Flexible Regression and Smoothing

Stasinopoulos, Mikis D.; Rigby, Robert A.; Heller, Gillian Z.; Voudouris, Vlasios; Bastiani, Fernanda De

doi:10.1201/b21973

Cited by 358 publications

(383 citation statements)

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“…For example, the Gamma distribution has the exponential family parametrization:

f false(y false| μ, ϕ false) = \frac{1}{Γ (1 / ϕ) y} {((), \frac{y}{μ ϕ})}^{1 / ϕ} exp (- \frac{y}{μ ϕ}),

where

E (Y) = μ

Var false(Y false) = ϕ μ^{2}

and ϕ is the exponential dispersion parameter. In the R glm function (R Core Team, ) and SPSS (IBM Corp, ), the dispersion parameter ϕ is estimated; in SAS proc genmod (SAS Institute Inc., ),

ν = 1 / ϕ

is the shape parameter; and in the R package gamlss (Stasinopoulos et al., ),

σ = \sqrt{ϕ}

is the shape parameter. As ν and σ are both differentiable functions of ϕ, they retain orthogonality to the mean μ.…”

Section: Models For Overdispersed Count Datamentioning

confidence: 99%

“…More recently, generalized additive models for location, scale and shape (GAMLSS; Rigby & Stasinopoulos ) enable the specification of regression models for the mean and up to three shape parameters on a wide range of response distributions. The GAMLSS for the PiG response specifies as response distribution and

g false(μ false) = x^{⊤} bold-italicβ; h false(σ false) = w^{⊤} bold-italicγ .

Estimation is available in the R package gamlss (Stasinopoulos et al., ). In Section 3 we compare estimation for PiG regression models for our data using the GAMLSS model and a model based on the orthogonal parametrization for which, by analogy, we assume:

g false(μ false) = x^{⊤} bold-italicβ; h false(α false) = w^{⊤} bold-italicδ .

…”

Section: Models For Overdispersed Count Datamentioning

confidence: 99%

“…Although interest is generally still focussed on modelling the mean, these models allow the flexibility of modelling shape parameters as a function of covariates. The PiG, parametrized in terms of its mean μ and a dispersion parameter σ, is available as a response distribution in existing regression software (Stasinopoulos, Rigby, Heller, Voudouris, & De Bastiani, ) and parameter estimates are easily obtained. However, in our study, estimates of the treatment effect on the mean μ were found to be sensitive to specification of the model for σ.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Beyond mean modelling: Bias due to misspecification of dispersion in Poisson‐inverse Gaussian regression

2018

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In clinical trials one traditionally models the effect of treatment on the mean response. The underlying assumption is that treatment affects the response distribution through a mean location shift on a suitable scale, with other aspects of the distribution (shape/dispersion/variance) remaining the same. This work is motivated by a trial in Parkinson's disease patients in which one of the endpoints is the number of falls during a 10-week period. Inspection of the data reveals that the Poisson-inverse Gaussian (PiG) distribution is appropriate, and that the experimental treatment reduces not only the mean, but also the variability, substantially. The conventional analysis assumes a treatment effect on the mean, either adjusted or unadjusted for covariates, and a constant dispersion parameter. On our data, this analysis yields a non-significant treatment effect. However, if we model a treatment effect on both mean and dispersion parameters, both effects are highly significant. A simulation study shows that if a treatment effect exists on the dispersion and is ignored in the modelling, estimation of the treatment effect on the mean can be severely biased. We show further that if we use an orthogonal parametrization of the PiG distribution, estimates of the mean model are robust to misspecification of the dispersion model. We also discuss inferential aspects that are more difficult than anticipated in this setting. These findings have implications in the planning of statistical analyses for count data in clinical trials.

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“…For example, the Gamma distribution has the exponential family parametrization:

f false(y false| μ, ϕ false) = \frac{1}{Γ (1 / ϕ) y} {((), \frac{y}{μ ϕ})}^{1 / ϕ} exp (- \frac{y}{μ ϕ}),

where

E (Y) = μ

Var false(Y false) = ϕ μ^{2}

and ϕ is the exponential dispersion parameter. In the R glm function (R Core Team, ) and SPSS (IBM Corp, ), the dispersion parameter ϕ is estimated; in SAS proc genmod (SAS Institute Inc., ),

ν = 1 / ϕ

is the shape parameter; and in the R package gamlss (Stasinopoulos et al., ),

σ = \sqrt{ϕ}

is the shape parameter. As ν and σ are both differentiable functions of ϕ, they retain orthogonality to the mean μ.…”

Section: Models For Overdispersed Count Datamentioning

confidence: 99%

g false(μ false) = x^{⊤} bold-italicβ; h false(σ false) = w^{⊤} bold-italicγ .

g false(μ false) = x^{⊤} bold-italicβ; h false(α false) = w^{⊤} bold-italicδ .

…”

Section: Models For Overdispersed Count Datamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Beyond mean modelling: Bias due to misspecification of dispersion in Poisson‐inverse Gaussian regression

2018

Self Cite

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“…As concerns the mixture model (2), the gamlss.mx package (Stasinopoulos and Rigby, ) provides the gamlssMX()function that we use for its fitting via the expectation–maximization algorithm; see Stasinopoulos, Rigby, Heller, Voudouris and De Bastiani () for details about the structure of gamlssMX(). Since finite mixture models are known for having local maxima, to ensure that a global maximum has been reached, we run the above function five times, with different starting values randomly determined by the function.…”

Section: Real Data Analysismentioning

confidence: 99%

Modelling the Loss Given Default Distribution via a Family of Zero-and-one Inflated Mixture Models

Tomarchio

Punzo

2019

Journal of the Royal Statistical Society Series A: Statistics in Society

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Summary The empirical distribution of the loss given default (LGD) has support [0,1], contains an excess of 0s and 1s, and is often multimodal on (0,1). Though some parametric models have been used in the credit risk literature to model the LGD distribution, these peculiarities call for more flexible approaches. Thus, we introduce a zero‐and‐one inflated mixture where a three‐level multinomial model is considered for the membership of the LGD values to the sets {0}, (0,1) and {1}, whereas a finite mixture of distributions is used on (0,1). To allow for more flexible shapes on (0,1), we consider component distributions already defined on (0,1) and distributions on (−∞,∞) mapped on (0,1) via the inverse logit transformation. This yields a family of 13 zero‐and‐one inflated mixture models. They are applied to two data sets of LGDs on loans: one from a European Bank and the other from the Bank of Italy. The best performers in our family, selected via classical information criteria, are then compared with several well‐established semiparameteric or non‐parametric approaches via a convenient simulation‐based procedure.

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“…In the second step RTM conducts a bidirectional stepwise regression using the "gamlss" R package [21] on the remaining risk factors resulting from the first step. Stepwise regression is a method to automatically reduce the complexity of a statistical model by identifying the predictive variables that significantly improve the fit to the data.…”

Section: Risk Terrain Mapmentioning

confidence: 99%

Predicting Dynamical Crime Distribution From Environmental and Social Influences

Garnier

Caplan

Kennedy

2018

Front. Appl. Math. Stat.

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Understanding how social and environmental factors contribute to the spatio-temporal distribution of criminal activities is a fundamental question in modern criminology. Thanks to the development of statistical techniques such as Risk Terrain Modeling (RTM), it is possible to evaluate precisely the criminogenic contribution of environmental features to a given location. However, the role of social information in shaping the distribution of criminal acts is largely understudied by the criminological research literature. In this paper we investigate the existence of spatio-temporal correlations between successive robbery events, after controlling for environmental influences as estimated by RTM. We begin by showing that a robbery event increases the likelihood of future robberies at and in the neighborhood of its location. This event-dependent influence decreases exponentially with time and as an inverse function of the distance to the original event.We then combine event-dependence and environmental influences in a simulation model to predict robbery patterns at the scale of a large city (Newark, NJ). We show that this model significantly improves upon the predictions of RTM alone and of a model taking into account event-dependence only when tested against real data that were not used to calibrate either model. We conclude that combining risk from exposure (past event) and vulnerability (environment), following from the Theory of Risky Places, when modeling crime distribution can improve crime suppression and prevention efforts by providing more accurate forecasting of the most likely locations of criminal events.

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Flexible Regression and Smoothing

Cited by 358 publications

References 0 publications

Beyond mean modelling: Bias due to misspecification of dispersion in Poisson‐inverse Gaussian regression

Beyond mean modelling: Bias due to misspecification of dispersion in Poisson‐inverse Gaussian regression

Modelling the Loss Given Default Distribution via a Family of Zero-and-one Inflated Mixture Models

Predicting Dynamical Crime Distribution From Environmental and Social Influences

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