A Sample Selection Model with Skew‐normal Distribution

Ogundimu, Emmanuel O.; Hutton, Jane

doi:10.1111/sjos.12171

Cited by 19 publications

(23 citation statements)

References 23 publications

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“…More preventive strategies aiming at relaxing the distributional assumptions have been proposed. They include more flexible parametric methods, such as a sample selection model based on the t ‐distribution by Marchenko and Genton (), an extension for the skew normal distribution by Ogundimu and Hutton (), a copula‐based approach by Smith () and the generalized additive model with location, scale and shape approach by Rigby and Stasinopoulos (). Although these models are more flexible than the standard normal model in that they contain additional parameters that can be used to accommodate skewness, kurtosis and possible outliers, they do not generate full neighbourhoods (in a topological sense) of the central model and do not offer full protection against possible distributional deviations from the central model; see Hampel et al .…”

Section: Introductionmentioning

confidence: 99%

Robust Inference in Sample Selection Models

Zhelonkin

Genton

Ronchetti

2015

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Summary The problem of non‐random sample selectivity often occurs in practice in many fields. The classical estimators introduced by Heckman are the backbone of the standard statistical analysis of these models. However, these estimators are very sensitive to small deviations from the distributional assumptions which are often not satisfied in practice. We develop a general framework to study the robustness properties of estimators and tests in sample selection models. We derive the influence function and the change‐of‐variance function of Heckman's two‐stage estimator, and we demonstrate the non‐robustness of this estimator and its estimated variance to small deviations from the model assumed. We propose a procedure for robustifying the estimator, prove its asymptotic normality and give its asymptotic variance. Both cases with and without an exclusion restriction are covered. This allows us to construct a simple robust alternative to the sample selection bias test. We illustrate the use of our new methodology in an analysis of ambulatory expenditures and we compare the performance of the classical and robust methods in a Monte Carlo simulation study.

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Section: Introductionmentioning

confidence: 99%

Robust Inference in Sample Selection Models

Zhelonkin

Genton

Ronchetti

2015

Journal of the Royal Statistical Society Series B: Statistical Methodology

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“…These predictors have been used previously in other context (see Ogundimu and Hutton (2015)). Initial analysis showed that there is no difference in the performance of the methods in terms of predictive accuracy.…”

Section: Discussionmentioning

confidence: 99%

Predictive performance of penalized beta regression model for continuous bounded outcomes

Ogundimu

Collins

2017

Journal of Applied Statistics

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Prediction models for continuous bounded outcomes are often developed by fitting ordinary least square regression. However, predicted values from such method may lie outside the range of the outcome as it is bounded within a fixed range, with non-linear expectation due to the ceiling and floor effects of the bounds. Thus, regular regression models such as normal linear or nonlinear models, are inadequate for prediction purposes for bounded response variable and the use of distributions that can model different shapes are essential. Beta regression, apart from modeling different shapes and constraining predictions to an admissible range, has been shown to be superior to alternative methods for data fitting but not for prediction purposes. We take data structures into account and compared various penalized beta regression method on predictive accuracy for bounded outcome variables using optimism corrected measures. Contrary to results obtained under many regression contexts, the classical maximum likelihood method produced good predictive accuracy in terms of R 2 and RMSE. The ridge penalized beta regression performed better in terms of g-index, which is a measure of performance of the methods in external data sets. We restricted attention to prespecified models throughout and as such variable selection methods are not evaluated.

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“…The data are MNAR because the observed data do not represent a random sample from the population, even after controlling for covariates. A model for selected sample was introduced by 8 and several extensions in the parametric framework [9][10][11][12] , semiparametric framework 13 and non-parametric framework 14 have been proposed. Earlier review of sample selection models can be found in 15 .…”

Section: Introductionmentioning

confidence: 99%

“…The use of a sample selection modelling framework as an imputation model for MI has been suggested in the literature 12,17 . This approach was implemented for missing covariates data by 18 and compared against competing methods.…”

Section: Introductionmentioning

confidence: 99%

A robust imputation method for missing responses and covariates in sample selection models

Ogundimu

Collins

2017

Stat Methods Med Res

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Sample selection arises when the outcome of interest is partially observed in a study. Although sophisticated statistical methods in the parametric and non-parametric framework have been proposed to solve this problem, it is yet unclear how to deal with selectively missing covariate data using simple multiple imputation techniques, especially in the absence of exclusion restrictions and deviation from normality. Motivated by the 2003-2004 NHANES data, where previous authors have studied the effect of socio-economic status on blood pressure with missing data on income variable, we proposed the use of a robust imputation technique based on the selection-t sample selection model. The imputation method, which is developed within the frequentist framework, is compared with competing alternatives in a simulation study. The results indicate that the robust alternative is not susceptible to the absence of exclusion restrictions - a property inherited from the parent selection-t model - and performs better than models based on the normal assumption even when the data is generated from the normal distribution. Applications to missing outcome and covariate data further corroborate the robustness properties of the proposed method. We implemented the proposed approach within the MICE environment in R Statistical Software.

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A Sample Selection Model with Skew‐normal Distribution

Cited by 19 publications

References 23 publications

Robust Inference in Sample Selection Models

Robust Inference in Sample Selection Models

Predictive performance of penalized beta regression model for continuous bounded outcomes

A robust imputation method for missing responses and covariates in sample selection models

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