Simulated Data Comparison Of The Predictive Validity Between Bi-factor And High-Order Factor Models

Bi-factor and high order factor models are two competitive models,both of them have general factors and specific factors,have been widely applied in psychology,education,management and in other fields.Most of the existing studies believe that the bi-factor model is superior to the high-order factor model,such as that the bi-factor model can be used to study the role of domain specific factors that are independent of the general factor,detect the non-significance factors;and it can also explore the predictive relationships between specific factors and external criteria,over and above the general factor.However,the bi-factor model also has its shortcomings: the model is more complex,with more parameters needed to estimate,and sometimes needed to provide the initial value to convergence when there are small sample.For the possible bias caused by this deficiency,existing studies mostly compares this two models from the perspective of model fit.Most of these studies are based on measured data or simulated studies based on measured data,with only a few of the simulation study,lack of systematic,and these results are inconsistent.So,it is difficult to draw a consistent conclusion which one of this two models is the best one.The purpose of psychology research is not just to describe and explain,more importantly is to predict and to control.In addition to the model fitting index,predictive validity is also an important aspect of model structure validity.In order to make up for the lack of results' consistency for the two models' comparison studies,based on the comparison of model fit between bi-factor and high-order factor models,this paper focuses on the discrepancy between two models' predictive accuracy by using Monte Carlo simulation method,and three experimental studies were made.Under large sample condition(N=1000),study one compared two models' difference on model fit indices in different level of factor loadings(0.4,0.5,0.6,0.7),and then compared their difference in predictive accuracy when criterion was exogenous variable;To make the conclusions more universal,study two focused on the comparison of two models' difference in predictive accuracy under the same experimental conditions when criterion was endogenous variable.In order to test the effect of sample size on the research results,Study 3 inspected two models' performance in predictive validity when sample sizes were 200 and 500,and the criterion variables were exogenous and endogenous variables,respectively.The results showed that:(1)There is no significant difference between the two models in fitness when the sample size is 1000.However,when the criterion was exogenous variable,the structural coefficients of the two models are estimated as unbiased.When the criterion was endogenous variable,the performance of high-order factor model is superior than Bi-factor model,The structural coefficients of high-order factor model is unbiased estimates,meanwhile,the bias of the structural coefficients of Bi-factor model happened in half cases.(2)When sample size were 200 and 500,the predictive validity of high-order factor model is generally better than that of Bi-factor model.(3)As the sample size increases,the structural coefficient bias of two models becomes smaller.(4)When the criterion variable is exogenous variable,the structural coefficient bias of the two models is lower than that as the criterion variable is endogenous variable.