Judul: Pengembangan Analisis Jalur Kekar dan Model Campuran Linier Terampat
Abstrak: Path analysis, termed classical path analysis in this study, aimed to discern direct and indirect effects among variables, with some variables serving as causes and others as outcomes or responses. It is a method used to examine integrated relationships among variables and constructed from correlation and regression analyses that presume a normal distribution. Violations of the normality assumption are often due to outliers. Pearson correlation is highly susceptible to outliers/anomalies in data. The Ordinary Least Squares (OLS) method in regression is known to perform poorly in the presence of outliers in the data. One approach to address this violation is to discard outliers and conduct estimation using classical methods on data uncontaminated by outliers. However, removing outliers reduces the amount of data, leading to a loss of information that should have been obtained. Moreover, outliers may contain significant information. Therefore, it is necessary to develop robust path analysis from robust correlation and regression against outliers, which includes analyzing data without removing outliers and comparing the classical path analysis results. In the discussion of the robust path analysis above, the proposed model is one that consists solely of fixed effects. The heterogeneous characteristics of samples often lead surveys to employ multistage random sampling. This sampling method results in hierarchically structured data, which are modeled using mixed linear models. The mixed model or Generalized Linear Mixed Model (GLMM) incorporates predictors containing random effects that is expected to minimize errors in the model. GLMM was initially limited to response following a gaussian or normal distribution (GLMM-N) or Linear Mixed Model (LMM). GLMM has now expanded to accommodate not only normal distributed response but also non-gaussian distributions, such as binomial. GLMM with binomial response, where random effects follow a normal distribution and the link function is logit, are referred to as Binomial GLMM (GLMM-B). Therefore, for hierarchically structured data, it is necessary to develop path analysis derived from GLMM models for both normal and binomial responses. Based on this background, this study objectives to (1) examine the impact of outliers on classical and robust path analysis, (2) develop and apply robust path analysis to real data and compare the results, and (3) develop and apply GLMM path analysis with binomial and normal responses to real data. The data used in this study is the same as that used in previous research by Usman and Lestari (2016) and Lestari et al. (2018b), which this study aims also to refine it. There are two prior studies that are significantly refined by this research or paper. The first study is an analysis of classical path analysis, presented at the ICSPI seminar (Usman and Lestari, 2016). The classical path analysis, which examines the determinants of Indonesian economic growth, does not take into account the presence of outliers. Therefore, further research is needed, namely robust path analysis, which considers the presence of outliers without the need to discard them. The second study is focused on GLMM-B was previously conducted by Lestari et al. (2018b), examining the impact of education and employment status of women of reproductive age (Wanita Usia Subur or
Keyword: Generalized Linear Mixed Model Path Analysis, Outlier, Path Analysis, Robust Correlation Regression, Robust Path Analysis