预测视角下双因子模型与高阶因子模型的一般性模拟比较

A general simulation comparison of the predictive validity between bifactor and high-order factor models

高阶因子模型本质上是一种特殊的双因子模型,应用中却常被当做双因子模型的竞争模型。已有研究以满足比例约束的双因子模型(此时等价于一个高阶因子模型)为真实测量模型产生模拟数据,比较了用双因子模型和高阶因子模型作为测量模型的预测效果。本文使用不满足比例约束的双因子模型(此时不与任何高阶因子模型等价)为真实测量模型产生模拟数据进行比较,所得结果与满足比例约束的双因子模型的结果有很大差别,双因子模型结构系数的相对偏差较小、检验力较高,但第Ⅰ类错误率略高。结论是,在比例约束条件成立时可以使用高阶因子模型,否则,从统计角度看,一般情况下使用双因子模型进行预测比较好。

Mathematically,a high-order factor model is nested within a bifactor model,and the two models are equivalent with a set of proportionality constraints of loadings.In applied studies,they are two alternative models.Using a true model with the proportional constraints to create simulation data(thus both the bifactor model and high-order factor model fitted the true model),Xu,Yu and Li(2017)studied structural coefficients based on bifactor models and high-order factor models by comparing the goodness of fit indexes and the relative bias of the structural coefficient in a simulation study.However,a bifactor model usually doesn’t satisfy the proportionality constraints,and it is very difficult to find a multidimensional construct that is well fitted by a bifactor model with the proportionality constraints.Hence their simulation results couldn’t extend to general situations.Using a true model with the proportionality constraints(thus both the bifactor model and high-order factor model fitted the true model)and a true model without the proportionality constraints(thus the bifactor model fitted the true model,whereas the high-order factor model fitted a misspecified model),this Monte Carlo study investigated structural coefficients based on bifactor models and high-order factor models for either a latent or manifest variable as the criterion.Experiment factors considered in the simulation design were:(a)the loadings on the general factor,(b)the loadings on the domain specific factors,(c)the magnitude of the structural coefficient,(d)sample size.When the true model without proportionality constraints,only factors(a),(c)and(d)were considered because the loadings on domain specific factors were fixed to different levels(0.4,0.5,0.6,0.7)that assured the model does not satisfy the proportionality constraints.The main findings were as follows.(1)When the proportionality constraints were held,the high-order factor model was preferred,because it had smaller relative bias of the structural coefficient,and lower typeⅠerror rates(but also lower statistical power,which was not a problem for a large sample).(2)When the proportionality constraints were not held,however,the bifactor model was better,because it had smaller relative bias of the structural coefficient,and higher statistical power(but also higher typeⅠerror rates,which was not a problem for a large sample).(3)Bi-factor models fitted the simulation data better than high-order factor models in terms of fit indexes CFI,TLI,RMSEA,and SRMR whether the proportionality constraints were held or not.However,the bifactor models were less fitted according to information indexes(i.e.,AIC,ABIC)when the proportionality constraints were held.(4)Whether the criterion was a manifest variable or a latent variable,the results were similar.However,for the manifest criterion variable,the relative bias of the structural coefficient was smaller.In conclusion,a high-order factor model could be the first choice to predict a criterion under the condition of proportionality constraints or well fitted for the sake of parsimony.Otherwise,a bifactor model is better for studying structural coefficients.The sample size should be large enough(e.g.,500+)no matter which model is employed.