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An Ecological Trap for Ecologists: Zero-Modified Models

Possible. ^. Western Mensurationists’ Meeting 2009 Tzeng Yih Lam 06.23.2009. An Ecological Trap for Ecologists: Zero-Modified Models. Tzeng Yih Lam, OSU Manuela Huso, OSU Doug Maguire, OSU.

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An Ecological Trap for Ecologists: Zero-Modified Models

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  1. Possible ^ Western Mensurationists’ Meeting 2009 Tzeng Yih Lam 06.23.2009 An Ecological Trap for Ecologists:Zero-Modified Models Tzeng Yih Lam, OSUManuela Huso, OSUDoug Maguire, OSU

  2. Western Mensurationists’ Meeting 2009 Tzeng Yih Lam 06.23.2009 Ecological Trap[ē-kə-ˈlä-ji-kəlˈtrap] A preference of falsely attractive habitat and a general avoidance of high-quality but less-attractive habitats. Wikipedia

  3. Western Mensurationists’ Meeting 2009 Tzeng Yih Lam 06.23.2009 • Cues for Zero-Modified Models • Possible Trap #1 • Possible Trap #2 • Discussions

  4. Cues for Using Zero-Modified Models Cues for Zero-Modified Models Possible Trap #1 Possible Trap #2 Discussions Discussions Count & Normal Theory The Cues & The Solutions Zero-Inflated Models Hurdle Models Expected Count – Observed Count Conclusions Western Mensurationists’ Meeting 2009 Tzeng Yih Lam 06.23.2009 • ‘The Cues’: • For rare species data, the marginal count frequency distribution contains large number of zeros, • Poisson and/or NB GLM have poor fit. • ‘The Solutions’: • Zero-modified Models: A general class of finite mixture models that account for excessive zeros, • Zero-Inflated Models (ZI)1, • Hurdle Models (H)2. 1Lambert (1992); 2Mullahy (1986)

  5. Cues for Using Zero-Modified Models Cues for Zero-Modified Models Possible Trap #1 Possible Trap #2 Discussions Discussions Count & Normal Theory The Cues & The Solutions Zero-Inflated Models Hurdle Models Expected Count – Observed Count Conclusions Probability of Belonging to Perfect State Western Mensurationists’ Meeting 2009 Tzeng Yih Lam 06.23.2009 Zero-Inflated Models (Poisson; ZIP) • Two States: Perfect and Imperfect States, • Finite Mixture Model (FMM) with 1 latent structure: • An observation belongs to either state. • Specify it as Zero-Inflated Negative Binomial (ZINB). Lambert (1992)

  6. Cues for Using Zero-Modified Models Cues for Zero-Modified Models Possible Trap #1 Possible Trap #2 Discussions Discussions Count & Normal Theory The Cues & The Solutions Zero-Inflated Models Hurdle Models Expected Count – Observed Count Conclusions Probability of Crossing the Hurdle Western Mensurationists’ Meeting 2009 Tzeng Yih Lam 06.23.2009 Hurdle Models (Poisson; HPOIS) • Under FMM framework comparable to ZI models, Hurdle Models with 2 latent structures2: • An observation either cross the ‘hurdle’ or not, • All observations are in the Imperfect State. • Specify it as Hurdle Negative Binomial (HNB). Mullahy (1986) 2Baughman (2007)

  7. Cues for Using Zero-Modified Models Cues for Zero-Modified Models Possible Trap #1 Possible Trap #2 Discussions Discussions Count & Normal Theory The Questions The Simulation Study The Bias & AICc Other Preliminary Key Findings Some Plausible Explanations Western Mensurationists’ Meeting 2009 Tzeng Yih Lam 06.23.2009 Given known data generating process (dgp): • Is there any bias when the data is fitted to different ZI and H model specifications? • Is/Are there any universally best fit models?

  8. Cues for Using Zero-Modified Models Cues for Zero-Modified Models Possible Trap #1 Possible Trap #2 Discussions Discussions Count & Normal Theory The Questions The Simulation Study The Bias & AICc Other Preliminary Key Findings Some Plausible Explanation Western Mensurationists’ Meeting 2009 Tzeng Yih Lam 06.23.2009 4 Factors • LAMBDA (λ): 0.3 1.5 5.0 • INFLA (p): 0.0 0.25 0.75 • RATIO (Var/Mean): 1.0 1.5 3.0 • SAMPLE : 25 50 75 100 250 • For each of the 27 dgp (LAMBDA × INFLA × RATIO), generate 1000 sets of SAMPLE random count, • Fit each set to six model specifications: POIS, NB, ZIP, ZINB, HPOIS, HNB, • Calculate mean %RBIAS for each parameter: λ, p, π and compute AICc.

  9. Western Mensurationists’ Meeting 2009 Tzeng Yih Lam 06.23.2009 SAMPLE = 100

  10. Western Mensurationists’ Meeting 2009 Tzeng Yih Lam 06.23.2009 Bias at LAMBDA = 0.3 SAMPLE = 100

  11. Western Mensurationists’ Meeting 2009 Tzeng Yih Lam 06.23.2009 Bias withZIP&HPOIS SAMPLE = 100

  12. Western Mensurationists’ Meeting 2009 Tzeng Yih Lam 06.23.2009 Bias with ZINB & HNB SAMPLE = 100

  13. Western Mensurationists’ Meeting 2009 Tzeng Yih Lam 06.23.2009 Lowest AICc SAMPLE = 100 ZIP ZINB HPOIS HNB POIS NB ZIP ZINB HPOIS HNB ZIP ZINB HPOIS HNB NB HNB ZIP ZINB HPOIS HNB NB ZINB HNB NB ZINB HNB NB ZIP ZINB HPOIS HNB

  14. Cues for Using Zero-Modified Models Cues for Zero-Modified Models Possible Trap #1 Possible Trap #2 Discussions Discussions Count & Normal Theory The Questions The Simulation Study The Bias & AICc Other Preliminary Key Findings Some Plausible Explanations Western Mensurationists’ Meeting 2009 Tzeng Yih Lam 06.23.2009 • Variance of estimated λ is the highest when LAMBDA = 0.3, • Variance of estimated λ decreases with increasing LAMBDA but it increases with increasing RATIO and/or INFLA, • Probability in Perfect State, p, from ZI models has largest (+ve and –ve) bias and variance at LAMBDA = 0.3, • Overdispersion parameter, θ, requires ≥ 250 SAMPLE to achieve negligible bias.

  15. Cues for Using Zero-Modified Models Cues for Zero-Modified Models Possible Trap #1 Possible Trap #2 Discussions Discussions Count & Normal Theory The Questions The Simulation Study The Bias & AICc Other Preliminary Key Findings Some Plausible Explanations Western Mensurationists’ Meeting 2009 Tzeng Yih Lam 06.23.2009 Maximum Likelihood Theory • Ingredient = a simulated set of count • Optimize the parameter estimates to match the marginal count distribution. • Large bias and variance of λ and p at LAMBDA = 0.3, • When there are either too many zeros or ones, Binomial GLM seems to be unstable Min and Agresti (2005) unstable estimates of p  unstable estimates of λandθ. • There might not be enough information when LAMBDA = 0.3. • ZI models estimation are based on EM algorithm, • H models separately maximize the likelihood functions of π and λ.

  16. Cues for Using Zero-Modified Models Cues for Zero-Modified Models Possible Trap #1 Possible Trap #2 Discussions Discussions Count & Normal Theory Perfect & Imperfect States Perfect & Imperfect States A Priori Knowledge Rarity Conclusions Western Mensurationists’ Meeting 2009 Tzeng Yih Lam 06.23.2009 • Perfect State in Ecology Context: • It is a set of habitat conditions that do not host the interested species, • Imperfect State in Ecology Context: • It is a set of habitat conditions that host the interested species but one may not find the species there, • This does not directly differentiate sink & source, saturated & unsaturated habitat, fundamental & realized niche etc. Zero Structural Random Accidental Stochastic Sampling True False

  17. Cues for Using Zero-Modified Models Cues for Zero-Modified Models Possible Trap #1 Possible Trap #2 Discussions Discussions Count & Normal Theory Perfect & Imperfect States Perfect & Imperfect States A Priori Knowledge Rarity Conclusions Zero-Inflated Models Hurdle Models Western Mensurationists’ Meeting 2009 Tzeng Yih Lam 06.23.2009 • Zero-Inflated Models have 2 states: • Perfect and Imperfect States • Main Assumption: You do not know the observation belong to which state. • Hurdle models have 1 state: • Imperfect State A: “Did you smoke any cigarette last week?” B: “No” ; 0 A: “Are you a smoker?” B: “Yes”

  18. Cues for Using Zero-Modified Models Cues for Zero-Modified Models Possible Trap #1 Possible Trap #2 Discussions Discussions Count & Normal Theory Perfect & Imperfect States Perfect & Imperfect States A Priori Knowledge Rarity Conclusions POIS NB ZIP ZINB HPOIS HNB Extent Western Mensurationists’ Meeting 2009 Tzeng Yih Lam 06.23.2009 A priori knowledge such as species habitat range, will likely influence the model choice In ecology, scale matters … Grains

  19. Cues for Using Zero-Modified Models Cues for Zero-Modified Models Possible Trap #1 Possible Trap #2 Discussions Discussions Count & Normal Theory Perfect & Imperfect States Perfect & Imperfect States A Priori Knowledge Rarity Conclusions and many others… Western Mensurationists’ Meeting 2009 Tzeng Yih Lam 06.23.2009 Modeling of rare species habitat association Cunningham & Lindenmayer (2005)

  20. Cues for Using Zero-Modified Models Cues for Zero-Modified Models Possible Trap #1 Possible Trap #2 Discussions Discussions Count & Normal Theory Perfect & Imperfect States Perfect & Imperfect States A Priori Knowledge Rarity, Extent & Grains Conclusions Western Mensurationists’ Meeting 2009 Tzeng Yih Lam 06.23.2009 What Do the Ecologists Need To Do?

  21. Cues for Using Zero-Modified Models Cues for Zero-Modified Models Possible Trap #1 Possible Trap #2 Discussions Discussions Count & Normal Theory Perfect & Imperfect States Perfect & Imperfect States A Priori Knowledge Rarity, Extent & Grains Conclusions Western Mensurationists’ Meeting 2009 Tzeng Yih Lam 06.23.2009 The Great Escape(1963) Capt. Hilts (The Cooler King) 1961 British 650cc Triumphs

  22. Cues for Using Zero-Modified Models Cues for Zero-Modified Models Possible Trap #1 Possible Trap #2 Discussions Discussions Count & Normal Theory Perfect & Imperfect States Perfect & Imperfect States A Priori Knowledge Rarity, Extent & Grains Conclusions Western Mensurationists’ Meeting 2009 Tzeng Yih Lam 06.23.2009 • Escape from defining the types of zeros: • There is no restriction on threshold for mixing & hurdle, • Change current threshold from 0  1, • Change perfect to near-perfect state (ZI models), changing ecological implication of the models. • N-mixture models (Royle 2004) • Escape from using ZI & H models : • If one is uncomfortable with two-states processes, • Small Area Estimation Rao(2003), • Extreme Value Model Coles(2001).

  23. Cues for Using Zero-Modified Models Cues for Zero-Modified Models Acknowledgement Possible Trap #2 Discussions Discussions Count & Normal Theory Perfect & Imperfect States Acknowledgement A Priori Knowledge Rarity, Extent & Grains Conclusions Western Mensurationists’ Meeting 2009 Tzeng Yih Lam 06.23.2009 Hayes Family Foundation Funds for Silviculture Alternatives Dilworth Awards, OSU Doug Maguire

  24. Cues for Using Zero-Modified Models Cues for Zero-Modified Models Acknowledgement Possible Trap #2 Discussions Discussions Count & Normal Theory Perfect & Imperfect States Acknowledgement A Priori Knowledge Rarity, Extent & Grains Conclusions Western Mensurationists’ Meeting 2009 Tzeng Yih Lam 06.23.2009 Thank You for Listening! Any *Err… Question?

  25. Cues for Using Zero-Modified Models Cues for Zero-Modified Models Possible Trap #1 Possible Trap #2 Discussions Discussions Count & Normal Theory The Questions The Simulation Study The Bias & AICc Other Preliminary Key Findings Some Plausible Explanations Western Mensurationists’ Meeting 2009 Tzeng Yih Lam 06.23.2009 • AICc, Information theory. • More flexible model parameterization will have better fit. • Sample size is an issue for ZINB and HNB models for fitting.

  26. Cues for Using Zero-Modified Models Cues for Zero-Modified Models Possible Trap #1 Possible Trap #2 Discussions Discussions Count & Normal Theory The Questions The Simulation Study The Bias & AICc Other Preliminary Key Findings Some Plausible Explanations Western Mensurationists’ Meeting 2009 Tzeng Yih Lam 06.23.2009

  27. Cues for Using Zero-Modified Models Cues for Zero-Modified Models Possible Trap #1 Possible Trap #2 Discussions Discussions Count & Normal Theory Perfect & Imperfect States Perfect & Imperfect States A Priori Knowledge Rarity Conclusions Western Mensurationists’ Meeting 2009 Tzeng Yih Lam 06.23.2009 A priori knowledge such as species habitat range, and extent and grains will likely influence the model choice.

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