Validity of factor score predictors in Bayesian and Maximum likelihood confirmatory factor analyses

预期项目的总体目标是为决定系数的大小提供基准，并尽量减少决定系数的偏差，以此作为通过贝叶斯和最大似然验证性因素分析计算的因素分数预测值和单位加权总和的因素有效性的指标。将重点放在因素分数预测值和单位加权总和表上，是因为每当个人被分配到工作或干预工作时，都需要估计个人分数。将在单独的模拟研究中调查三个子目标：第一个子目标是比较根据基于最大似然估计和贝叶斯估计的验证性因素分析计算的决定系数的大小和偏差。比较了极大似然估计中非指定交叉载荷引起的模型误指定的后果和贝叶斯估计中非显著载荷期望变化(先验)指定的后果。除了总体模型和样本量的影响外，分类数据与连续、多变量正态分布数据的影响也将被考察。第二个分目标是指决定系数的大小和偏差对标准效度的影响，因为它们可以从因素得分预测因子中计算出来。将对结构方程模型内的预测指标-标准关系与基于因素得分预测指标的预测指标-标准关系进行直接比较。将确定在潜在建模和因素得分预测值的基础上实现可接受的预测标准关系相似性所需的决定系数的大小。第三个分目标是调查决定系数的大小对基于因素得分预测因子和单位加权和量表估计组间平均差异的影响。为此，在多因素总体模型中会产生潜在的组间平均差异。然后，将在样本中调查基于因子得分预测因子和单位加权和量表的组间差异在多大程度上可以确定它们在人群中出现的那些因素。不仅要正确识别群体间在各个因素上的差异，而且要正确地不出现群体间在因素上的差异，即群体中不会出现群体间的差异。在第二和第三个次级目标的背景下，还将比较不同总体模型、样本大小以及连续变量和分类变量的最大似然估计和贝叶斯估计。

The overarching goal of the intended project is to provide benchmarks for the magnitude for coefficients of determination and to minimize bias for coefficients of determination as indicators of the factorial validity of factor score predictors and unit-weighted sum scales computed from Bayesian and maximum likelihood confirmatory factor analysis. The focus on factor score predictors and unit-weighted sum scales is due to the necessity to estimate individual scores whenever individuals are assigned to jobs or interventions. Three subgoals are to be investigated in separated simulation studies: The first subgoal is the comparison of magnitude and bias of coefficients of determination computed from confirmatory factor analyses based on maximum likelihood estimation and Bayesian estimation. The consequences of model misspecification due to non-specified cross-loadings in maximum likelihood estimation and the consequences of specification of expected variations of non-salient loadings (priors) in Bayesian estimation are compared. Besides the effect of population models and sample size, the effect of categorical data versus continuous, multivariate normal distributed data will also be investigated. The second subgoal refers to the effect of magnitude and bias of coefficients of determination on criterion validities, as they can be computed from factor score predictors. A direct comparison of modelling predictor-criterion relationships within structural equation models with the predictor-criterion relationships based on factor score predictors will be performed. The magnitude of the coefficient of determination necessary to achieve an acceptable similarity of predictor-criterion relationships based on latent modeling and factor score predictors will be ascertained. The third subgoal is the investigation of the effect of the magnitude of determination coefficients on the estimation of between-group mean differences based on factor score predictors and unit-weighted sum scales. For this purpose, latent between-group mean differences will be generated in multifactorial population models. It will then be investigated in the samples to what degree between-group differences based on factor score predictors and unit-weighted sum scales can be identified on those factors on which they occur in the population. Not only the correct identification of between-group differences on the respective factors is in the focus but also the correct non-occurrence of between-group differences on factors, where no between-group differences occur in the population. In the context of the second and third subgoal the maximum likelihood estimation and the Bayesian estimation will also be compared for different population models, sample sizes, as well as for continuous and categorical variables.