Abstract When data are collected from n individuals for m items over p time points, the data can be stored as three-mode data of size $$n \times m \times p$$ . In order to analyze such three-mode data, the three-mode generalized multivariate analysis of variance (3mGMANOVA) model can be applied. Although this model has been shown to be useful, the available algorithms for its implementation assume that both a between-individuals design matrix and a between-items design matrix should be set prior to the analysis. This limits the model’s practical application. In this study, we propose estimation methods for the 3mGMANOVA model that accommodate various conditions related to the availability of between-individuals and between-items design matrices. In addition, the similarities and differences between the 3mGMANOVA model and three-mode principal component analysis model, also known as the Tucker 3 model, are illustrated, using real data.

Abstract Bootstrapping offers a flexible approach to estimating statistical power, when planning a new study based on a previous one. In this article, we explore both parametric and non-parametric bootstrap power calculations and demonstrate how to incorporate uncertainty about effect size in bootstrap power analysis. We use real examples to illustrate bootstrap power calculations in independent t -test and ANCOVA. Finally, we discuss the broader implications of bootstrap power calculation for a variety of research designs.

Abstract The present study focuses on parametric-regression-based causal mediation analysis for binary outcomes. Existing methodologies of parametric causal mediation analysis often specify logistic and probit outcome models. However, logistic and probit models implicitly assume a symmetric shape of binary response curves and fail to capture the true relationship between explanatory variables and the outcome when the binary response curves are asymmetric. Alternatively, the present study explores parametric-regression-based causal mediation analysis using the complementary log-log model that models the outcome success probability asymmetrically. Following existing literature on causal mediation analysis, we define the controlled direct effect, natural direct effect, and natural indirect effect of the exposure on a scale suitable for the complementary log-log model. We discuss the confounding assumptions to identify these effects. We derive simple closed-form analytic expressions for these effects that are easily estimated by regression analyses. The validity of our proposed estimators is demonstrated through numerical simulations, and the methodology is illustrated with real-world data from psychological research.