University of California, UCLA/CRESST, 315 GSEIS Bldg, Los Angeles, 90095-1522, CA, USA.
University of Minnesota, Twin Cities, USA.
Prev Sci. 2023 Apr;24(3):455-466. doi: 10.1007/s11121-021-01253-4. Epub 2021 May 10.
The Tucker-Lewis index (TLI; Tucker & Lewis, 1973), also known as the non-normed fit index (NNFI; Bentler & Bonett, 1980), is one of the numerous incremental fit indices widely used in linear mean and covariance structure modeling, particularly in exploratory factor analysis, tools popular in prevention research. It augments information provided by other indices such as the root-mean-square error of approximation (RMSEA). In this paper, we develop and examine an analogous index for categorical item level data modeled with item response theory (IRT). The proposed Tucker-Lewis index for IRT (TLIRT) is based on Maydeu-Olivares and Joe's (2005) [Formula: see text] family of limited-information overall model fit statistics. The limited-information fit statistics have significantly better Chi-square approximation and power than traditional full-information Pearson or likelihood ratio statistics under realistic situations. Building on the incremental fit assessment principle, the TLIRT compares the fit of model under consideration along a spectrum of worst to best possible model fit scenarios. We examine the performance of the new index using simulated and empirical data. Results from a simulation study suggest that the new index behaves as theoretically expected, and it can offer additional insights about model fit not available from other sources. In addition, a more stringent cutoff value is perhaps needed than Hu and Bentler's (1999) traditional cutoff criterion with continuous variables. In the empirical data analysis, we use a data set from a measurement development project in support of cigarette smoking cessation research to illustrate the usefulness of the TLIRT. We noticed that had we only utilized the RMSEA index, we could have arrived at qualitatively different conclusions about model fit, depending on the choice of test statistics, an issue to which the TLIRT is relatively more immune.
Tucker-Lewis 指数（TLI；Tucker & Lewis，1973），也称为非标准化拟合指数（NNFI；Bentler & Bonett，1980），是众多广泛应用于线性均值和协方差结构模型，特别是探索性因素分析的增量拟合指数之一，这些工具在预防研究中很受欢迎。它增加了其他指数（如近似均方根误差（RMSEA））提供的信息。在本文中，我们为使用项目反应理论（IRT）建模的分类项目水平数据开发并检验了一个类似的指数。所提出的 IRT 的 Tucker-Lewis 指数（TLIRT）基于 Maydeu-Olivares 和 Joe 的（2005）[公式：见文本]有限信息整体模型拟合统计量。在现实情况下，与传统的完全信息 Pearson 或似然比统计量相比，有限信息拟合统计量具有更好的卡方逼近和更强的功效。基于增量拟合评估原则，TLIRT 沿着从最差到最佳可能模型拟合情况的范围比较所考虑模型的拟合情况。我们使用模拟和实证数据来检验新指数的性能。模拟研究的结果表明，新指数的表现符合理论预期，并且它可以提供其他来源无法提供的有关模型拟合的额外见解。此外，与连续变量的 Hu 和 Bentler（1999）传统截止标准相比，可能需要更严格的截止值。在实证数据分析中，我们使用来自测量开发项目的数据来支持戒烟研究，以说明 TLIRT 的有用性。我们注意到，如果我们仅使用 RMSEA 指数，根据测试统计量的选择，我们可能会对模型拟合得出定性不同的结论，而 TLIRT 相对更能避免这个问题。
