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Generalized Additive Models

Generalized Additive Models. Variety of “smoothing” procedures exist LOESS Splines Many are variations on theme of fitting smooth curve through time series, with amount of smoothness varying due to number of parameters. Chimney Swift, Alabama BBS route 20. Generalized Additive Models.

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Generalized Additive Models

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  1. Generalized Additive Models • Variety of “smoothing” procedures exist • LOESS • Splines • Many are variations on theme of fitting smooth curve through time series, with amount of smoothness varying due to number of parameters

  2. Chimney Swift, Alabama BBS route 20

  3. Generalized Additive Models • Extend “smoothing” procedures into modeling framework • Observer covariates in BBS analysis • Site effects, strata • Semiparametric LOESS incorporated into BBS analysis • Route-specific trends • Regional analysis in the route-regression

  4. Semiparametric LOESS With Observer Effects

  5. Generalized Additive Models and NPS Survey Data • Log(μit) = αi + s(t) • Expected count depends on site effects and the “smooth” s(t) • Extremes of these are GLM’s • Poisson regression s(t) = β • Year effects model s(t) = βt • Amount of smooth depends on smooth-specific parameter • Loess: f • Splines: df (piecewise cubic polynomials)

  6. Use Programs Developed for Statistical Package “R” • Rachel Fewster et al. provided code • http://dolphin.mcs.st-and.ac.uk/~rachel/gams/R/ • Ecology 81:1970-1984 • Allow covariates • Summarize time series as ratio of predicted abundance at year t to that of year 1 • Estimate “Change Points” • 2nd derivatives of curve • Bootstrapped Confidence Intervals

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