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Assessing the changing flowering date of the common lilac in North America: a random coefficient model approach

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Abstract

A data set consisting of Volunteered geographical information (VGI) and data provided by expert researchers monitoring the first bloom dates of lilacs from 1956 to 2003 is used to investigate changes in the onset of the North American spring. It is argued that care must be taken when analysing data of this kind, with particular focus on the issues of lack of experimental design, and Simpson’s paradox. Approaches used to overcome this issue make use of random coefficient modelling, and bootstrapping approaches. Once the suggested methods have been employed, a gradual advance in the onset of spring is suggested by the results of the analysis. A key lesson learned is that the appropriateness of the model calibration technique used given the process of data collection needs careful consideration.

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Notes

  1. ftp://ftp.ncdc.noaa.gov/pub/data/paleo/phenology/north_america_lilac.txt

  2. http://www.naturalearthdata.com/downloads/50m-cultural-vectors/50m-admin-0-countries-2/

  3. Centred on 1980—the midpoint of the time interval, as this reduces rounding error when calibrating the model.

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Correspondence to Chris Brunsdon.

Appendix: Computational considerations

Appendix: Computational considerations

In this section, some more detail is supplied about the software tools and techniques that were used to carry out this analysis. All of the statistical modelling was carried out using the R statistical programming language [25]. In particular, the random coefficient models were calibrated using the lme4 package.

The functions supplied in the R base library and lme4 were sufficient for all of the computations, except for the standard errors associated with the τ i values, and Δ. For these, a regression bootstrap approach as set out in [9] is used. Briefly, this estimates the sampling variation of parameters of interest by simulating data sets drawn from the model that is being fitted to the data (in this case the model given by Eq. 8). The sampling variation simulated is just that due to the variability in ε ij —so that rather than randomly assigning new values for the τ j ’s and υ i ’s for each simulated sample, it is assumed they are fixed at the estimated values. By simulating a large number of data sets in this way (say 1000, as in this paper), and applying the random coefficient estimation function supplied by lme4 to each simulated data set, an estimate of the sampling variability of the τ j ’s is obtained.

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Brunsdon, C., Comber, L. Assessing the changing flowering date of the common lilac in North America: a random coefficient model approach. Geoinformatica 16, 675–690 (2012). https://doi.org/10.1007/s10707-012-0159-6

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  • DOI: https://doi.org/10.1007/s10707-012-0159-6

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