Robust Inference in Sample Selection Models

Zhelonkin, Mikhail; Genton, Marc G.; Ronchetti, Elvezio

doi:10.1111/rssb.12136

Cited by 30 publications

(38 citation statements)

References 54 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This paper discusses a copula‐based selection model, which can help make more plausible assumptions about the distribution of the data and proposes a flexible imputation procedure that generates plausible imputed values from the copula selection model. Our paper expands on recent work on developing selection models that can accommodate departures from bivariate normality, by advocating a flexible approach for addressing MNAR in a wide range of nonnormal (continuous) outcomes (as well as discrete and count endpoints). The paper directly extends previous applications of the copula approach to address MNAR in settings with binary outcomes (see the work of Marra et al) and continuous outcomes assuming a particular copula function such as the Gaussian or Archimedean copulae .…”

Section: Discussionmentioning

confidence: 98%

“…Recent studies have considered various generalizations to address possible deviations from normality. For example, the Heckman selection model has been extended to accommodate outcomes with heavier tails by considering a bivariate t ‐distribution, whereas Zhelonkin and others introduced a procedure for robustifying the Heckman's two‐step estimator by using M‐estimators of Mallows' type for both steps. However, most of these approaches are restricted to a specific joint distribution for the selection and outcome processes, and extension to other non‐Gaussian outcomes may not be straightforward.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Copula selection models for non‐Gaussian outcomes that are missing not at random

Gomes

Radice

Brenes

et al. 2018

Statistics in Medicine

View full text Add to dashboard Cite

Missing not at random (MNAR) data pose key challenges for statistical inference because the substantive model of interest is typically not identifiable without imposing further (eg, distributional) assumptions. Selection models have been routinely used for handling MNAR by jointly modeling the outcome and selection variables and typically assuming that these follow a bivariate normal distribution. Recent studies have advocated parametric selection approaches, for example, estimated by multiple imputation and maximum likelihood, that are more robust to departures from the normality assumption compared with those assuming that nonresponse and outcome are jointly normally distributed.However, the proposed methods have been mostly restricted to a specific joint distribution (eg, bivariate t-distribution). This paper discusses a flexible copula-based selection approach (which accommodates a wide range of non-Gaussian outcome distributions and offers great flexibility in the choice of functional form specifications for both the outcome and selection equations) and proposes a flexible imputation procedure that generates plausible imputed values from the copula selection model. A simulation study characterizes the relative performance of the copula model compared with the most commonly used selection models for estimating average treatment effects with MNAR data.We illustrate the methods in the REFLUX study, which evaluates the effect of laparoscopic surgery on long-term quality of life in patients with reflux disease.We provide software code for implementing the proposed copula framework using the R package GJRM. In such cases, the data are said to be missing not at random (MNAR), and nonresponse must be modeled together with the substantive model for the observed data.Selection models have been commonly used to handle MNAR data in clinical and epidemiological research, 4-6 by jointly modeling the outcome and missingness models and typically assuming bivariate normality. Heckman 7 was one of the first to propose such model (Heckman selection model) using a simultaneous equation approach, where the error terms were assumed to follow a bivariate Gaussian. At that time, to circumvent some of the difficulties associated with direct likelihood maximization, Heckman proposed a two-stage least-squares estimation procedure. 8 This involved combining a probit model for the probability of observing the outcome (first stage) with a linear regression model for the outcome (second stage), which was a function of the estimates obtained in the first stage. Although this approach (method of moments estimator) is somehow robust to deviations from normality, it relies crucially on the availability of exclusion restrictions, ie, variables that predict missingness but are unrelated to the outcome of interest. 9 An alternative approach to estimating selection models is the single-step full-information maximum likelihood (FIML), which jointly estimates the outcome and missing data equations. For example, Diggle and Kenward 10 combined a marg...

show abstract

Section: Discussionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Copula selection models for non‐Gaussian outcomes that are missing not at random

Gomes

Radice

Brenes

et al. 2018

Statistics in Medicine

View full text Add to dashboard Cite

show abstract

“…Frequentist counterparts of these Bayesian methods are given in Marra and Radice (2013b) in the context of binary responses and Marra and Radice (2013a) for continuous Gaussian outcomes. Zhelonkin et al (2016) introduced a procedure for robustifying the Heckman's two stage estimator by using M-estimators of Mallows' type for both stages. Marchenko and Genton (2012) and Ding (2014) considered a bivariate Student-t distribution for the model's errors as a way of tackling heavy-tailed data.…”

Section: Introductionmentioning

confidence: 99%

Copula based generalized additive models for location, scale and shape with non-random sample selection

Wojtyś

Marra

Radice

2018

Computational Statistics & Data Analysis

View full text Add to dashboard Cite

Citation: Wojtys, M., Marra, G. and Radice, R. ORCID: 0000-0002- 6316-3961 (2018).Copula based generalized additive models for location, scale and shape with non-random sample selection. AbstractNon-random sample selection is a commonplace amongst many empirical studies and it appears when an output variable of interest is available only for a restricted non-random sub-sample of data. An extension of the generalized additive models for location, scale and shape which accounts for non-random sample selection by introducing a selection equation is discussed. The proposed approach allows for potentially any parametric distribution for the outcome variable, any parametric link function for the selection equation, several dependence structures between the (outcome and selection) equations through the use of copulae, and various types of covariate effects. Using a special case of the proposed model, it is shown how the score equations are corrected for the bias deriving from non-random sample selection. Parameter estimation is carried out within a penalized likelihood based framework. The empirical effectiveness of the approach is demonstrated through a simulation study and a case study. The models can be easily employed via the gjrm() function in the R package GJRM.

show abstract

“…2 Regarding other software for selection models, the R package ssmrob estimates sample selection models for which the assumption of bivariate normality is relaxed (Zhelonkin et al, 2013). The Stata package heckt estimates a Heckman-style model with a bivariate t distribution.…”

mentioning

confidence: 99%

The Effect of Hearing Impairments on Wage Earnings: Evidence from a Copula‐Based Spline Selection Model

Zimmer

2019

Labour

View full text Add to dashboard Cite

This paper investigates the effect of hearing impairments on annual wage earnings. A standard Heckman‐style selection model suggests that hearing impairments reduce earnings by approximately 14 per cent, with no evidence of selection bias. The paper then relaxes the assumption of bivariate normality using a copula specification, and the paper allows for potentially nonlinear links between nonbinary covariates and earnings using smooth spline functions. By incorporating those two deviations, not only does the model appear to provide a better fit to the data, but hearing impairments appear to reduce earnings by 19 per cent, an effect 36 per cent larger than what is suggested by the standard selection setup. The model also uncovers evidence of statistically significant selection bias.

show abstract

Robust Inference in Sample Selection Models

Cited by 30 publications

References 54 publications

Copula selection models for non‐Gaussian outcomes that are missing not at random

Copula selection models for non‐Gaussian outcomes that are missing not at random

Copula based generalized additive models for location, scale and shape with non-random sample selection

The Effect of Hearing Impairments on Wage Earnings: Evidence from a Copula‐Based Spline Selection Model

Contact Info

Product

Resources

About