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## A general class of zero-or-one inflated beta regression models (2012)

Venue: | Computational Statistics & Data Analysis |

Citations: | 13 - 0 self |

### Citations

4630 |
A new look at the statistical model identification
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- 1974
(Show Context)
Citation Context ...hand side of (4.4) as a measure of the lack of fit and the second term as a “penalty” for adding d parameters. The model with the smallest GAIC is then selected. The Akaike information criterion AIC (=-=Akaike, 1974-=-), the Schwarz Bayesian criterion SBC (Schwarz, 1978), and the consistent Akaike information criterion (CAIC) are special cases of GAIC corresponding to ℘ = 2, ℘ = log(n), and ℘ = log(n) + 1, respecti... |

2378 |
Conditional Logit Analysis of Qualitative Choice Behavior
- McFadden
- 1973
(Show Context)
Citation Context ... values, µ̂•1, . . . , µ̂ • n, where µ̂ • t = Ê(yt) = cα̂t + (1 − α̂t)µ̂t. A perfect agreement between the y’s and µ̂•’s yields R2p = 1. Other pseudo R 2’s are defined as R2∗p = 1 − log L̂/ log L̂0 (=-=McFadden, 1974-=-) and R2LR = 1 − (L̂0/L̂)2/n (Cox and Snell, 1989, p. 208-209), where L̂0 and L̂ are the maximized likelihood functions of the null model and the fitted model, respectively. The ratio of the likelihoo... |

1983 |
R: A Language for Data Analysis and Graphics
- Ihaka, Gentleman
- 1996
(Show Context)
Citation Context ...an, and v3, x3, and z3 were generated from the Binomial(0.2, 5) distribution. The total number of Monte Carlo replications was set at 5000 for each sample size. All simulations were carried out in R (=-=Ihaka & Gentleman, 1996-=-). Computations for fitting inflated beta regression models were performed using the gamlss package. The MLEs were obtained by maximizing the log-likelihood function using the RS algorithm (Rigby & St... |

754 |
Theoretical statistics
- Cox, Hinckley
- 1974
(Show Context)
Citation Context ...R library at http://www.r-project.org/. Large sample inference. If the model specified by (2.2) and (2.3) is valid and the usual regularity conditions for maximum likelihood estimation are satisfied (=-=Cox & Hinkley, 1974-=-, p. 107), the MLEs of θ and K(θ), θ̂ = (ρ̂⊤β̂⊤, γ̂)⊤ and K(θ̂), respectively, are consistent. Assuming that I(θ) = limn→∞{n−1K(θ)} exists and is nonsingular, we have √ n(θ̂ − θ) D→ Np+k+m(0, I(θ)−1),... |

481 |
Analysis of binary data.
- Cox, Snell
- 1990
(Show Context)
Citation Context ...= Ê(yt) = cα̂t + (1 − α̂t)µ̂t. A perfect agreement between the y’s and µ̂•’s yields R2p = 1. Other pseudo R 2’s are defined as R2∗p = 1 − log L̂/ log L̂0 (McFadden, 1974) and R2LR = 1 − (L̂0/L̂)2/n (=-=Cox and Snell, 1989-=-, p. 208-209), where L̂0 and L̂ are the maximized likelihood functions of the null model and the fitted model, respectively. The ratio of the likelihoods or log-likelihoods may be regarded as measures... |

233 |
Parameter Orthogonality and Approximate Conditional Inference” (with discussion
- Cox, Reid
- 1987
(Show Context)
Citation Context ...V ∗A∗−1}TΦ, W3 = T{Φ(MV ∗ + C)A∗−1}H, and W4 = H{(M2V ∗ + 2MC + V †)A∗−1}H. Notice that Kρβ = Kβρ⊤ = 0 and Kργ = Kγρ⊤ = 0, thus indicating that the parameters γ and (β⊤, γ⊤)⊤ are globally orthogonal (=-=Cox & Reid, 1987-=-) and their MLEs, ρ̂ and (β̂⊤, γ̂⊤)⊤, are asymptotically independent. The inverse of Fisher’s information matrix is useful for computing asymptotic standard errors of MLEs. From (3.7) and a standard f... |

107 | Beta regression for modelling rates and proportions. - Ferrari, Cribari-Neto - 2004 |

83 | Generalized additive models for location, scale and shape.
- Rigby, Stasinopoulos
- 2005
(Show Context)
Citation Context ...−1Z⊤W3X (X⊤(W2 − W3Z(Z⊤W4Z)−1Z⊤W3)X )−1 X⊤W3Z × (Z⊤W4Z)−1. Fitting the model using the GAMLSS implementation. The zero-or-one inflated beta distribution has been incorporated in the GAMLSS framework (=-=Rigby & Stasinopoulos, 2005-=-); see Ospina (2006). GAMLSS allows the flexible modeling of each of the three parameters that index the distribution using parametric terms involving linear or nonlinear predictors, smooth nonparamet... |

63 | A general definition of residuals. - Cox, Snell - 1968 |

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52 |
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Citation Context ...e trend in the plot of some residual against the predictors may be suggestive of link function misspecification. Also, normal probability plots with simulated envelopes are a helpful diagnostic tool (=-=Atkinson, 1985-=-). Simulation results not presented here indicated that the randomized quantile residuals perform well in detecting whether the distribution assumption is incorrect. Global goodness-of-fit measure. A ... |

46 | A better lemon squeezer? Maximum-likelihood regression with beta-distributed dependent variables. - Smithson, Verkuilen - 2006 |

43 | Continuous Univariate Distributions, 2nd ed. - Johnson, Kotz, et al. - 1995 |

43 | Regression analysis of variates observed on (0, 1): percentages, proportions and fractions. - Kieschnick, McCullough - 2003 |

39 | Randomized quantile residuals.
- Dunn, Smyth
- 1996
(Show Context)
Citation Context ... the leverage of the tth observation into account. 9 To assess the overall adequacy of the zero-or-one inflated beta regression model to the data at hand, we propose the randomized quantile residual (=-=Dunn & Smyth, 1996-=-). It is a randomized version of the Cox & Snell (1968) residual and given by rqt = Φ −1(ut), t = 1, . . . , n, (4.3) where Φ(·) denotes the standard normal distribution function, ut is a uniform rand... |

29 | Second stage DEA: comparison of approaches for modelling the DEA score,” - Hoff - 2007 |

29 |
Principles of Statistical Inference: from a NeoFisherian Perspective. Singapore: World Scientific.
- Pace, Salvan
- 1997
(Show Context)
Citation Context ...ikelihood function L(θ) factorizes in two terms, the first of which depends only on ρ (discrete component), and the second, only on (β, γ) (continuous component). Hence, the parameters are separable (=-=Pace & Salvan, 1997-=-, p. 128) and the maximum likelihood inference for (β, γ) can be performed separately from that for ρ, as if the value of ρ were known, and vice-versa. The log-likelihood function is given by ℓ(θ) = ℓ... |

28 | Maximum likelihood estimation of models with beta-distributed dependent variables’. - Paolino - 2001 |

21 | Regression Analysis of Proportions in Finance with Self Selection. - Cook, Kieschnick, et al. - 2008 |

19 | Improved estimators for a general class of beta regression models. - Simas, Barreto-Souza, et al. - 2010 |

17 | Exponential Family Nonlinear Models - Wei - 1998 |

10 | On beta regression residuals. - ESPINHEIRA, FERRARI, et al. - 2008 |

9 | Inflated beta distributions - Ospina, Ferrari - 2010 |

7 | Influence diagnostics in beta regression - Espinheira, Ferrari, et al. - 2008 |

5 |
Improved likelihood inference in beta regression
- Ferrari, Pinheiro
- 2010
(Show Context)
Citation Context ...t β and h3(φt) = z ⊤ t γ. Here, V = (v⊤1 , . . . , v⊤n )⊤, X = (x⊤1 , . . . , x⊤n )⊤, and Z = (z⊤1 , . . . , z⊤n )⊤. Also, the nonlinear beta regression model (Simas, Barreto-Souza & Rocha, 2010, and =-=Ferrari & Pinheiro, 2010-=-) is a limiting case of our model obtained by setting αt = α→ 0. If, in addition, the predictor for µt is linear and φt is constant through the observations, we arrive at the beta regression model def... |

4 | Local models for forest canopy cover with beta regression. - KORHONEN, KORHONEN, et al. - 2007 |

3 |
Estimating the dimension of a mode
- Schwarz
- 1978
(Show Context)
Citation Context ...and the second term as a “penalty” for adding d parameters. The model with the smallest GAIC is then selected. The Akaike information criterion AIC (Akaike, 1974), the Schwarz Bayesian criterion SBC (=-=Schwarz, 1978-=-), and the consistent Akaike information criterion (CAIC) are special cases of GAIC corresponding to ℘ = 2, ℘ = log(n), and ℘ = log(n) + 1, respectively. 5 An application This section contains an appl... |

2 | The zero-inflated beta distribution for fitting a GAMLSS. Extra distributions to be used for GAMLSS modelling. Available at gamlss.dist package. http://www.gamlss.org - Ospina - 2006 |