Bayesian Hierarchical Models can Infer Interpretable Predictions of Leaf Area Index From Heterogeneous Datasets

Environmental scientists often face the challenge of predicting a complex phenomenon from a heterogeneous collection of datasets that exhibit systematic differences. Accounting for these differences usually requires including additional parameters in the predictive models, which increases the probability of overfitting, particularly on small datasets. We investigate how Bayesian hierarchical models can help mitigate this problem by allowing the practitioner to incorporate information about the structure of the dataset explicitly. To this end, we look at a typical application in remote sensing: the estimation of leaf area index of white winter wheat, an important indicator for agronomical modeling, using measurements of reflectance spectra collected at different locations and growth stages. Since the insights gained from such a model could be used to inform policy or business decisions, the interpretability of the model is a primary concern. We, therefore, focus on models that capture the association between leaf area index and the spectral reflectance at various wavelengths by spline-based kernel functions, which can be visually inspected and analyzed. We compare models with three different levels of hierarchy: a non-hierarchical baseline model, a model with hierarchical bias parameter, and a model in which bias and kernel parameters are hierarchically structured. We analyze them using Markov Chain Monte Carlo sampling diagnostics and an intervention-based measure of feature importance. The improved robustness and interpretability of this approach show that Bayesian hierarchical models are a versatile tool for the prediction of leaf area index, particularly in scenarios where the available data sources are heterogeneous.

Prioritization and ranking of lean practices: a case study

PurposeThe paper aims to identify, prioritize and rank lean practices in the context of an Indian automotive component manufacturing organization using interpretive ranking process (IRP) and interpretive structural modeling (ISM) approaches.Design/methodology/approachLean practices are identified from the literature. Then, two hierarchical models were are developed using two distinct modeling approaches – ISM and IRP with expert opinions from an Indian automotive component manufacturing organization to analyze the contextual relationships among the various lean practices and to prioritize and rank them with respect to performance dimensions.FindingsIn the study, the hierarchical structural models are developed using ISM and IRP approaches for an Indian automotive component manufacturing organization. In ISM-based modeling, lean practices can be categorized into five levels. Top priority should be given to the motivators followed by value chain, system/technology and organization centric practices. IRP model shows the dominance relationship among the various lean practices with respect to performance dimensions.Practical implicationsThe models are constructed from the organizational standpoint to evaluate their impact to the implementation of lean manufacturing. The study leverages the organizations to prioritize limited resources as per the hierarchy. Managers get the inter-linkages and ranking of various lean practices, which leads to a better perspective for the effective implementation of lean. The structural models also assist management to assign proper roles to employees/departments for effective lean implementation.Originality/valueThere is hardly any structural model of lean practices in the literature for clustering, prioritizing and ranking of lean practices. The study fills this gap and develops the hierarchical models of lean practices through IRP and ISM approaches for an Indian automotive component manufacturing organization. The results from both approaches are compared for illustrating the benefits of one over the other.

Spatial and temporal models in plant ecology: logic and causality

In the paper, I argue that in order to make credible ecological predictions for terrestrial ecosystems in a changing environment, we need empirical plant ecological models that are fitted to spatial and temporal ecological data. Here, it is advocated to use structural equation models in a hierarchical framework with latent variables. Furthermore, it is an advantage that the proposed hierarchical models are analogous to well-known theoretical epistemological models of how knowledge is obtained.

A First Approach to Closeness Distributions

Probabilistic graphical models allow us to encode a large probability distribution as a composition of smaller ones. It is oftentimes the case that we are interested in incorporating in the model the idea that some of these smaller distributions are likely to be similar to one another. In this paper we provide an information geometric approach on how to incorporate this information and see that it allows us to reinterpret some already existing models. Our proposal relies on providing a formal definition of what it means to be close. We provide an example on how this definition can be actioned for multinomial distributions. We use the results on multinomial distributions to reinterpret two already existing hierarchical models in terms of closeness distributions.

Putting the individual into reliability: Bayesian testing of homogeneous within-person variance in hierarchical models

Measurement reliability is a fundamental concept in psychology. It is traditionally considered a stable property of a questionnaire, measurement device, or experimental task. Although intraclass correlation coefficients (ICC) are often used to assess reliability in repeated measure designs, their descriptive nature depends upon the assumption of a common within-person variance. This work focuses on the presumption that each individual is adequately described by the average within-person variance in hierarchical models. And thus whether reliability generalizes to the individual level, which leads directly into the notion of individually varying ICCs. In particular, we introduce a novel approach, using the Bayes factor, wherein a researcher can directly test for homogeneous within-person variance in hierarchical models. Additionally, we introduce a membership model that allows for classifying which (and how many) individuals belong to the common variance model. The utility of our methodology is demonstrated on cognitive inhibition tasks. We find that heterogeneous within-person variance is a defining feature of these tasks, and in one case, the ratio between the largest to smallest within-person variance exceeded 20. This translates into a tenfold difference in person-specific reliability! We also find that few individuals belong to the common variance model, and thus traditional reliability indices are potentially masking important individual variation. We discuss the implications of our findings and possible future directions. The methods are implemented in the R package vICC