Confidence bands for measured economically optimal nitrogen rates

Confidence bands for measured economically optimal nitrogen rates While numerous researchers have computed economically optimal nitrogen rate (EONR) values from measured yield–N rate data, nearly all have neglected to compute or estimate the statistical reliability of these EONR values. In this study, a simple method for computing EONR and its confidence bands is described and demonstrated. The method is illustrated for seven yield response functions, namely, the linear plateau, quadratic, quadratic plateau, square root quadratic, spherical plateau, and exponential and exponential plateau. Only the quadratic and square root quadratic functions are linear in their parameters, with least squares regression yielding parameters that are normally distributed. The other five functions are non-linear and give parameter estimates that are non-normal and biased in their distribution when fit by least squares. Prior to computing EONR distributions, the non-linear functions were reparameterized to give fitted parameters that were nearly unbiased and normally distributed. EONR distributions were computed using a Monte Carlo method to generate 1,000 realizations of EONR based on the fitted response function parameters. From the 1,000 realizations, the expectation, confidence bands, and cumulative probability distributions for EONR were easily computed. Applying the approach to six yield data sets from the literature illustrated that the 68% confidence bands for computed EONR can span several tens of kilograms per hectare and are typically skewed about the expectation. There were considerable differences among the distributions of EONR computed from the seven functions, with the cumulative probability distributions sometimes not overlapping. Given the limited statistical reliability possible for EONR, it is essential that confidence bands always be reported when EONR values are computed from yield data. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Precision Agriculture Springer Journals

Confidence bands for measured economically optimal nitrogen rates

Loading next page...
 
/lp/springer_journal/confidence-bands-for-measured-economically-optimal-nitrogen-rates-s0O5yTnbT4
Publisher
Springer Journals
Copyright
Copyright © 2010 by US Government
Subject
Life Sciences; Agriculture; Soil Science & Conservation; Remote Sensing/Photogrammetry; Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences; Atmospheric Sciences
ISSN
1385-2256
eISSN
1573-1618
D.O.I.
10.1007/s11119-010-9168-3
Publisher site
See Article on Publisher Site

Abstract

While numerous researchers have computed economically optimal nitrogen rate (EONR) values from measured yield–N rate data, nearly all have neglected to compute or estimate the statistical reliability of these EONR values. In this study, a simple method for computing EONR and its confidence bands is described and demonstrated. The method is illustrated for seven yield response functions, namely, the linear plateau, quadratic, quadratic plateau, square root quadratic, spherical plateau, and exponential and exponential plateau. Only the quadratic and square root quadratic functions are linear in their parameters, with least squares regression yielding parameters that are normally distributed. The other five functions are non-linear and give parameter estimates that are non-normal and biased in their distribution when fit by least squares. Prior to computing EONR distributions, the non-linear functions were reparameterized to give fitted parameters that were nearly unbiased and normally distributed. EONR distributions were computed using a Monte Carlo method to generate 1,000 realizations of EONR based on the fitted response function parameters. From the 1,000 realizations, the expectation, confidence bands, and cumulative probability distributions for EONR were easily computed. Applying the approach to six yield data sets from the literature illustrated that the 68% confidence bands for computed EONR can span several tens of kilograms per hectare and are typically skewed about the expectation. There were considerable differences among the distributions of EONR computed from the seven functions, with the cumulative probability distributions sometimes not overlapping. Given the limited statistical reliability possible for EONR, it is essential that confidence bands always be reported when EONR values are computed from yield data.

Journal

Precision AgricultureSpringer Journals

Published: Apr 18, 2010

References

  • A conceptual framework for judging the precision agriculture hypothesis with regard to site-specific nitrogen application
    Bachmaier, M; Gandorfer, M

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off