LOCAL INFLUENCE IN COMPOUND-POISSON MODELS: PERTURBING THE MEAN-VARIANCE RELATION
0
Citation
22
Reference
20
Related Paper
Abstract:
Local influence is a useful tool to detect abnormalities in regression models, Cook proposed this method in 1986 for classical regression models and, since then, numerous extensions have been developed. The aim of this paper is to derive methods to asses local influence under various perturbation schemes, for compound-Poisson regression models. These models can be applied to continuous data with positive probability in zero, and they are characterized by the variance function that defines the mean-variance relationship. Formulas are obtained to apply local influence methods for different perturbations and it is of particular interest the perturbation of the parameter that defines the mean-variance relation. These schemes are applied to perturbed data generated by simulations and the sensibility of the method is compared for different values of the parameters. Finally, a real data set about home expenditures is analyzed and local influence graphics are obtained to detect influential points.Keywords:
Variance function
Variance-based sensitivity analysis
Cite
Lasso
Cite
Citations (3)
This paper describes a compound Poisson-based random effects structure for modeling zero-inflated data. Data with large proportion of zeros are found in many fields of applied statistics, for example in ecology when trying to model and predict species counts (discrete data) or abundance distributions (continuous data). Standard methods for modeling such data include mixture and two-part conditional models. Conversely to these methods, the stochastic models proposed here behave coherently with regards to a change of scale, since they mimic the harvesting of a marked Poisson process in the modeling steps. Random effects are used to account for inhomogeneity. In this paper, model design and inference both rely on conditional thinking to understand the links between various layers of quantities : parameters, latent variables including random effects and zero-inflated observations. The potential of these parsimonious hierarchical models for zero-inflated data is exemplified using two marine macroinvertebrate abundance datasets from a large scale scientific bottom-trawl survey. The EM algorithm with a Monte Carlo step based on importance sampling is checked for this model structure on a simulated dataset : it proves to work well for parameter estimation but parameter values matter when re-assessing the actual coverage level of the confidence regions far from the asymptotic conditions.
Statistical Inference
Cite
Citations (1)
Data set
Regression diagnostic
Cite
Citations (4)
Abstract We consider the assessment of local influence for generalized linear models when the covariates are measured with errors. We show how to evaluate the effect that perturbations to the data, case weights, and model assumptions may have on the parameter estimates. Based on the likelihood displacement functions, some useful influence diagnostics are derived. Two examples illustrate application of the proposed diagnostics and assessment of the measurement error assumptions.
Errors-in-Variables Models
Cite
Citations (17)
Growth curve models for the analysis of longitudinal data often involve many parameters, which may be the cause of loss of efficiency in the inference or poor interpretation of the results of analysis. This paper proposes to introduce a family of linear structures into the fixed location parameters and the variance-covariance parameters in growth curve models. This leads to the models with fewer unknown paremeters, resulting in increased efficiency and easier interpetation in analysis. A noniterative algorithm is also provided for estimating unknown parameters in the model.
Growth curve (statistics)
Analysis of covariance
Cite
Citations (2)
Analyzing processes are important to make a good prediction. Based on the results, right decisions can be made. However, there is some kind of results anyway and therefore it can be hard to differ the real result from the results which occurred randomly, despite of the validations which were used during the process. In this work, we analyzed the environment, where these random results can be appeared. After presenting a framework to deal with these random results, simulation techniques are also introduced.
Cite
Citations (0)
Polytomous Rasch model
Contingency table
Polychoric correlation
Cite
Citations (16)
General linear model
Kullback–Leibler divergence
Cite
Citations (47)
Estimating equations
Cite
Citations (16)
In this paper we present various diagnostic methods for a linear regression model under a logarithmic Birnbaum-Saunders distribution for the errors, which may be applied for accelerated life testing or to compare the median lives of several populations. Some influence methods, such as the local influence, total local influence of an individual and generalized leverage are derived, analysed and discussed. We also present a connection between the local influence and generalized leverage methods. A discussion of the computation of the likelihood displacement as well as the normal curvature in the local influence method are presented. Finally, an example with real data is given for illustration.
Leverage (statistics)
Cite
Citations (98)