deben emplearse métodos adicionales que incluyan la inspección gráfica.