Catching Up on Multilevel Modeling

This review focuses on the use of multilevel models in psychology and other social sciences. We target readers who are catching up on current best practices and sources of controversy in the specification of multilevel models. We first describe common use cases for clustered, longitudinal, and cross-classified designs, as well as their combinations. Using examples from both clustered and longitudinal designs, we then address issues of centering for observed predictor variables: its use in creating interpretable fixed and random effects of predictors, its relationship to endogeneity problems (correlations between predictors and model error terms), and its translation into multivariate multilevel models (using latent-centering within multilevel structural equation models). Finally, we describe novel extensions—mixed-effects location–scale models—designed for predicting differential amounts of variability.

Visual Measurement and Calibration of Geometric Errors of Rotating Axes for Five-axis Platform

In this paper, a method for identifying and decoupling geometric errors of rotation axes using vision measurement is proposed. Based on screw theory and exponential product formula, identification equations of position-dependent geometric errors (PDGEs) and position-independent geometric errors (PIGEs) of the rotation axes are established. The mapping relationships between the error twist and geometric errors are established. The error model provides the coupling mechanism of PDGEs and PIGEs. Furthermore, a progressive decoupling method is proposed to separate PDGEs and PIGEs without additional assumptions. The pose parameters, required for solving the identification equations, are obtained by visual measurement. Then, the error terms of PIGEs and PDGEs are determined. Lastly, the error calibration of the rotation axes is investigated, thus providing an average rotary table orientation error reduction of 28.1% compared to the situation before calibration.

Willingness To COVID-19 Vaccination: Empirical Evidence From EU

The unforgettable COVID-19 shock can only be reversed by a viable vaccination strategy. In this paper, we investigate willingness to be vaccinated (WTV) against the COVID-19. We provide first of its kind empirical evidence on the citizens (N=11,932) of the EU-27 by employing the recent data from the European Commission. Controlling for the correlations in the error terms, we utilize a simulated multivariate probit regression model. Our results show that amongst all the statistically significant drivers of the WTV, the positive perception (vaccination works and has no side effects); R&D information (clarity on how vaccination is developed, tested, authorized) has the largest impact on the WTV. We find that the group of variables on social feedback, and on trustworthy sources of information are to be considered for WTV policy. The counteracting policy gaps are also identified. Our work is novel and has implications for COVID-19 vaccination policies across the EU.

Validation of Korean Version of the Hardiness Resilience Gauge

Hardiness and resilience are known as internal traits that buffer the negative effects of stress and play important roles in individuals’ well-being and psychological sustainability. This study aimed to validate the Korean version of the hardiness resilience gauge (HRG Korean). Reliability and validity were analyzed using data obtained from 389 Korean adults. Confirmatory factor analysis with three factors (challenge, control, and commitment) for the HRG Korean showed acceptable model fit, with satisfactory RMSEA and SRMR indices, allowing for some covariance in error terms. Cronbach’s α for challenge, control, commitment subscales, and the total HRG Korean were 0.84, 0.74, 0.86, and 0.92, respectively. Analyses of the concurrent validity revealed that the total score of the HRG Korean was closely correlated with the scores of the KHD-SF and MR-KA, which measure hardiness and resilience in Korea, respectively. In addition, the HRG Korean was relatively strongly correlated with life satisfaction and subjective happiness. These findings suggest that the HRG is a valid instrument for measuring Koreans’ hardiness and resilience to promote their well-being and sustainability.

An Improved Asymptotic on the Representations of Integers as Sums of Products

In this paper, we improve the error terms of Chace’s results in the study by Chace (1994) on the number of ways of writing an integer N as a sum of k products of l factors, valid for k ≥ 3 and l = 2 , 3. More precisely, for l = 2 , 3, we improve the upper bound N k − 1 − 2 k − 2 / k − 1 l + 1 + ε , k ≥ 3 for the error term, to N 2 − 2 / 2 l + 1 + ε when k = 3 and N k − 1 − 4 k − 2 / l + 1 k + l − 2 + ε when k ≥ 4 .

Fourth derivative singularly P-stable method for the numerical solution of the Schrödinger equation

In this paper, we construct a method with eight steps that belongs to the family of Obrechkoff methods. Due to the explicit nature of the new method, not only does it not require another method as predictor, but it can also be considered as a suitable predictive technique to be used with implicit methods. Periodicity and error terms are studied when applied to solve the radial Schrödinger equation, considering different energy levels. We show its advantages in terms of accuracy, consistency, and convergence in comparison with other methods of the same order appearing in the literature.

Statistical Modelling with Birnbaum-Saunders Distribution

In this article, it is assumed that the distribution of the error terms is the Birnbaum-Saunders distribution in the process of one-way ANOVA. The Birnbaum-Saunders distribution has been widely used in reliability analysis especially in fatigue-life models. In reliability analysis, nonnormal distribution is much more common than the normal distribution. We obtain the estimation of the parameters og interest by maximum likelihood method. We also propose new test statistics based on these estimators . The efficiencies of the maximum likelihood estimators and the Type I errors obtained by using the proposed estimators are compared with normal theory via Monte Carlo simulation study. At the end of the study, the real life example is given just for the illustration of the method.

Robustness Test of Selected Estimators of Linear Regression with Autocorrelated Error Term: A Monte-Carlo Simulation Study

Assumptions in the classical linear regression model include that of lack of autocorrelation of the error terms and the zero covariance between the explanatory variable and the error terms. This study is channeled towards the estimation of the parameters of the linear models for both time series and cross-sectional data when the above two assumptions are violated. The study used the Monte-Carlo simulation method to investigate the performance of six estimators: ordinary least square (OLS), Prais-Winsten (PW), Cochrane-Orcutt (CC), Maximum Likelihood (MLE), Restricted Maximum- Likelihood (RMLE) and the Weighted Least Square (WLS) in estimating the parameters of a single linear model in which the explanatory variable is also correlated with the autoregressive error terms. Using the models’ finite properties(mean square error) to measure the estimators’ performance, the results shows that OLS should be preferred when autocorrelation level is relatively mild (ρ = 0.3) and the PW, CC, RMLE, and MLE estimator will perform better with the presence of any level of AR (1) disturbance between 0.4 to 0.8 level, while WLS shows better performance at 0.9 level of autocorrelation and above. The study thus recommended the application of the various estimators considered to real-life data to affirm the results of this simulation study.