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

Abstract

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.

Civic engagement in the Indonesia health sector

“…The data collection involves an on-line purposive sampling survey, that asked about the experience and perception of respondents with engagement in the health sector. Purposive online samples enhance the probability samples through participant observation of online discussion to access hidden population (Barratt et al, 2015), which is also called as non-random sample selection (Wojtys et al, 2018) The survey sent an invitation to the groups of young people in five cities in Indonesia: Medan, Jakarta, Bandung, Semarang, and Surabaya. We found the groups in social media that expose their community engagement in the health sector.…”

Mixed binary‐continuous copula regression models with application to adverse birth outcomes

“…The formulas used to compute the basis functions and penalties for many spline definitions are provided in the works of Ruppert et al and Wood . For their theoretical properties, see, for instance, the works of Wojtyś and Marra and Yoshida and Naito . As a simple approximate version, Eilers and Marx suggest using , where D j is a first‐ or second‐order difference matrix.…”

“…However, for our case study, we do not deem this necessary as argued in the previous section. Proving consistency of the proposed estimator is beyond the scope of this paper, but the results presented, for instance, in Wojtyś and Marra can be easily adapted to the current context.…”

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

“…Instead, this paper follows an alternative strand of literature, started by Lee (), generalized by Prieger (), Smith (), and Wojtys et al . (), and recently summarized by Pigini () that remains parametric in its focus, but uses copula functions to relax the distributional assumptions in . The copula‐based approach is attractive because it is close in spirit to the classic Heckman setup.…”

“…This paper follows methods proposed by Lee (), generalized by Prieger (), Smith (), and Wojtys et al . (), and recently summarized by Pigini (), in replacing the bivariate normal distribution with a copula function that better fits the data. In addition, the model also uses a spline approach to accommodate nonlinear relationships between covariates and earnings (Marra and Radice, ).…”