Accounting for Parcel-Allocation Variability in Practice: Combining Sources of Uncertainty and Choosing the Number of Allocations

Item parceling remains widely used under conditions that can lead to parcel-allocation variability in results. Hence, researchers may be interested in quantifying and accounting for parcel-allocation variability within sample. To do so in practice, three key issues need to be addressed. First, how can we combine sources of uncertainty arising from sampling variability and parcel-allocation variability when drawing inferences about parameters in structural equation models? Second, on what basis can we choose the number of repeated item-to-parcel allocations within sample? Third, how can we diagnose and report proportions of total variability per estimate arising due to parcel-allocation variability versus sampling variability? This article addresses these three methodological issues. Developments are illustrated using simulated and empirical examples, and software for implementing them is provided.     

项目组合在结构方程模型中的应用

项目组合（itemparceling）是对同一量表中的若干项目进行整合并形成新的观测指标的过程。虽然一直以来它都是一个有争议的议题,但随着其在结构方程模型中的应用日益广泛,它越来越受到研究者重视。文章从项目组合的基本逻辑、优缺点以及具体方法等方面对项目组合的研究进行了概括,并在此基础上提出了使用的具体建议：（1）根据研究的目的与具体情境选择是否需要组合;（2）组合之前必须首先确定概念的维度性;（3）项目组合最好建立在一定的理论基础上等等。未来的研究可以深入探讨各种组合方法对模型拟合以及参数估计的影响以及项目组合在一些SEM高阶应用中的效果,并进一步与项目反应理论等测量理论相结合     

结构方程建模中的题目打包策略

结构方程建模中题目打包法的优缺点包括：指标数据质量变好、模型拟合程度提高; 估计偏差不大, 可校正; 估计稳定, 但降低了敏感性与可证伪性。打包法的前提条件是单维、同质, 适合结构模型分析, 不适合测量模型分析。对于单维测验, 给出了一个打包流程。对于通常的多个子量表(多维结构)测验, 推荐在子量表内打包, 每个子量表打包成1个指标或者3个指标, 用于结构方程建模。     

Problems with Rationales for Parceling that Fail to Consider Parcel-Allocation Variability

In structural equation modeling applications, parcels—averages or sums of subsets of item scores—are often used as indicators of latent constructs. Parcel-allocation variability (PAV) is variability in results that arises within sample across alternative item-to-parcel allocations. PAV can manifest in all results of a parcel-level model (e.g., model fit, parameter estimates, standard errors, and inferential decisions). It is a source of uncertainty in parcel-level model results that can be investigated, reported, and accounted for. Failing to do so raises representativeness and replicability concerns. However, in recent methodological literature (Cole, Perkins, &; Zelkowitz, 2016 Cole, D. A., Perkins, C. E., &; Zelkowitz, R. L. (2016). Impact of homogeneous and heterogeneous parceling strategies when latent variables represent multidimensional constructs. Psychological Methods, 21(2), 164–174. doi: 10.1037/met0000047[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]; Little, Rhemtulla, Gibson, &; Shoemann, 2013 Little, T. D., Rhemtulla, M., Gibson, K., &; Schoemann, A. M. (2013). Why the items versus parcels controversy needn't be one. Psychological Methods, 18(3), 285–300. doi: 10.1037/a0033266[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]; Marsh, Ludtke, Nagengast, Morin, &; von Davier, 2013 Marsh, H. W., Lüdtke, O., Nagengast, B., Morin, A., &; von Davier, M. (2013). Why item parcels are (almost) never appropriate: Two wrongs do not make a right—camouflaging misspecification with item parcels in CFA models. Psychological Methods, 18(3), 257–284. doi: 10.1037/a0032773[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]; Rhemtulla, 2016 Rhemtulla, M. (2016). Population performance of SEM parceling strategies under measurement and structural model misspecification. Psychological Methods, 21(3), 348–368. doi: 10.1037/met0000072[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) parceling has been justified and recommended in several situations without quantifying or accounting for PAV. In this article, we explain and demonstrate problems with these rationales. Overall, we find that: (1) using a purposive parceling algorithm for a multidimensional construct does not avoid PAV; (2) passing a test of unidimensionality of the item-level model need not avoid PAV; and (3) a desire to improve power for detecting structural misspecification does not warrant parceling without addressing PAV; we show how to simultaneously avoid PAV and obtain even higher power by comparing item-level models differing in structural constraints. Implications for practice are discussed.