Judul: Mixed effect models for high –dimensional longitudinal data with latent variables
Abstrak: A set of data that consist of repeated measurements on a large number of outcomes and covariates are known as high-dimensional longitudinal data. The high-dimensional longitudinal data may consist of several effects of interest that cannot be directly measured, known as latent factors or latent variables. During the last decade, the multivariate responses or high-dimensional in longitudinal data have been a big issue. The analysis of high-dimensional longitudinal data is complicated due to its complex correlation structures between outcomes. To understand changes over time of outcome variables, having correlations in individuals with explanatory variables is not enough. Hence, complex correlation structures between outcomes need to be considered. One approach that is commonly used to overcome high-dimensional longitudinal data is simultaneous equation modeling. A well-known simultaneous equation modeling method is the structural equation model (SEM). This approach has several appealing modeling abilities and can be used for high-dimensional longitudinal data. Under the SEM framework, the continuous time SEM is developed to avoid some issues associated with autoregressive and cross-lagged problems in SEM. Another simultaneous equation modeling method is by combining factor analysis and multivariate analysis methods to overcome high dimensional longitudinal data, namely latent factor linear mixed model (LFLMM). The factor analysis is used to reduce the high-dimensional outcomes, and the multivariate linear mixed model is used to study the longitudinal trends of several latent factors. One example of high-dimensional longitudinal data is the General Election Study. This study is carried out repeatedly to observe tendencies towards political attitudes and behavior over time in Belgium. The data contain political information, knowledge, perceptions, and preferences of a political party and the level of participation in politics. One of the most interesting things to study from the data is to analyze the change of political attitudes and behavior of respondents over time. Also, the relationship of changes in these outcomes is important to analyze. The General Election Study in Belgium was designed to include a representative sample of the target population under the Belgian electorate, so accurate estimates about the population could be made. This sampling design was created by the Institute for Social and Political Opinion (ISPO) and the Inter-university Center for Political Opinion Research (PIOP). The Belgian data set contained three subsamples, the Flemish (Dutch-speaking), the Walloon (French-speaking), and the Brussels Capital Region (Dutch and French-speaking). Several studies conducted on the Belgium data are carried out to understand the relationships between the latent variables Individualism (I), Ethnocentrism (E), and Authoritarianism (A) in Flanders. Cross-sectional or a longitudinal studies have also been carried out. In such cases, it is critical to capture the trend of the latent variables over time and, more importantly, whether there is any association or relationships between the development of nationalism (N), ethnocentrism (E), individualism (I), and authoritarianism (A) in Belgium. An empirical analysis of CT-SEM has been done to present the interdependencies among the four latent variables mentioned above on the basis of the General Election Studies for Belgium in 1991, 1995, and 1999 (Interuniversitair steunpunt politieke-opinieonderzoek, 1991, 1995, 1999). Although the four variables have been the subject of
Keyword: Belgium, CT-SEM, high-dimensional longitudinal data, LFLMM, Supplemented EM Algorithm