## Predictive model assessment for count data (2007)

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Citations: | 14 - 1 self |

### BibTeX

@TECHREPORT{Czado07predictivemodel,

author = {Claudia Czado and Tilmann Gneiting and Leonhard Held},

title = {Predictive model assessment for count data},

institution = {},

year = {2007}

}

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### Abstract

Summary. We discuss tools for the evaluation of probabilistic forecasts and the critique of statistical models for ordered discrete data. Our proposals include a non-randomized version of the probability integral transform, marginal calibration diagrams and proper scoring rules, such as the predictive deviance. In case studies, we critique count regression models for patent data, and assess the predictive performance of Bayesian age-period-cohort models for larynx cancer counts in Germany.

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Citation Context ... Armstrong and Moolgavkar, 2005). To this date, statistical methods for the assessment of predictive performance have been studied primarily from biomedical, meteorological and economic perspectives (=-=Pepe, 2003-=-; Jolliffe and Stephenson, 2003; Clements, 2005), focusing on predictions of dichotomous events or real-valued continuous variables. Here, we consider the hybrid case of count data, in which methods d... |

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Citation Context ...l, ecological, environmental, climatological, demographic and economic applications (Christensen and Waagepetersen, 2002; Gotway and Wolfinger, 2003; McCabe and Martin, 2005; Elsner and Jagger, 2006; =-=Frühwirth-Schnatter and Wagner, 2006-=-; Nelson and Leroux, 2006). Our focus is on the low count situation in which continuum approximations fail; however, our results apply to high counts and rates as well, as they occur routinely in epid... |

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Citation Context ... be strictly proper. If s(Q, Q) ≤ s(P, Q) for all P and Q, the scoring rule is said to be proper. Propriety is an essential property of a scoring rule that encourages honest and coherent predictions (=-=Bröcker and Smith, 2007-=-; Gneiting and Raftery, 2007). Strict propriety ensures that both calibration and sharpness are being addressed. A scoring rule s for count data is regular if s(P, x) is finite, except possibly that s... |

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Citation Context ...y, 1998; Gneiting et al., 2007). The PIT histogram is typically used informally as a diagnostic tool; formal tests can also be employed though they require care in their interpretation (Hamill, 2001; =-=Jolliffe, 2007-=-). Deviations from uniformity hint at reasons for forecast failures and model deficiencies. U-shaped histograms indicate underdispersed predictive distributions, hump or inverse-U shaped histograms po... |

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Citation Context ...). Our focus is on the low count situation in which continuum approximations fail; however, our results apply to high counts and rates as well, as they occur routinely in epidemiological projections (=-=Knorr-Held and Rainer, 2001-=-; Clements, Armstrong and Moolgavkar, 2005). To this date, statistical methods for the assessment of predictive performance have been studied primarily from biomedical, meteorological and economic per... |

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Citation Context ... score, where µP and σ 2 P nses(P, x) = � � x − µP 2 σP , (12) denote the mean and the variance of P , ought be approximately one when averaged over the predictions (Carroll and Cressie, 1997, p. 52; =-=Liesenfeld et al., 2006-=-, pp. 811, 818). Gotway and Wolfinger (2003, p. 1423) call the mean normalized squared error score the average empirical-to-model variability ratio, arguing also that it should be close to 11 issone. ... |

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Citation Context ...sidual or normalized squared error score, where µP and σ 2 P nses(P, x) = � � x − µP 2 σP , (12) denote the mean and the variance of P , ought be approximately one when averaged over the predictions (=-=Carroll and Cressie, 1997-=-, p. 52; Liesenfeld et al., 2006, pp. 811, 818). Gotway and Wolfinger (2003, p. 1423) call the mean normalized squared error score the average empirical-to-model variability ratio, arguing also that i... |

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Citation Context ...distributions, for count data, as they occur in a wide range of epidemiological, ecological, environmental, climatological, demographic and economic applications (Christensen and Waagepetersen, 2002; =-=Gotway and Wolfinger, 2003-=-; McCabe and Martin, 2005; Elsner and Jagger, 2006; Frühwirth-Schnatter and Wagner, 2006; Nelson and Leroux, 2006). Our focus is on the low count situation in which continuum approximations fail; howe... |

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Citation Context ...ect cancer incidence and mortality rates. Data from younger age groups (typically age < 30 years) for which rates are low are often excluded from the analysis. However, a recent empirical comparison (=-=Baker and Bray, 2005-=-) based on data from Hungary suggests that age-specific predictions based on full data are more accurate. A natural question arises here in how to quantify the quality of the predictive distributions.... |

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Citation Context ...ctive distribution, x ∼ P is a random count and v is standard uniform and independent of x, then u = Px−1 + v(Px − Px−1), x ≥ 1, (1) u = vP0, x = 0, (2) is standard uniform (Smith, 1985, pp. 286–287; =-=Frühwirth-Schnatter, 1996-=-, p. 297; Liesenfeld, Nolte and Pohlmeier, 2006, pp. 819–820). For time series data one typically considers onestep (or k-step) ahead predictions, based on a time series model fitted on past and curre... |

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Citation Context ...ial or Poisson, the standardizing term is routinely taken to be the saturated deviance (McCullagh and Nelder, 1989, pp. 33-34; Knorr-Held and Rainer, 2001, p. 114; Spiegelhalter et al., 2002, p. 606; =-=Clements et al., 2005-=-, p. 581). However, when the predictive distributions come from possibly distinct parametric or non-parametric families, it is vital that the standardizing terms in the deviance are common (Spiegelhal... |

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Citation Context ...nd Moolgavkar, 2005). To this date, statistical methods for the assessment of predictive performance have been studied primarily from biomedical, meteorological and economic perspectives (Pepe, 2003; =-=Jolliffe and Stephenson, 2003-=-; Clements, 2005), focusing on predictions of dichotomous events or real-valued continuous variables. Here, we consider the hybrid case of count data, in which methods developed for either type of sit... |

2 |
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Citation Context ...ogical, demographic and economic applications (Christensen and Waagepetersen, 2002; Gotway and Wolfinger, 2003; McCabe and Martin, 2005; Elsner and Jagger, 2006; Frühwirth-Schnatter and Wagner, 2006; =-=Nelson and Leroux, 2006-=-). Our focus is on the low count situation in which continuum approximations fail; however, our results apply to high counts and rates as well, as they occur routinely in epidemiological projections (... |

1 | Re: “Bayesian projections: What are the effects of excluding data from younger age groups - Clements, Hakulinen, et al. - 2006 |