From Nuisance to Novel Research Questions: Using Multilevel Models to Predict Heterogeneous Variances

Constructs that reflect differences in variability are of interest to many researchers studying workplace phenomena. The aggregation methods typically used to investigate “variability-based” constructs suffer from several limitations, including the inability to include Level 1 predictors and a failure to account for uncertainty in the variability estimates. We demonstrate how mixed-effects location-scale (MELS) and heterogeneous variance models, which are direct extensions of traditional mixed-effects (or multilevel) models, can be used to test mean (location)- and variability (scale)-related hypotheses simultaneously. The aims of this article are to demonstrate (a) how the MELS and heterogeneous variance models can be estimated with both nested cross-sectional and longitudinal data to answer novel research questions about constructs of interest to organizational researchers, (b) how a Bayesian approach allows for the inclusion of random intercepts and slopes when predicting both variability and mean levels, and finally (c) how researchers can use a multilevel approach to predict between-group heterogeneous variances. In doing so, this article highlights the added value of viewing variability as more than a statistical nuisance in organizational research.

Application of Short-term Forecasting Models for Energy Entity Stock Price (Study on Indika Energi Tbk., JII)

Share price as one of financial data is the time series data that indicates both a level of fluctuate movement and heterogeneous variances called heteroscedasticity. The method that can be used to overcome the effect of autoregressive conditional heteroscedasticity (ARCH effect) is GARCH model. This study aims to design the best model that can estimate the parameters, to predict share price based on the best model, and to show its volatility. In addition, this paper also discuss the predicted-based-model investment decision. The finding indicating the best model correspond to the data is AR(4) – GARCH(1,1). It is then implemented to forecast the stock prices of Indika Energy, Tbk, Indonesia, for upcoming 40 days that presents significantly good findings with the error percentage below the mean absolute.

Comparison of Test Statistics of Nonnormal and Unbalanced Samples for Multivariate Analysis of Variance in terms of Type-I Error Rates

In this study, we investigate how Wilks’ lambda, Pillai’s trace, Hotelling’s trace, and Roy’s largest root test statistics can be affected when the normal and homogeneous variance assumptions of the MANOVA method are violated. In other words, in these cases, the robustness of the tests is examined. For this purpose, a simulation study is conducted in different scenarios. In different variable numbers and different sample sizes, considering the group variances are homogeneous σ12=σ22=⋯=σg2 and heterogeneous (increasing) σ12<σ22<⋯<σg2, random numbers are generated from Gamma(4-4-4; 0.5), Gamma(4-9-36; 0.5), Student’s t(2), and Normal(0; 1) distributions. Furthermore, the number of observations in the groups being balanced and unbalanced is also taken into account. After 10000 repetitions, type-I error values are calculated for each test for α = 0.05. In the Gamma distribution, Pillai’s trace test statistic gives more robust results in the case of homogeneous and heterogeneous variances for 2 variables, and in the case of 3 variables, Roy’s largest root test statistic gives more robust results in balanced samples and Pillai’s trace test statistic in unbalanced samples. In Student’s t distribution, Pillai’s trace test statistic gives more robust results in the case of homogeneous variance and Wilks’ lambda test statistic in the case of heterogeneous variance. In the normal distribution, in the case of homogeneous variance for 2 variables, Roy’s largest root test statistic gives relatively more robust results and Wilks’ lambda test statistic for 3 variables. Also in the case of heterogeneous variance for 2 and 3 variables, Roy’s largest root test statistic gives robust results in the normal distribution. The test statistics used with MANOVA are affected by the violation of homogeneity of covariance matrices and normality assumptions particularly from unbalanced number of observations.