Generalized Latent Variable Models With Non-linear Effects

In the study of latent variable models,such as factor analysis model and latent trait model,only the relationship between observed variables and the linear combination of latent variables is considered in the model.However,the non-linear latent terms also affects the observed variables.The generalized latent variable model with non-linear effect has been studied.The hybrid integration-maximization algorithm is proposed to calculate the full information maximum likelihood(FIML)estimation of parameters,the standard error of parameters is calculated by sandwich estimation and bootstrap,and a method for obtaining factor scores based on multiple imputation is proposed for the non-linear model.Based on above methods,the latent trait model with non-linear term is explored in this paper.This paper simulates a two-factor latent trait model with non-linear terms.The parameter estimation is calculated by the hybrid integration-maximization algorithm,and exploring the improvement of computational efficiency of the hybrid integration-maximization algorithm compared to the BFGS algorithm.The model is simulated in four different situations,and the influence of the number of observed variables and the sample size on the parameter estimation effect is studied.The deviation and root mean square error are used to evaluate the parameter estimation.Taking the questionnaire on the physical health of the Chinese Nutrition Health Survey database in 2001 as an example,different latent variable models were established for the data,and the model evaluation indicators were used to select the models.The model evaluation indicators mainly include: AIC,BIC,log likelihood function value,likelihood ratio test and chi-square residual value of two-dimensional marginal distribution.The indicators support a constrained two-factor latent trait model with non-linear effects.The parameter estimation is calculated by the hybrid integration-maximization algorithm,the sandwich estimation method and the bootstrap method are used to calculate the standard error of the parameter estimation value.Factor scores were calculated using multiple imputation methods,and the relationship between factor loading and observed variables and factor scores and conditional density of observed variables were analyzed.The two factors were interpreted as: stage disease factor and long-term health factor.The value of the two factors can reflect the physical health of the respondents in a concise manner and reduce the data dimension.