Structural Equation Mixture Modeling And Their Application In Genetic Association Analysis

Structural equation mixture modeling (SEMM) is a theoretical system which integrates continuous and discretelatent variable models. SEMM as a second-generation structural equation modeling which combines factoranalysis, latent class analysis and the potential profile analysis formed its own unique advantages; it aims toprovide a new idea for the analysis of latent variable and approach. It not only makes up the defect that thestructural equation model can only deal with the continuous latent variable and latent class analysis can onlydeal with the classification of latent variable but also provides new ideas for complex data such as medical,social, psychological researchers. These advantages of the hybrid latent variable precisely in order to adapt tothe emerging complex data in the development of modern medicine and the emergence of new statisticalmethods. Therefore, the introduction of the SEMM has the important practical significance of the medicalresearch.The paper systematically introduces the theory of hybrid latent variable models including therelevant theoretical knowledge of the sub-model and hybrid structural equation modeling,parameter estimation and model evaluation. Model parameter estimation contain maximumlikelihood estimation (ML) and Expected Maximum (EM), EM algorithm is a request to explainthe parameters likelihood estimation iterative algorithm, is a very popular very likelihoodestimation method algorithm, commonly used to deal with the existence of missing data. Theevaluation of the model are the AIC (Akaike information criterion) score ,the BIC (Bayesianinformation criterion) score, CAIC (consistent to the Akaike information criterion) and ofICL-BIC (integrated completed likelihood criterion with BIC).The basis of the theory, confirmatory factor analysis of the mixed model and structural equationmixture modeling are showed. In the example, the data of SNPs were analyzed using mixedlatent variable model. The data is provided by GAW17, it contains 697 individual, 22 autonomictens of thousands of SNP and the SNP simulated 697 individual trait characteristics (threequantitative trait and a qualitative trait). In this study, randomly selected from the four SNPs onchromosome 1 and three quantitative traits were latent class analysis as a research variable, andmixed structural equation modeling analysis. The analysis showed that: According to four SNPSdata, the crowd was divided into three potential categories, each category probability were 0.53,0.34, 0.13. Factors mean Q of latent class 1 and 2 are -4.029 and -2.052 (Factor mean Q of latentclass 3 is set to 0).we known that factor mean of latent class 1, 2 are lower than the latent class 3(P <0.001). The discussion section of this article has done a brief description of the significance and thebuilding and parameter estimation, model evaluation of SEMM are discussed, The discussionsection also describes the advantages and disadvantages of this study.