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We study discrete panel data methods where unobserved heterogeneity is revealed in a first step, in environments where population heterogeneity is not discrete. We focus on two‐step grouped fixed‐effects (GFE) estimators, where individuals are first classified into groups using kmeans clustering, and the model is then estimated allowing for group‐specific heterogeneity. Our framework relies on two key properties: heterogeneity is a function—possibly nonlinear and time‐varying—of a low‐dimensional continuous latent type, and informative moments are available for classification. We illustrate the method in a model of wages and labor market participation, and in a probit model with time‐varying heterogeneity. We derive asymptotic expansions of two‐step GFE estimators as the number of groups grows with the two dimensions of the panel. We propose a data‐driven rule for the number of groups, and discuss bias reduction and inference.
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Temporal heterogeneity increases with spatial heterogeneity in ecological communities
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Abstract Enhancing resilience in formerly degraded ecosystems is an important goal of restoration ecology. However, evidence for the recovery of resilience and its underlying mechanisms require long‐term experiments and comparison with reference ecosystems. We used data from an experimental prairie restoration that featured long‐term soil heterogeneity manipulations and data from two long‐term experiments located in a comparable remnant (reference) prairie to (1) quantify the recovery of ecosystem functioning (i.e., productivity) relative to remnant prairie, (2) compare the resilience of restored and remnant prairies to a natural drought, and (3) test whether soil heterogeneity enhances resilience of restored prairie. We compared sensitivity and legacy effects between prairie types (remnant and restored) and among four prairie sites that included two remnant prairie sites and prairie restored under homogeneous and heterogeneous soil conditions. We measured sensitivity and resilience as the proportional change in aboveground net primary productivity (ANPP) during and following drought (sensitivity and legacy effects, respectively) relative to average ANPP based on 4 pre‐drought years (2014–2017). In nondrought years, total ANPP was similar between remnant and restored prairie, but remnant prairie had higher grass productivity and lower forb productivity compared with restored prairie. These ANPP patterns generally persisted during drought. The sensitivity of total ANPP to drought was similar between restored and remnant prairie, but grasses in the restored prairie were more sensitive to drought. Post‐drought legacy effects were more positive in the restored prairie, and we attributed this to the more positive and less variable legacy response of forb ANPP in the restored prairie, especially in the heterogeneous soil treatment. Our results suggest that productivity recovers in restored prairie and exhibits similar sensitivity to drought as in remnant prairie. Furthermore, creating heterogeneity promotes forb productivity and enhances restored prairie resilience to drought.more » « less
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Spatial systems with heterogeneities are ubiquitous in nature, from precipitation, temperature, and soil gradients controlling vegetation growth to morphogen gradients controlling gene expression in embryos. Such systems, generally described by nonlinear dynamical systems, often display complex parameter dependence and exhibit bifurcations. The dynamics of heterogeneous spatially extended systems passing through bifurcations are still relatively poorly understood, yet recent theoretical studies and experimental data highlight the resulting complex behaviors and their relevance to real-world applications. We explore the consequences of spatial heterogeneities passing through bifurcations via two examples strongly motivated by applications. These model systems illustrate that studying heterogeneity-induced behaviors in spatial systems is crucial for a better understanding of ecological transitions and functional organization in brain development.more » « less
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Biofilms, and collections of embedded microbial communities, present structural heterogeneities with functional consequences for important processes, such as transport. The origin of such structures has been unclear. Here, we propose that they can arise as a consequence of diffusive transport limitation. To illustrate, a model allowing internal heterogeneity is developed. Linear analysis is applied to a simplified version of the model suggesting that heterogeneity forms on (or below) the active layer length, a length scale that may not be suitable for homogenization, with non-trivial implications for system scale properties such as reduction in system-wide diffusive transport efficiency. Numerics suggest that the simplified model provides useful insight into behaviour of the full model. We then show examples based on microcolony formation in host domains and argue that internal heterogeneity can be related to community function.more » « less
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1002/ecy.2154
