Impact of Sampling Variability When Estimating the Explained Common Variance

IF 1 4区 心理学 Q4 PSYCHOLOGY, MATHEMATICAL
Björn Andersson, Hao Luo
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引用次数: 1

Abstract

Assessing multidimensionality of a scale or test is a staple of educational and psychological measurement. One approach to evaluate approximate unidimensionality is to fit a bifactor model where the subfactors are determined by substantive theory and estimate the explained common variance (ECV) of the general factor. The ECV says to what extent the explained variance is dominated by the general factor over the specific factors, and has been used, together with other methods and statistics, to determine if a single factor model is sufficient for analyzing a scale or test (Rodriguez et al., 2016). In addition, the individual item-ECV (I-ECV) has been used to assess approximate unidimensionality of individual items (Carnovale et al., 2021; Stucky et al., 2013). However, the ECVand I-ECVare subject to random estimation error which previous studies have not considered. Not accounting for the error in estimation can lead to conclusions regarding the dimensionality of a scale or item that are inaccurate, especially when an estimate of ECVor I-ECV is compared to a pre-specified cut-off value to evaluate unidimensionality. The objective of the present study is to derive standard errors of the estimators of ECV and I-ECV with linear confirmatory factor analysis (CFA) models to enable the assessment of random estimation error and the computation of confidence intervals for the parameters. We use Monte-Carlo simulation to assess the accuracy of the derived standard errors and evaluate the impact of sampling variability on the estimation of the ECV and I-ECV. In a bifactor model for J items, denote Xj, j 1⁄4 1, ..., J , as the observed variable and let G denote the general factor. We define the S subfactors Fs, s2f1,..., Sg, and Js as the set of indicators for each subfactor. Each observed indicator Xj is then defined by the multiple factor model (McDonald, 2013)
抽样变异性在估计解释的共同方差时的影响
评估量表或测试的多维度是教育和心理测量的主要内容。评估近似单维性的一种方法是拟合由实体理论确定子因子的双因子模型,并估计总因子的解释共同方差(ECV)。ECV表示被解释的方差在多大程度上由一般因素而不是特定因素主导,并与其他方法和统计数据一起使用,以确定单因素模型是否足以分析量表或测试(Rodriguez et al., 2016)。此外,单个项目的ecv (I-ECV)已被用于评估单个项目的近似单维性(Carnovale等人,2021;Stucky et al., 2013)。然而,ecv和i - ecv存在随机估计误差,这是以往研究没有考虑到的。不考虑估计误差可能导致关于量表或项目维度的结论不准确,特别是当将ECVor I-ECV的估计与预先指定的截止值进行比较以评估单维性时。本研究的目的是利用线性验证性因子分析(CFA)模型推导出ECV和I-ECV估计量的标准误差,以便评估随机估计误差和计算参数的置信区间。我们使用蒙特卡罗模拟来评估衍生标准误差的准确性,并评估抽样变异性对ECV和I-ECV估计的影响。在J项的双因子模型中,记为Xj, J 1 / 4 1,…, J为观测变量,设G为一般因子。我们定义S个子因子Fs, s2f1,…, Sg和Js作为每个子因子的指标集。然后用多因素模型定义每个观测到的指标Xj (McDonald, 2013)。
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来源期刊
CiteScore
2.30
自引率
8.30%
发文量
50
期刊介绍: Applied Psychological Measurement publishes empirical research on the application of techniques of psychological measurement to substantive problems in all areas of psychology and related disciplines.
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