MATS: Inference for potentially Singular and Heteroscedastic MANOVA

In many experiments in the life sciences, several endpoints are recorded per subject. The analysis of such multivariate data is usually based on MANOVA models assuming multivariate normality and covariance homogeneity. These assumptions, however, are often not met in practice. Furthermore, test statistics should be invariant under scale transformations of the data, since the endpoints may be measured on different scales. In the context of high-dimensional data, Srivastava and Kubokawa (2013) proposed such a test statistic for a specific one-way model, which, however, relies on the assumption of a common non-singular covariance matrix. We modify and extend this test statistic to factorial MANOVA designs, incorporating general heteroscedastic models. In particular, our only distributional assumption is the existence of the group-wise covariance matrices, which may even be singular. We base inference on quantiles of resampling distributions, and derive confidence regions and ellipsoids based on these quantiles. In a simulation study, we extensively analyze the behavior of these procedures. Finally, the methods are applied to a data set containing information on the 2016 presidential elections in the USA with unequal and singular empirical covariance matrices

A single-level random-effects cross-lagged panel model for longitudinal mediation analysis

Cross-lagged panel models (CLPMs) are widely used to test mediation with longitudinal panel data. One major limitation of the CLPMs is that the model effects are assumed to be fixed across individuals. This assumption is likely to be violated (i.e., the model effects are random across individuals) in practice. When this happens, the CLPMs can potentially yield biased parameter estimates and misleading statistical inferences. This article proposes a model named a random-effects cross-lagged panel model (RE-CLPM) to account for random effects in CLPMs. Simulation studies show that the RE-CLPM outperforms the CLPM in recovering the mean indirect and direct effects in a longitudinal mediation analysis when random effects exist in the population. The performance of the RE-CLPM is robust to a certain degree, even when the random effects are not normally distributed. In addition, the RE-CLPM does not produce harmful results when the model effects are in fact fixed in the population. Implications of the simulation studies and potential directions for future research are discussed

The wild bootstrap for multilevel models

In this paper we study the performance of the most popular bootstrap schemes for multilevel data. Also, we propose a modified version of the wild bootstrap procedure for hierarchical data structures. The wild bootstrap does not require homoscedasticity or assumptions on the distribution of the error processes. Hence, it is a valuable tool for robust inference in a multilevel framework. We assess the finite size performances of the schemes through a Monte Carlo study. The results show that for big sample sizes it always pays off to adopt an agnostic approach as the wild bootstrap outperforms other techniques

Model Choice and Diagnostics for Linear Mixed-Effects Models Using Statistics on Street Corners

The complexity of linear mixed-effects (LME) models means that traditional diagnostics are rendered less effective. This is due to a breakdown of asymptotic results, boundary issues, and visible patterns in residual plots that are introduced by the model fitting process. Some of these issues are well known and adjustments have been proposed. Working with LME models typically requires that the analyst keeps track of all the special circumstances that may arise. In this paper we illustrate a simpler but generally applicable approach to diagnosing LME models. We explain how to use new visual inference methods for these purposes. The approach provides a unified framework for diagnosing LME fits and for model selection. We illustrate the use of this approach on several commonly available data sets. A large-scale Amazon Turk study was used to validate the methods. R code is provided for the analyses.Comment: 52 pages, 15 figures, 3 table

Multilevel Models with Stochastic Volatility for Repeated Cross-Sections: an Application to tribal Art Prices

In this paper we introduce a multilevel specification with stochastic volatility for repeated cross-sectional data. Modelling the time dynamics in repeated cross sections requires a suitable adaptation of the multilevel framework where the individuals/items are modelled at the first level whereas the time component appears at the second level. We perform maximum likelihood estimation by means of a nonlinear state space approach combined with Gauss-Legendre quadrature methods to approximate the likelihood function. We apply the model to the first database of tribal art items sold in the most important auction houses worldwide. The model allows to account properly for the heteroscedastic and autocorrelated volatility observed and has superior forecasting performance. Also, it provides valuable information on market trends and on predictability of prices that can be used by art markets stakeholders

Simultaneous comparisons of treatments at multiple time points: combined marginal models versus joint modeling

We discuss several aspects of multiple inference in longitudinal settings, focusing on many-to-one and all-pairwise comparisons of (a) treatment groups simultaneously at several points in time, or (b) time points simultaneously for several treatments. We assume a continuous endpoint that is measured repeatedly over time and contrast two basic modeling strategies: fitting a joint model across all occasions (with random effects and/or some residual covariance structure to account for heteroscedasticity and serial dependence), and a novel approach combining a set of simple marginal, i.e. occasion-specific models. Upon parameter and covariance estimation with either modeling approach, we employ a variant of multiple contrast tests that acknowledges correlation between time points and test statistics. This method provides simultaneous confidence intervals and adjusted p-values for elementary hypotheses as well as a global test decision. We compare via simulation the powers of multiple contrast tests based on a joint model and multiple marginal models, respectively, and quantify the benefit of incorporating longitudinal correlation, i.e. the advantage over Bonferroni. Practical application is illustrated with data from a clinical trial on bradykinin receptor antagonism