Skip to main content
Log in

Abstract

The flowers of strawberry plants grow on very variable branched structures called inflorescences, in which each branch gives rise to 0, 1, or 2 offspring branches. We extend previous modeling of the number of strawberry flowers at each individual level in the inflorescence structure conditional on the number of strawberry flowers at the previous level. We consider a range of logistic regression models, including models that incorporate inflorescence effects and random effects. The models can be used to summarize the overall structure of any particular variety and to indicate the main differences between varieties. For the data of the article, we show that models based on convolutions of correlated Bernoulli random variables outperform binomial regression models.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Abramowitz, M., and Stegun, I. A. (1972), Handbook of Mathematical Functions, New York: Dover Publications.

    MATH  Google Scholar 

  • Altham, P. M. E. (1976), “Discrete Variable Analysis for Individuals Grouped into Families,” Biometrika, 63, 263–269.

    Article  MATH  MathSciNet  Google Scholar 

  • —(1978), “Two Generalizations of the Binomial Distribution,” Applied Statistics, 27, 162–167.

    Article  MATH  MathSciNet  Google Scholar 

  • Bahadur, R. R. (1961), “A Representation of the Joint Distribution of Responses to n Dichotomous Items,” in Studies in Item Analysis and Prediction, ed. H. Salomon, Palo Alto, CA: Stanford University Press, pp. 158–176.

    Google Scholar 

  • Brier, S. S. (1980), “Analysis of Contingency Tables Under Cluster Sampling,” Biometrika, 67, 591–596.

    Article  MATH  MathSciNet  Google Scholar 

  • Cole, D. J. (2003), “Stochastic Branching Processes in Biology,” unpublished Ph.D. thesis, University of Kent, England.

    Google Scholar 

  • Cole, D. J., Morgan, B. J. T., and Ridout, M. S. (2003), “Generalized Linear Mixed Models for Strawberry Inflorescence Data,” Statistical Modelling, 3, 273–290.

    Article  MATH  MathSciNet  Google Scholar 

  • Cohen, J. E. (1976), “The Distribution of the Chi-Squared Statistic Under Clustered Sampling from Contingency Tables,” Journal of the American Statistical Association, 71, 665–670.

    Article  MATH  MathSciNet  Google Scholar 

  • Dobson, A. J. (2002), An Introduction to Generalized Linear Models (2nd ed.), London: Chapman and Hall.

    MATH  Google Scholar 

  • McCulloch, C. E., and Searle, S.R. (2001), Generalized, Linear, and Mixed Models, New York: Wiley.

    MATH  Google Scholar 

  • Molenberghs, G. (2002), “Model Familes,” in Topics in Modelling Clustered Data, eds. M. Aerts, H. Geys, G. Moelenberghs, and L. M. Ryan, Boca Raton, FL: Chapman and Hall/CRC, pp. 47–75.

    Google Scholar 

  • Ridout, M. S., Morgan, B. J. T., and Taylor, D. R. (1999), “Modelling Variability in the Branching Structure of Strawberry Inflorescences,” Applied Statistics, 48, 185–196.

    MATH  Google Scholar 

  • Skellam, J. G. (1948), “A Probability Distribution Derived from the Binomial Distribution by Regarding the Probability of Success as Variable Between Sets of Trials,” Journal of the Royal Statistical Society, Series B, 10, 257–261.

    MATH  MathSciNet  Google Scholar 

  • Steele, B. M. (1996), “A Modified EM algorithm for Estimation in Generalized Mixed Models,” Biometrics, 52, 1295–1310.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to D. J. Cole.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cole, D.J., Morganp, B.J.T. & Ridout, M.S. Models for strawberry inflorescence data. JABES 10, 411 (2005). https://doi.org/10.1198/108571105X80761

Download citation

  • Received:

  • Revised:

  • DOI: https://doi.org/10.1198/108571105X80761

Key Words

Navigation