In many regression applications, users are often faced with difficulties due to nonlinear relationships, heterogeneous subjects, or time series which are best represented by splines. In such applications, two or more regression functions are often necessary to best summarize the underlying structure of the data. Unfortunately, in most cases, it is not known a priori which subset of observations should be approximated with which specific regression function. This paper presents a methodology which simultaneously clusters observations into a preset number of groups and estimates the corresponding regression functions' coefficients, all to optimize a common objective function. We describe the problem and discuss related procedures. A new simulated annealing-based methodology is described as well as program options to accommodate overlapping or nonoverlapping clustering, replications per subject, univariate or multivariate dependent variables, and constraints imposed on cluster membership. Extensive Monte Carlo analyses are reported which investigate the overall performance of the methodology. A consumer psychology application is provided concerning a conjoint analysis investigation of consumer satisfaction determinants. Finally, other applications and extensions of the methodology are discussed.

This paper presents an analysis, based on simulation, of the stability of principal components. Stability is measured by the expectation of the absolute inner product of the sample principal component with the corresponding population component. A multiple regression model to predict stability is devised, calibrated, and tested using simulated Normal data. Results show that the model can provide useful predictions of individual principal component stability when working with correlation matrices. Further, the predictive validity of the model is tested against data simulated from three non-Normal distributions. The model predicted very well even when the data departed from normality, thus giving robustness to the proposed measure. Used in conjunction with other existing rules this measure will help the user in determining interpretability of principal components.

Guttman's assumption underlying his definition of “total images” is rejected: Partial images are not generally convergent everywhere. Even divergence everywhere is shown to be possible. The convergence type always found on partial images is convergence in quadratic mean; hence, total images are redefined as quadratic mean-limits. In determining the convergence type in special situations, the asymptotic properties of certain correlations are important, implying, in some cases, convergence almost everywhere, which is also effected by a countable population or multivariate normality or independent variables. The interpretations of a total image as a predictor, and a “common-factor score”, respectively, are made precise.

Whenever statistical analyses are applied to multiply imputed datasets, specific formulas are needed to combine the results into one overall analysis, also called combination rules. In the context of regression analysis, combination rules for the unstandardized regression coefficients, the t-tests of the regression coefficients, and the F-tests for testing $R^2$\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$R^{2}$$\end{document} for significance have long been established. However, there is still no general agreement on how to combine the point estimators of $R^2$\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$R^{2}$$\end{document} in multiple regression applied to multiply imputed datasets. Additionally, no combination rules for standardized regression coefficients and their confidence intervals seem to have been developed at all. In the current article, two sets of combination rules for the standardized regression coefficients and their confidence intervals are proposed, and their statistical properties are discussed. Additionally, two improved point estimators of $R^2$\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$R^{2}$$\end{document} in multiply imputed data are proposed, which in their computation use the pooled standardized regression coefficients. Simulations show that the proposed pooled standardized coefficients produce only small bias and that their 95% confidence intervals produce coverage close to the theoretical 95%. Furthermore, the simulations show that the newly proposed pooled estimates for $R^2$\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$R^{2}$$\end{document} are less biased than two earlier proposed pooled estimates.

SARS-CoV-2 transmission dynamics within households involving children are complex. We examined the association between paediatric index case (PIC) age and subsequent household SARS-CoV-2 transmission among cases reported to the Minnesota Department of Health between March 2021 and February 2022. In our primary analysis, we used logistic regression to estimate odds ratios adjusted for race/ethnicity, sex, geographic region, and disease severity among households with an unvaccinated PIC. We performed a secondary analysis among households where the PIC was eligible for vaccination adjusting for the same covariates plus time since the last vaccination. Both analyses were stratified by variant wave. During the Alpha wave, PICs of all age groups had similar odds of subsequent transmission. During Delta and Omicron waves, PICs aged 16–17 had higher odds of subsequent transmission than PICs aged 0–4 (Delta OR, 1.32; [95% CI, 1.16–1.51], Omicron OR, 4.21; [95% CI, 3.25–5.45]). In the secondary analysis, unvaccinated PICs had higher odds of subsequent transmission than vaccinated PICs (Delta OR 2.89 [95% CI, 2.18–3.84], Omicron OR 1.35 [95% CI, 1.21–1.50]). Enhanced preventative measures, especially for 12–17-year-olds, may limit SARS-CoV-2 transmission within households involving children.

Neurotechnology has been applied to gain insights on creativity-related cognitive factors. Prior research has identified relations between cognitive factors and creativity qualitatively; while quantitative relations, such as the relative importance of cognitive factors and creativity, have not been fully determined. Therefore, taking the creative design process as an example, this study using electroencephalography (EEG) aims to objectively identify how creativity-related cognitive factors of retrieval, recall, association, and combination contribute to creativity. The theoretical basis for an EEG-based decoding method to objectively identify which cognitive factors occur in a creative process is developed. Thirty participants were recruited for a practical study to verify the reliability of the decoding method. Based on the methodology, relationships between the relative importance level of the cognitive factor and creative output quality levels were detected. Results indicated that the occurrence of recall and association are reported with a high reliability level by the decoding method. The results also indicated that association is the dominant cognitive factor for higher creative output quality levels. Recall is the dominant cognitive factor for lower creative output quality levels.

Indices of cumulative risk (CR) have long been used in developmental research to encode the number of risk factors a child or adolescent experiences that may impede optimal developmental outcomes. Initial contributions concentrated on indices of cumulative environmental risk; more recently, indices of cumulative genetic risk have been employed. In this article, regression analytic methods are proposed for interrogating strongly the validity of risk indices by testing optimality of compositing weights, enabling more informative modeling of effects of CR indices. Reanalyses of data from two studies are reported. One study involved 10 environmental risk factors predicting Verbal IQ in 215 four-year-old children. The second study included an index of genetic CR in a G×E interaction investigation of 281 target participants assessed at age 15 years and then again at age 31 years for observed hostility during videotaped interactions with close family relations. Principles to guide evaluation of results of statistical modeling are presented, and implications of results for research and theory are discussed. The ultimate goals of this paper are to develop stronger tests of conjectures involving CR indices and to promote methods for improving replicability of results across studies.

The aim of this study is to investigate Dutch citizens’ care attitudes by looking at care-giving norms and citizens’ welfare state orientation and to explore to what extent these attitudes can be explained by combinations of diversity characteristics. We combined two datasets (2016 and 2018, N = 5,293) containing citizens’ opinions regarding society and conducted multivariate linear and ordered probit regression analyses. An intersectional perspective was adopted to explore the influence of combinations of diversity characteristics. Results show that citizens’ care-giving norms are relatively strong, meaning they believe persons in need of care should receive help from their families or social networks. However, citizens consider the government responsible for care as well. Men, younger people, people in good health and people of non-Western origin have stronger care-giving norms than others, and younger people assign relatively more responsibility to the family than the government. Level of education and religiosity are also associated with care attitudes. Primary diversity dimensions are more related to care attitudes than secondary, circumstantial dimensions. Some of the secondary dimensions interact with primary dimensions. These insights offer policy makers, social workers and (allied) health professionals the opportunity to align with citizens’ care attitudes, as results show that people vary to a large extent in their care-giving norms and welfare state orientation.

Thirty-one accessions of Oryza glaberrima were evaluated to study the genetic variability, correlation, path, principal component analysis (PCA) and D2 analysis. Box plots depicted high estimates of variability for days to 50% flowering and grain yield per plant in Kharif 2016, plant height, productive tillers, panicle length and 1000 seed weight in Kharif 2017. Correlation studies revealed days to 50% flowering, plant height, panicle length, number of productive tillers, spikelets per panicle having a high direct positive association with grain yield, while path analysis identified the number of productive tillers having the maximum direct positive effect on grain yield. Days to 50% flowering via spikelets per panicle, productive tillers and plant height via spikelets per panicle exhibited high positive indirect effects on grain yield per plant. PCA showed that a cumulative variance of 54.752% from yield per plant, days to 50% flowering, spikelets per panicle and panicle length, contributing almost all the variation of traits while D2 analysis identified days to 50% flowering and grain yield per plant contributing maximum to the genetic diversity. Therefore, selection of accessions with more number of productive tillers and early maturity would be most suitable for yield improvement programme. The study has revealed the utility of African rice germplasm and its potential to utilize in the genetic improvement of indica rice varieties.