A comparison of using weighted distribution and joint modeling for analyzing non-ignorable missing responses

ABSTRACT

In this study, we reconsider weighted distribution from the perspective of missing mechanism since weighted distribution instead of being the distribution of the whole population of interest is only the distribution of respondents (sub-population). After defining some weighted distributions by different mechanisms for indicator of response, we show, by some simulation studies, that using weighted distributions may lead to biased estimates of parameters under the non-ignorable missing mechanism. On the other hand, joint modeling of the response and selection mechanism could result in more efficient and valid estimates of parameters. The lower root of mean squared errors of estimates from the joint modeling approach than those of the weighted distribution is a warranty to the statement that the joint modeling method is more efficient than weighted distribution; this is proved by diverse simulation studies along the article. However, these two methods of the weighted approach and joint modeling give similar results if the selection mechanism is at random. Finally, the methods are applied and compared in the analysis of one well-used real dataset.

KEYWORDS:

• Joint modeling
• Length-biased
• Missing mechanism
• Missingness
• Weighted distribution

MATHEMATICS SUBJECT CLASSIFICATION:

• 62P10
• 62F99

Notes

1 ${\Psi }_0\left(z\right)=\frac{{\Gamma }^{\text{'}}\left(z\right)}{\Gamma \left(z\right)}$

2 $H\left(n\right)={\sum }_{k=1}^n\frac{1}{k}$