Grouped and right-censored (GRC) counts are widely used in criminology, demography, epidemiology, marketing, sociology, psychology and other related disciplines to study behavioural and event frequencies, especially when sensitive research topics or individuals with possibly lower cognitive capacities are at stake. Yet, the co-existence of grouping and right-censoring poses major difficulties in regression analysis. To implement generalised linear regression of GRC counts, we derive modified Poisson estimators and their asymptotic properties, develop a hybrid line search algorithm for parameter inference, demonstrate the finite-sample performance of these estimators via simulation, and evaluate its empirical applicability based on survey data of drug use in America. This method has a clear methodological advantage over the ordered logistic model for analysing GRC counts.

中文翻译：

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分组和右删失计数的修正泊松回归分析

分组和右删失 (GRC) 计数广泛用于犯罪学、人口学、流行病学、市场营销、社会学、心理学和其他相关学科，以研究行为和事件频率，尤其是当敏感的研究主题或认知能力可能较低的个人处于危险之中时. 然而，分组和右删失的共存给回归分析带来了重大困难。为了实现 GRC 计数的广义线性回归，我们推导出修正的泊松估计量及其渐近特性，开发了一种用于参数推断的混合线搜索算法，通过模拟证明这些估计量的有限样本性能，并根据调查数据评估其经验适用性在美国吸毒。