Enabling analytical power calculations for multilevel models with autocorrelated errors through deriving and approximating the precision matrix.

To unravel how within-person psychological processes fluctuate in daily life, and how these processes differ between persons, intensive longitudinal (IL) designs in which participants are repeatedly measured, have become popular. Commonly used statistical models for those designs are multilevel models with autocorrelated errors. Substantive hypotheses of interest are then typically investigated via statistical hypotheses tests for model parameters of interest. An important question in the design of such IL studies concerns the determination of the number of participants and the number of measurements per person needed to achieve sufficient statistical power for those statistical tests. Recent advances in computational methods and software have enabled the computation of statistical power using Monte Carlo simulations. However, this approach is computationally intensive and therefore quite restrictive. To ease power computations, we derive simple-to-use analytical formulas for multilevel models with AR(1) within-person errors. Analytic expressions for a model family are obtained via asymptotic approximations of all sample statistics in the precision matrix of the fixed effects. To validate this analytical approach to power computation, we compare it to the simulation-based approach via a series of Monte Carlo simulations. We find comparable performances making the analytic approach a useful tool for researchers that can drastically save them time and resources.

The reproducibility of statistical results in psychological research: An investigation using unpublished raw data.

We investigated the reproducibility of the major statistical conclusions drawn in 46 articles published in 2012 in three APA journals. After having identified 232 key statistical claims, we tried to reproduce, for each claim, the test statistic, its degrees of freedom, and the corresponding p value, starting from the raw data that were provided by the authors and closely following the Method section in the article. Out of the 232 claims, we were able to successfully reproduce 163 (70%), 18 of which only by deviating from the article's analytical description. Thirteen (7%) of the 185 claims deemed significant by the authors are no longer so. The reproduction successes were often the result of cumbersome and time-consuming trial-and-error work, suggesting that APA style reporting in conjunction with raw data makes numerical verification at least hard, if not impossible. This article discusses the types of mistakes we could identify and the tediousness of our reproduction efforts in the light of a newly developed taxonomy for reproducibility. We then link our findings with other findings of empirical research on this topic, give practical recommendations on how to achieve reproducibility, and discuss the challenges of large-scale reproducibility checks as well as promising ideas that could considerably increase the reproducibility of psychological research. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

Heteroscedasticity as a Basis of Direction Dependence in Reversible Linear Regression Models.

Heteroscedasticity is a well-known issue in linear regression modeling. When heteroscedasticity is observed, researchers are advised to remedy possible model misspecification of the explanatory part of the model (e.g., considering alternative functional forms and/or omitted variables). The present contribution discusses another source of heteroscedasticity in observational data: Directional model misspecifications in the case of nonnormal variables. Directional misspecification refers to situations where alternative models are equally likely to explain the data-generating process (e.g., x → y versus y → x). It is shown that the homoscedasticity assumption is likely to be violated in models that erroneously treat true nonnormal predictors as response variables. Recently, Direction Dependence Analysis (DDA) has been proposed as a framework to empirically evaluate the direction of effects in linear models. The present study links the phenomenon of heteroscedasticity with DDA and describes visual diagnostics and nine homoscedasticity tests that can be used to make decisions concerning the direction of effects in linear models. Results of a Monte Carlo simulation that demonstrate the adequacy of the approach are presented. An empirical example is provided, and applicability of the methodology in cases of violated assumptions is discussed.