| In recent years,with the development of statistical analysis methods,more and more researchers in psychology,sociology and other fields have conducted longitudinal data studies to infer reciprocal relations between variables.The Cross-lagged Panel Model(CLPM)is widely used by researchers to solve this kind of problems.Considering the limitations of the CLPM,statisticians have extended this model,and the longitudinal model has gradually become more and more complex,i.e.,the autoregressive latent growth model(ALT),the random intercept cross-lagged model(RI-CLPM)and other models can discuss the causal or reciprocal relations in more detail.Complex models can sometimes produce better fitting results than the simple models do,but they can also cause some potential estimation problems.In the situation that unknown longitudinal data structure or theoretical basis is unknown,empirical researchers are confused about how to choose longitudinal models with different levels of complexity to better estimate reciprocal effects.In addition,the latent variable modeling has become another way for empirical researchers to try to analyze longitudinal data,such as the factor cross-lagged panel model(Factor-CLPM),the trait-state-error model(TSE),and latent variable-autoregressive latent growth model(LV-ALT).Is it worthwhile for researchers to sacrifice the simplicity of models and apply the single-indicator latent-variable longitudinal models to examine reciprocal relations instead of the explicit-variable models? Even though previous studies have involved the multiple-indicator longitudinal models,few researchers have further compared differences in the model fit between the multiple-indicator models.The performance in parameter estimation of multiple-indicator models with different levels of complexity still needs to be further explored.From the perspective of the level of complexity of the model,this paper mainly discusses the accuracy and stability of parameter estimates of reciprocal relations for longitudinal models with explicit and latent variables,and provides suggestions for empirical researchers on how to choose longitudinal models when the theoretical premise or the data structure is unknown.The research problems above are discussed based on the three sub-studies,among which the Study 1 and 2 are simulation studies,and Study 3 is an empirical study.In Study1,the performance of parameter estimates of explicit variable,single-indicator and latent variable longitudinal models with different complexity levels was investigated under different conditions(including sample size,measurement waves and cross-lagged relations),and the performance of parameter estimates of these models was compared.Study 2 explores the performance of parameter estimates of multiple-indicator latent-variable longitudinal models under different conditions(including sample size,measurement waves,cross-lagged relations and factor loading).Study 1 and 2 compared the estimated performance of the models by Root Mean Square Error(RMSE),Relative Bias,95% coverage and statistical power.Study 3 aims to compare the performance of explicit variable and latent variable-longitudinal models in model fitting and parameter estimation based on empirical data which is the Longitudinal Study of American Youth(LSAY).The results of Study 1 show that the CLPM and single-indicator Factor-CLPM always show large estimated bias in autoregressive parameters when fitting to relatively complex data,i.e.,the datasets containing the intercept terms.In most conditions,the estimated bias of RI-CLPM in autoregressive parameters is smaller than that of CLPM and ALT models.The estimated bias of single-indicator TSE in autoregressive parameters is smaller than that of single-indicator CLPM and ALT.The increase of measurement waves and sample size improve the accuracy of parameter estimation.The cross-lagged relation has almost no effect on the estimated performance,and the estimated performance of latent-variable models is close to that of the explicit-variable models.In Study 2,we find that when fitting to the relatively complex datasets,the multiple-indicator Factor-CLPM always has a large estimated bias in autoregressive parameters.Compared with the multiple-indicator Factor-CLPM,multiple-indicator TSE has a relatively good performance in various evaluation indicators.The multiple-indicator LV-ALT shows large bias and instability of parameter estimation.The number of measurement waves,sample size,and cross-lagged relations show the similar influence on the estimated performance of each longitudinal models with Study1.The results of Study 3 show that the estimated values of autoregressive and cross-lagged parameters decrease when the intercept term is added to the model;when the slope term is added to the model,the estimated values of the parameters continue to decrease.The single-indicator latent-variable longitudinal models tend to model non-convergence easily.Based on the above results,this paper mainly draws the following conclusions:(1)It is not true that the more complex or reduced model is,it can better estimate the reciprocal effect.If the model with the growth factor is not very different from the model without the growth factor,then the reduced model without the growth factor will be preferred.When researchers are not clear about the structural characteristics of the data set or the theoretical premise is unknown,RI-CLPM and TSE may be a more conservative choice to investigate the reciprocal relationship between variables.(2)Compared with the explicit-variable longitudinal models,the single-indicator latent-variable models are prone to cause model non-convergence and problems of parameter estimation during the process of model fitting,so manifest-variable models are recommended.(3)At the level of latent variables,the TSE model showes a more stable performance in estimating reciprocal relations.When the single-indicator TSE model does not converge,the multiple-indicator TSE model can be used as an alternative model. |
