An Investigation of Factored Regression Missing Data Methods for Multilevel Models with Cross-Level Interactions

Exploration of the MCMC Wald test with linear regression

Recently, Asparouhov and Muthén Structural Equation Modeling: A Multidisciplinary Journal, 28, 1-14, (2021a, 2021b) proposed a variant of the Wald test that uses Markov chain Monte Carlo machinery to generate a chi-square test statistic for frequentist inference. Because the test's composition does not rely on analytic expressions for sampling variation and covariation, it potentially provides a way to get honest significance tests in cases where the likelihood-based test statistic's assumptions break down (e.g., in small samples). The goal of this study is to use simulation to compare the new MCM Wald test to its maximum likelihood counterparts, with respect to both their type I error rate and power. Our simulation examined the test statistics across different levels of sample size, effect size, and degrees of freedom (test complexity). An additional goal was to assess the robustness of the MCMC Wald test with nonnormal data. The simulation results uniformly demonstrated that the MCMC Wald test was superior to the maximum likelihood test statistic, especially with small samples (e.g., sample sizes less than 150) and complex models (e.g., models with five or more predictors). This conclusion held for nonnormal data as well. Lastly, we provide a brief application to a real data example.

Propensity Score Weighting with Missing Data on Covariates and Clustered Data Structure

Propensity score (PS) analyses are increasingly popular in behavioral sciences. Two issues often add complexities to PS analyses, including missing data in observed covariates and clustered data structure. In previous research, methods for conducting PS analyses with considering either issue alone were examined. In practice, the two issues often co-occur; but the performance of methods for PS analyses in the presence of both issues has not been evaluated previously. In this study, we consider PS weighting analysis when data are clustered and observed covariates have missing values. A simulation study is conducted to evaluate the performance of different missing data handling methods (complete-case, single-level imputation, or multilevel imputation) combined with different multilevel PS weighting methods (fixed- or random-effects PS models, inverse-propensity-weighting or the clustered weighting, weighted single-level or multilevel outcome models). The results suggest that the bias in average treatment effect estimation can be reduced, by better accounting for clustering in both the missing data handling stage (such as with the multilevel imputation) and the PS analysis stage (such as with the fixed-effects PS model, clustered weighting, and weighted multilevel outcome model). A real-data example is provided for illustration.

Kinematic viscosity prediction of jet fuels and alternative blending components via comprehensive two-dimensional gas chromatography, partial least squares, and Yeo-Johnson transformation

This work presents an accurate yet simplified partial least squares model to predict the kinematic viscosity of conventional and alternative jet fuels at -20°C using comprehensive two-dimensional gas chromatography coupled to a flame ionization detector (GC × GC/FID). Three different normalization methods (mean-centering, logarithmic, and Yeo-Johnson) were evaluated to identify their impact in the prediction of middle distillates' physical properties. Results using Yeo-Johnson transformation exhibited improved viscosity prediction capabilities over the validation set with a mean absolute percentage error of 5.3%, a root-mean-squared error of 0.23, and a coefficient of determination (R2 ) of 0.9404 using only 10 latent variables. Unlike previously reported correlations, this model allowed the identification of specific hydrocarbon groups and carbon numbers that drive jet fuel viscosity at low temperatures. The presence of even small amounts of large branched-alkanes (C15 -C17 ), dicyclic-alkanes (C10 ), and cycloaromatics (C11 ) have the potential to strongly increase the kinematic viscosity of jet fuels. Contrastingly, light monocycloalkanes and branched-alkanes (≤ C10 ) were associated with lower viscosity values. Novelly, this model suggests the implementation of Yeo-Johnson transformations to predict the physical properties of middle distillates to further improve the performance metrics of partial least squares models based on GC data.