Combining envelope methodology and aster models for variance reduction in life history analyses

Daniel J. Eck; Charles J. Geyer; R. Dennis Cook

doi:10.1016/j.jspi.2019.08.002

Combining envelope methodology and aster models for variance reduction in life history analyses

Daniel J. Eck, Charles J. Geyer, R. Dennis Cook

Statistics (Twin Cities)

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

Precise estimation of expected Darwinian fitness, the expected lifetime number of offspring of organism, is a central component of life history analysis. The aster model serves as a defensible statistical model for distributions of Darwinian fitness. The aster model is equipped to incorporate the major life stages an organism travels through which separately may effect Darwinian fitness. Envelope methodology reduces asymptotic variability by establishing a link between unknown parameters of interest and the asymptotic covariance matrices of their estimators. It is known both theoretically and in applications that incorporation of envelope methodology reduces asymptotic variability. We develop an envelope framework, including a new envelope estimator, that is appropriate for aster analyses. The level of precision provided from our methods allows researchers to draw stronger conclusions about the driving forces of Darwinian fitness from their life history analyses than they could with the aster model alone. Our methods are illustrated on a simulated dataset and a life history analysis of Mimulus guttatus flowers is provided. Useful variance reduction is obtained in both analyses.

Original language	English (US)
Pages (from-to)	283-292
Number of pages	10
Journal	Journal of Statistical Planning and Inference
Volume	205
DOIs	https://doi.org/10.1016/j.jspi.2019.08.002
State	Published - Mar 2020

Bibliographical note

Funding Information:
Daniel J. Eck's research is supported by NIH/NIHCD grant 1DP2HD091799-01 (United States). We would like to thank David B. Lowry for providing the dataset used in Example 2, Xin Zhang for the code that implements the 1D algorithm, and Forrest W. Crawford for helpful discussion that led to the strengthening of this paper. We would also like to especially thank Amber Eule-Nashoba for helpful comments on the technical report. We are grateful to two anonymous reviewers whose comments led to improvements in clarity.

Funding Information:
Daniel J. Eck’s research is supported by NIH/NIHCD grant 1DP2HD091799-01 (United States). We would like to thank David B. Lowry for providing the dataset used in Example 2, Xin Zhang for the code that implements the 1D algorithm, and Forrest W. Crawford for helpful discussion that led to the strengthening of this paper. We would also like to especially thank Amber Eule-Nashoba for helpful comments on the technical report. We are grateful to two anonymous reviewers whose comments led to improvements in clarity.

Publisher Copyright:
© 2019 Elsevier B.V.

Keywords

Darwinian fitness
Envelope model
Fitness landscape
Parametric bootstrap

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title = "Combining envelope methodology and aster models for variance reduction in life history analyses",

abstract = "Precise estimation of expected Darwinian fitness, the expected lifetime number of offspring of organism, is a central component of life history analysis. The aster model serves as a defensible statistical model for distributions of Darwinian fitness. The aster model is equipped to incorporate the major life stages an organism travels through which separately may effect Darwinian fitness. Envelope methodology reduces asymptotic variability by establishing a link between unknown parameters of interest and the asymptotic covariance matrices of their estimators. It is known both theoretically and in applications that incorporation of envelope methodology reduces asymptotic variability. We develop an envelope framework, including a new envelope estimator, that is appropriate for aster analyses. The level of precision provided from our methods allows researchers to draw stronger conclusions about the driving forces of Darwinian fitness from their life history analyses than they could with the aster model alone. Our methods are illustrated on a simulated dataset and a life history analysis of Mimulus guttatus flowers is provided. Useful variance reduction is obtained in both analyses.",

keywords = "Darwinian fitness, Envelope model, Fitness landscape, Parametric bootstrap",

author = "Eck, {Daniel J.} and Geyer, {Charles J.} and Cook, {R. Dennis}",

note = "Funding Information: Daniel J. Eck's research is supported by NIH/NIHCD grant 1DP2HD091799-01 (United States). We would like to thank David B. Lowry for providing the dataset used in Example 2, Xin Zhang for the code that implements the 1D algorithm, and Forrest W. Crawford for helpful discussion that led to the strengthening of this paper. We would also like to especially thank Amber Eule-Nashoba for helpful comments on the technical report. We are grateful to two anonymous reviewers whose comments led to improvements in clarity. Funding Information: Daniel J. Eck{\textquoteright}s research is supported by NIH/NIHCD grant 1DP2HD091799-01 (United States). We would like to thank David B. Lowry for providing the dataset used in Example 2, Xin Zhang for the code that implements the 1D algorithm, and Forrest W. Crawford for helpful discussion that led to the strengthening of this paper. We would also like to especially thank Amber Eule-Nashoba for helpful comments on the technical report. We are grateful to two anonymous reviewers whose comments led to improvements in clarity. Publisher Copyright: {\textcopyright} 2019 Elsevier B.V.",

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Combining envelope methodology and aster models for variance reduction in life history analyses

Abstract

Bibliographical note

Keywords

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