Determining the number of components in the PARAFAC model with a nonnegative tensor structure: A simulated EEG data study

Background and Objective: Parallel factor analysis (PARAFAC) is a powerful tool for detecting latent components in higher-order arrays (tensors). As an essential input parameter, the number of latent components should be set in advance. However, any component number selection method already proposed in the literature became a rule of thumb. The study demonstrates the advantages and disadvantages of twelve different methods applied to well-controlled simulated data with a nonnegative structure that mimics the character of a real electroencephalogram.Methods: Existing studies have compared the methods’ performance on simulated data with a simplified structure. It was shown that the obtained results are not directly generalizable to real data. Using a real head model and cortical activation, our study focuses on nontrivial and nonnegative simulated data that resemble real electroencephalogram properties as closely as possible. Different noise levels and disruptions from the optimal structure are considered. Moreover, we validate a new method for component number selection, which we have already successfully applied to real electroencephalogram tasks. We also demonstrate that the existing approaches must be adapted whenever a nonnegative data structure is assumed. Results: We identified four methods that produce promising but not ideal results on nontrivial simulated data and present superior performance in electroencephalogram analysis practice.Conclusions: Component number selection in PARAFAC is a complex and unresolved problem. The nonnegative data structure assumption makes the problem more challenging. Although several methods have shown promising results, the issue remains open, and new approaches are needed.

Change of human mobility during COVID-19: A United States case study

With the onset of COVID-19 and the resulting shelter in place guidelines combined with remote working practices, human mobility in 2020 has been dramatically impacted. Existing studies typically examine whether mobility in specific localities increases or decreases at specific points in time and relate these changes to certain pandemic and policy events. However, a more comprehensive analysis of mobility change over time is needed. In this paper, we study mobility change in the US through a five-step process using mobility footprint data. (Step 1) Propose the Delta Time Spent in Public Places (ΔTSPP) as a measure to quantify daily changes in mobility for each US county from 2019-2020. (Step 2) Conduct Principal Component Analysis (PCA) to reduce the ΔTSPP time series of each county to lower-dimensional latent components of change in mobility. (Step 3) Conduct clustering analysis to find counties that exhibit similar latent components. (Step 4) Investigate local and global spatial autocorrelation for each component. (Step 5) Conduct correlation analysis to investigate how various population characteristics and behavior correlate with mobility patterns. Results show that by describing each county as a linear combination of the three latent components, we can explain 59% of the variation in mobility trends across all US counties. Specifically, change in mobility in 2020 for US counties can be explained as a combination of three latent components: 1) long-term reduction in mobility, 2) no change in mobility, and 3) short-term reduction in mobility. Furthermore, we find that US counties that are geographically close are more likely to exhibit a similar change in mobility. Finally, we observe significant correlations between the three latent components of mobility change and various population characteristics, including political leaning, population, COVID-19 cases and deaths, and unemployment. We find that our analysis provides a comprehensive understanding of mobility change in response to the COVID-19 pandemic.

A multivariate method to correct for batch effects in microbiome data

Microbial communities are highly dynamic and sensitive to changes in the environment. Thus, microbiome data are highly susceptible to batch effects, defined as sources of unwanted variation that are not related to, and obscure any factors of interest. Existing batch correction methods have been primarily developed for gene expression data. As such, they do not consider the inherent characteristics of microbiome data, including zero inflation, overdispersion and correlation between variables. We introduce a new multivariate and non-parametric batch correction method based on Partial Least Squares Discriminant Analysis. PLSDA-batch first estimates treatment and batch variation with latent components to then subtract batch variation from the data. The resulting batch effect corrected data can then be input in any downstream statistical analysis. Two variants are also proposed to handle unbalanced batch x treatment designs and to include variable selection during component estimation. We compare our approaches with existing batch correction methods removeBatchEffect and ComBat on simulated and three case studies. We show that our three methods lead to competitive performance in removing batch variation while preserving treatment variation, and especially when batch effects have high variability. Reproducible code and vignettes are available on GitHub.

How meaningful are parameter estimates from models of inter-temporal choice?

Decades of work has been dedicated to developing and testing models that characterize how people make inter-temporal choices. Although parameter estimates from these models are often interpreted as indices of latent components of the choice process, little work has been done to examine their reliability. This is problematic, because estimation error can bias conclusions that are drawn from these parameter estimates. We examine the reliability of inter-temporal choice model parameter estimates by conducting a parameter recovery analysis of 11 prominent models. We find that the reliability of parameter estimation varies considerably between models and the experimental designs upon which parameter estimates are based. We conclude that many parameter estimates reported in previous research are likely unreliable and provide recommendations on how to enhance reliability for those wishing to use inter-temporal choice models for measurement purposes.