A popular method for simultaneously modeling of correlated count response with excess zeros and time to event is by means of the joint models. In these models, the likelihood‐based methods (such as expectation‐maximization algorithm and Newton‐Raphson) are used for estimating the parameters, but in the presence of contaminations, these methods are unstable. To overcome this challenge, we extend the M‐estimator methods and propose a robust estimator approach to obtain a robust estimation of the regression parameters in the joint model. Our proposed algorithm has two steps (Expectation and Solution). In the expectation step, the likelihood function is expected by conditioning on the observed data and in the solution step, the parameters are computed, with solving robust estimating equations. Therefore, this algorithm achieves robustness by applying robust estimating equations and weighted likelihood in the S‐step. Simulation studies under various situations of contaminations show that the robust algorithm gives us consistent estimates with a smaller bias than likelihood‐based methods. The application section uses data on factors affecting fertility and birth spacing.

中文翻译：

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多级零膨胀Poisson和Cox模型联合建模中的稳健推断

通过联合模型可以同时建模具有过量零和事件发生时间的相关计数响应，这是一种流行的方法。在这些模型中，使用了基于似然性的方法（例如期望最大化算法和Newton-Raphson）来估计参数，但是在存在污染的情况下，这些方法是不稳定的。为了克服这一挑战，我们扩展了M估计器方法，并提出了一种鲁棒的估计器方法来获得联合模型中回归参数的鲁棒估计。我们提出的算法有两个步骤（期望和解决方案）。在期望步骤中，似然函数是通过对观测数据进行调节来实现的，而在求解步骤中，通过求解鲁棒的估计方程来计算参数。因此，该算法通过在S步中应用鲁棒的估计方程和加权似然来实现鲁棒性。在各种污染情况下的仿真研究表明，与基于可能性的方法相比，健壮的算法可为我们提供一致的估计，且偏差较小。应用部分使用有关影响生育力和出生间隔的因素的数据。