带有工具变量的MIMIC建模：一种2SLS- MIMIC方法
MIMIC modelling with instrumental variables: A 2SLS-MIMIC approach
摘要：
多指标多原因（MIMIC）模型是一种结构方程模型，它是一种基于理论的方法，用来确定一组外生因果变量对潜变量的影响，以及潜变量对观测指标变量的影响。在一个常见的MIMIC模型中，多个指标反映潜在的潜在变量/因素，多个原因（观察到的预测因素）影响潜在变量/因素。如果一个变量既是指标又是原因，即存在反向因果关系，则MIMIC的基本假设显然被违反。此外，该模型是无法识别的。为了解决这种经常出现的情况，并且由于MIMIC估计缺乏参数的封闭形式解，我们利用Bollen（1996）的结构方程模型的2SLS估计量，结合Jöreskog（1970）的协方差结构分析方法，导出MIMIC模型的新的2SLS估计量。我们的2SLS经验估计是基于静态MIMIC规范，但我们也指出动态/误差校正MIMIC规范和2SLS解决方案，我们推导了基本的渐近理论，静态2SLS-MIMIC，提出了一个模拟研究，并应用研究结果估计老年工人的不稳定状态的一个有趣的经验案例（使用欧洲健康、老龄化和退休调查的数据集），解决了将不稳定工作定义为一个多层面概念的重要问题，迄今尚未充分建模。
英文摘要：
Multiple Indicators Multiple Causes (MIMIC) models are type of structural equation models, a theory-based approach to confirm the influence of a set of exogenous causal variables on the latent variable, and also the effect of the latent variable on observed indicator variables. In a common MIMIC model, multiple indicators reflect the underlying latent variables/factors, and the multiple causes (observed predictors) affect latent variables/factors. Basic assumptions of MIMIC are clearly violated in case of a variable being both an indicator and a cause, i.e. in the presence of reverse causality. Furthermore, the model is then unidentified. To resolve the situation, which can arise frequently, and as MIMIC estimation lacks closed form solutions for parameters we utilize a version of Bollen's (1996) 2SLS estimator for structural equation models combined with Jöreskog (1970)'s method of the analysis of covariance structures to derive a new, 2SLS estimator for MIMIC models. Our 2SLS empirical estimation is based on static MIMIC specification but we point also to dynamic/error-correction MIMIC specification and 2SLS solution for it. We derive basic asymptotic theory for static 2SLS-MIMIC, present a simulation study and apply findings to an interesting empirical case of estimating precarious status of older workers (using dataset of Survey of Health, Ageing and Retirement in Europe) which solves an important issue of the definition of precarious work as a multidimensional concept, not modelled adequately so far.
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