A Poisson ridge regression estimator

Månsson, Kristofer; Shukur, Ghazi

doi:10.1016/j.econmod.2011.02.030

Cited by 130 publications

(108 citation statements)

References 13 publications

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“…This method is a generalization of the one suggested for the Poisson model in [10,11]:Ŵ is a matrix where the non-diagonal elements are equal to zero and the ith diagonal elements are equal toμ i . This estimator is a biased shrinkage estimator in the same spirit as the ones proposed by, for example, Hoerl and Kennard [5,6], Schaeffer et al [14] and Månsson and Shukur [10,11] for the linear, logit and Poisson models, respectively. Hence, the theoretical foundation outlined in, for example, [14] is that this type of shrinkage estimator minimizes the increase in the weighted sum of squared error.…”

Section: The Zip Modelmentioning

confidence: 99%

“…However, when π i is high and the sample size is low, we sometimes obtain a dependent variable consisting of only zeros. Therefore, we need, just as in [10,11], to increase the sample size with the intercept of the logit model in order to achieve convergence of the simplex algorithm. The different combinations of intercept and sample sizes are given in Table 1.…”

Section: The Design Of the Experimentsmentioning

confidence: 99%

“…Hoerl and Kennard [5,6] showed that one may reduce the variance of the estimated coefficients substantially by introducing a small amount of bias. This method was then generalized in order to be used for models estimated by maximum likelihood (ML) such as the logit and Poisson models by Schaeffer et al [14] and Månsson and Shukur [10,11], among others.…”

Section: Introductionmentioning

confidence: 99%

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Some ridge regression estimators for the zero-inflated Poisson model

Kibria

Månsson

Shukur

2013

Journal of Applied Statistics

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The zero-inflated Poisson regression model is commonly used when analyzing economic data that come in the form of non-negative integers since it accounts for excess zeros and overdispersion of the dependent variable. However, a problem often encountered when analyzing economic data that has not been addressed for this model is multicollinearity. This paper proposes ridge regression (RR) estimators and some methods for estimating the ridge parameter k for a non-negative model. A simulation study has been conducted to compare the performance of the estimators. Both mean squared error and mean absolute error are considered as the performance criteria. The simulation study shows that some estimators are better than the commonly used maximum-likelihood estimator and some other RR estimators. Based on the simulation study and an empirical application, some useful estimators are recommended for practitioners.

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Section: The Zip Modelmentioning

confidence: 99%

Section: The Design Of the Experimentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Some ridge regression estimators for the zero-inflated Poisson model

Kibria

Månsson

Shukur

2013

Journal of Applied Statistics

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“…However, as multicollinearity is not a serious issue to the predictive performance of the model, it may cause the coefficient estimates to be unreliable [48] (i.e., the estimated coefficients may not coincide with the true influence of the explanatory location factor on the number of software firms). A possible solution for instable estimates in Poisson regression models due to multicollinearity is the application of a Poisson Ridge regression estimator [82].…”

Section: Discussion Of Model Adequacymentioning

confidence: 99%

Analyzing and Predicting Micro-Location Patterns of Software Firms

Kinne

Resch

2017

IJGI

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While the effects of non-geographic aggregation on statistical inference are well studied in economics, research on the effects of geographic aggregation on regression analysis is rather scarce. This knowledge gap, together with the use of aggregated spatial units in previous firm location studies, results in a lack of understanding of firm location determinants at the microgeographic level. Suitable data for microgeographic location analysis has become available only recently through the emergence of Volunteered Geographic Information (VGI), especially the OpenStreetMap (OSM) project, and the increasing availability of official (open) geodata. In this paper, we use a comprehensive dataset of three million street-level geocoded firm observations to explore the location pattern of software firms in an Exploratory Spatial Data Analysis (ESDA). Based on the ESDA results, we develop a software firm location prediction model using Poisson regression and OSM data. Our findings offer novel insights into the mode of operation of the Modifiable Areal Unit Problem (MAUP) in the context of a microgeographic location analysis: We find that non-aggregated data can be used to detect information on location determinants, which are superimposed when aggregated spatial units are analyzed, and that some findings of previous firm location studies are not robust at the microgeographic level. However, we also conclude that the lack of high-resolution geodata on socio-economic population characteristics causes systematic prediction errors, especially in cities with diverse and segregated populations.

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“…We systematically review and compare the estimators in a broad variety of high-dimensional settings. For estimation of λ in low-dimensional settings, we refer to [4,5,6]. We address the effect of multi-collinearity and robustness against model misspecifications, such as sparsity and non-Gaussian errors.…”

Section: Introductionmentioning

confidence: 99%

Estimation of variance components, heritability and the ridge penalty in high-dimensional generalized linear models

Veerman

Leday

Wiel

2019

Communications in Statistics - Simulation and Computation

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For high-dimensional linear regression models, we review and compare several estimators of variances τ 2 and σ 2 of the random slopes and errors, respectively. These variances relate directly to ridge regression penalty λ and heritability index h 2 , often used in genetics. Direct and indirect estimators of these, either based on cross-validation (CV) or maximum marginal likelihood (MML), are also discussed. The comparisons include several cases of covariate matrix X n×p , with p n, such as multi-collinear covariates and data-derived ones. In addition, we study robustness against departures from the model such as sparse instead of dense effects and non-Gaussian errors.An example on weight gain data with genomic covariates confirms the good performance of MML compared to CV. Several extensions are presented. First, to the high-dimensional linear mixed effects model, with REML as an alternative to MML. Second, to the conjugate Bayesian setting, which proves to be a good alternative. Third, and most prominently, to generalized linear models for which we derive a computationally efficient MML estimator by re-writing the marginal likelihood as an n-dimensional integral. For Poisson and Binomial ridge regression, we demonstrate the superior accuracy of the resulting MML estimator of λ as compared to CV. Software is provided to enable reproduction of all results presented here.

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A Poisson ridge regression estimator

Cited by 130 publications

References 13 publications

Some ridge regression estimators for the zero-inflated Poisson model

Some ridge regression estimators for the zero-inflated Poisson model

Analyzing and Predicting Micro-Location Patterns of Software Firms

Estimation of variance components, heritability and the ridge penalty in high-dimensional generalized linear models

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