page_title: Generalized functional linear model
section_title: Application
hierarchical_section_title: Generalized functional linear model / Application
caption_attribution_description: English: This plot shows the egg laying trajectories of about 600 female medflies for the first 25 days of their lifetime. The red curves correspond to those flies that have more than the median number of remaining eggs and the blue ones are those with less than the median number of remaining eggs.
context_page_description: The generalized functional linear model is an extension of the generalized linear model that allows one to regress univariate responses of various types on functional predictors, which are mostly random trajectories generated by a square-integrable stochastic processes. Similarly to GLM, a link function relates the expected value of the response variable to a linear predictor, which in case of GFLM is obtained by forming the scalar product of the random predictor function with a smooth parameter function. Functional Linear Regression, Functional Poisson Regression and Functional Binomial Regression, with the important Functional Logistic Regression included, are special cases of GFLM. Applications of GFLM include classification and discrimination of stochastic processes and functional data.
context_section_description: A popular data set that has been used for a number of analysis in the domain of functional data analysis consists of the number of eggs laid daily until death of 1000 Mediterranean fruit flies (or medflies for short). The plot here shows the egg laying trajectories in the first 25 days of life of about 600 female medflies (those that have at least 20 remaining eggs in their lifetime). The red colored curves belong to those flies that will lay less than the median number of remaining eggs, while the blue colored curves belong to the flies that will lay more than the median number of remaining eggs after age 25. An related problem of classifying medflies  as long-lived or short-lived based on the initial egg laying trajectories as predictors and the subsequent longevity of the flies as response has been studied with the GFLM
caption: Egg laying trajectories of medflies for the first 25 days
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