In many applications of two-component mixture models such as the popular zero-inflated model for discrete-valued data, it is customary for the data analyst to evaluate the inherent heterogeneity in view of observed data. To this end, the score test, acclaimed for its simplicity, is routinely performed. It has long been recognised that this test may behave erratically under model misspecification, but the implications of this behaviour remain poorly understood for popular two-component mixture models. For the special case of zero-inflated count models, we use data simulations and theoretical arguments to evaluate this behaviour and discuss its implications in settings where the working model is restrictive with regard to the true data-generating mechanism. We enrich this discussion with an analysis of count data in HIV research, where a one-component model is shown to fit the data reasonably well despite apparent extra zeros. These results suggest that a rejection of homogeneity does not imply that the underlying mixture model is appropriate. Rather, such a rejection simply implies that the mixture model should be carefully interpreted in the light of potential model misspecifications, and further evaluated against other competing models.

中文翻译：

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从模型错误指定的角度测试零膨胀模型的同质性

在二元混合模型的许多应用中，例如流行的离散值数据零膨胀模型，数据分析师通常根据观察到的数据来评估固有的异质性。为此，例行进行因其简单性而广受赞誉的分数测试。人们早就认识到，该测试在模型指定错误的情况下可能表现不稳定，但对于流行的二组分混合模型，这种行为的影响仍然知之甚少。对于零膨胀计数模型的特殊情况，我们使用数据模拟和理论论证来评估这种行为，并讨论其在工作模型对真实数据生成机制受到限制的情况下的影响。我们通过对艾滋病毒研究中计数数据的分析来丰富这一讨论，其中显示单成分模型尽管有明显的额外零，但仍能很好地拟合数据。这些结果表明，拒绝同质性并不意味着底层的混合模型是合适的。相反，这种拒绝仅仅意味着应该根据潜在的模型错误指定仔细解释混合模型，并根据其他竞争模型进一步评估。