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Waterloo GLMM talk

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Generalized linear mixed models for quantitative biology at GLMM

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Waterloo GLMM talk

  1. 1. Denitions Estimation Inference Challenges open questions References Generalized linear mixed models Ben Bolker McMaster University, Mathematics Statistics and Biology 26 September 2014
  2. 2. Denitions Estimation Inference Challenges open questions References Acknowledgments lme4: Doug Bates, Martin Mächler, Steve Walker Data: Josh Banta, Adrian Stier, Sea McKeon, David Julian, Jada-Simone White NSERC (Discovery) SHARCnet
  3. 3. Denitions Estimation Inference Challenges open questions References Outline 1 Examples and denitions 2 Estimation Overview Methods 3 Inference 4 Challenges open questions
  4. 4. Denitions Estimation Inference Challenges open questions References Outline 1 Examples and denitions 2 Estimation Overview Methods 3 Inference 4 Challenges open questions
  5. 5. Denitions Estimation Inference Challenges open questions References (Generalized) linear mixed models (G)LMMs: a statistical modeling framework incorporating: combinations of categorical and continuous predictors, and interactions (some) non-Normal responses (e.g. binomial, Poisson, and extensions) (some) nonlinearity (e.g. logistic, exponential, hyperbolic) non-independent (grouped) data
  6. 6. Denitions Estimation Inference Challenges open questions References (Generalized) linear mixed models (G)LMMs: a statistical modeling framework incorporating: combinations of categorical and continuous predictors, and interactions (some) non-Normal responses (e.g. binomial, Poisson, and extensions) (some) nonlinearity (e.g. logistic, exponential, hyperbolic) non-independent (grouped) data
  7. 7. Denitions Estimation Inference Challenges open questions References (Generalized) linear mixed models (G)LMMs: a statistical modeling framework incorporating: combinations of categorical and continuous predictors, and interactions (some) non-Normal responses (e.g. binomial, Poisson, and extensions) (some) nonlinearity (e.g. logistic, exponential, hyperbolic) non-independent (grouped) data
  8. 8. Denitions Estimation Inference Challenges open questions References } correlation nonlinearity random nonlinear least−squares linear regression ANOVA analysis of covariance multiple linear regression (non−normal errors) (nonlinearity) repeated−measures models; time series (ARIMA) } generalized (non−normal errors) linear models random smooth nonlinearity scaled variance effects nonlinearity nonlinear time series models thresholds; mixtures; compound distributions; etc. etc. etc. etc. effects correlation (nonlinearity) general linear models logistic regression binomial regression log−linear models GLMM mixed models generalized additive models quasilikelihood negative binomial models
  9. 9. Denitions Estimation Inference Challenges open questions References Coral protection from seastars (Culcita) by symbionts (McKeon et al., 2012) Number of predation events 2 2 1 2 2 1 none shrimp crabs both Symbionts 10 8 Number of blocks 0 6 4 2 1 0 0 0
  10. 10. Denitions Estimation Inference Challenges open questions References Environmental stress: Glycera cell survival (D. Julian unpubl.) Anoxia Anoxia Anoxia Copper Normoxia Normoxia Osm=12.8 Osm=22.4 133.3 66.6 33.3 0 0 0.03 0.1 0.32 H2S Normoxia Osm=32 0 0.03 0.1 0.32 Anoxia Normoxia Osm=41.6 Anoxia Normoxia Osm=51.2 0 0.03 0.1 0.32 Osm=12.8 0 0.03 0.1 0.32 Osm=22.4 Osm=32 0 0.03 0.1 0.32 Osm=41.6 133.3 66.6 33.3 0 Osm=51.2 1.0 0.8 0.6 0.4 0.2 0.0
  11. 11. Denitions Estimation Inference Challenges open questions References Arabidopsis response to fertilization herbivory (Banta et al., 2010) Log(1+fruit set) 5 4 3 2 1 0 nutrient : 1 l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l ll l ll l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l ll l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l ll l l l l l l ll ll ll l ll lll ll l l l ll ll l l lll l l l l l l l l l ll ll unclipped clipped nutrient : 8 l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l ll l l l l l l l l l l l l l l l l l l l l l l l l l l l l ll l l l l l l l l l l l l l l l l l l l l ll l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l ll l l l l l l ll l l ll l ll l l l l l l l l l l l l l l l l l l l ll l l ll l ll l l ll lll l lll ll l l l l ll llll l l unclipped clipped
  12. 12. Denitions Estimation Inference Challenges open questions References Coral demography (J.-S. White unpubl.) Before Experimental l l l l l l l l l l l l l l l l l l l l lll l ll l l l l l l l l l l l l l l ll l l l l l ll l l ll l l l l ll l l ll l l l l l l llll l l l l l l l l l l l l l l l l l l l lll ll l l l l l l l l l l l ll l l l l l l l l l l l l l l l l l l l l l l l lll l l l l l l l l l l l l l l ll l l ll l l l l l l lll l l l ll l l l l l l l l l 1.00 0.75 0.50 0.25 0.00 l 0 10 20 30 40 50 0 10 20 30 40 50 Previous size (cm) Mortality probability Treatment l l Present Removed
  13. 13. Denitions Estimation Inference Challenges open questions References Technical denition Yi |{z} response conditional disztr}ib|u{tion Distr (g

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