The Choice Between Unidimensional And Bifactor Model

The bifactor model has a long history,excellent theoretical advantages and a wide range of applications.Unidimensional model,oblique factor model and high-order factor model can all be considered as special cases of two-factor models.However,unidimensional models are more convenient to use in actual data analysis.Researchers now mainly use two indicators to choose between unidimensional model and bifactor model:the PUC(percentage of uncontaminated correlations)and ECV(explained common variance).When the PUC value is high,the data of bifactor model can be fitted using unidimensional model.If the value of PUC is low,only when the value of ECV is high can the data of bifactor model be fitted using unidimensional model.Through the formula reasoning of PUC,this study found that the value of PUC is affected by the structure of bifactor model and the total number of items.But previous researchers did not consider these two important factors.Secondly,in the previous studies,the criterion was used to estimate the fitting deviation(including the absolute structural coefficient bias and the relative structural coefficient bias).It is proposed that the absolute structural coefficient bias is affected by the correlation of the criterion,while the relative structural coefficient bias is not.However,the researchers did not provide a proof process,nor did they explore whether different criterion would affect the accuracy of model selection.Furthermore,the factor loading situation of the bifactor model used in the Monte Carlo simulation experiment does not conform to the real test situation,so the results obtained have generalized limitations.Finally,this study found out that pervious researchers has used two different indicators as the estimated deviation,one is the structural coefficient bias and the other is the factor loading bias.Using different estimated deviations may affect the accuracy of the model selection.Based on the above reasoning,this study speculates that there are some deviations in the selection and application of PUC,ECV and ?H indicators.Therefore,based on the previous research,this study referred to the real bifactor model test,considering the number of bifactor model items and the complexity of model structure,exploring the choice of bifactor model and unidimensional from a predictive perspective.The number of items in bifactor model is at least 9 and at most 240.The study designed 49 model structures,considering both balanced and unbalanced structure types.Then,based on this model design,the study used three different criterions,and explored whether the relevance of criterion would affect the accuracy of model selection.Thirdly,this study mainly compared whether the factor loading distributions of the bifactor model affects the selection of models for PUC,ECV and?H.Finally,this study verified how PUC,ECV and coH are applied to model selection from the perspective of factor loading bias.Finally,the main results are as follows:1)ECV is more suitable as a model selection index than PUC and ?H.In the case of balanced model structure,when ECV is greater than 0.7,the data of the bifactor model can be fitted using a unidimensional model.In the case of unbalanced model structure,the ECV needs to be greater than 0.75 if the researchers want to use unidimensional model to fit bifactor model data.2)The values of criterion have an influence on the absolute structural coefficient bias but no influence on the relative structural coefficient bias.There is no difference in the judgment range of model selection indicators calculated using different criterion or different structural coefficient bias.3)When the general factor loading is the same and the group factor loading is the same,the estimated deviation of the unidimensional model fitting bifactor model data is smaller.However,the range of model selection indicators in the two cases was not found to be different.4)There is no difference in the judgment range of model selection indicators from predictive perspective or factor loading perspective.