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，并最大限度地减少决定系数的偏差，作为因子得分预测因子的因子效度指标和从贝叶斯和最大似然验证因子分析计算的单位加权和量表。对因素得分预测因子和单位加权和量表的关注是由于每当个人被分配到工作或干预措施时，估计个人得分的必要性。在分离的模拟研究中，将研究三个子目标：第一个子目标是基于最大似然估计和贝叶斯估计的验证性因子分析计算的决定系数的大小和偏差的比较。比较了最大似然估计中由于未指定交叉负荷而导致的模型不规范的后果和贝叶斯估计中指定非显著负荷（先验）的预期变化的后果。除了总体模型和样本量的影响外，分类数据与连续、多元正态分布数据的影响也将被研究。第二个子目标是指决定系数的大小和偏差对标准效度的影响，因为它们可以从因子得分预测因子中计算出来。将对结构方程模型中的预测-标准关系与基于因子得分预测因子的预测-标准关系进行直接比较。将确定基于潜在建模和因子评分预测因子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。第三个子目标是研究决定系数的大小对基于因子评分预测因子和单位加权和量表的组间平均差异估计的影响。为此，在多因子种群模型中会产生潜在的组间均值差异。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尺度的组间差异在多大程度上可以确定这些因素在人群中发生的差异。重点不仅在于正确识别各自因素上的组间差异，还在于正确不存在组间差异，即在人群中不存在组间差异。在第二和第三个子目标的背景下，最大似然估计和贝叶斯估计也将对不同的人口模型、样本量以及连续变量和分类变量进行比较。

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.