Research in education often involves a latent variable. Statistical analysis technique that has the ability to analyze the pattern of relationship among latent variables as well as between latent variables and their indicators is Structural Equation Modeling (SEM). SEM partial least square (PLS) was developed as an alternative if these conditions are met: the theory that underlying the design of the model is weak, does not assume a certain scale measurement, the sample size should not be large and the data does not have the multivariate normal distribution. The purpose of this paper is to compare the results of modeling of the educational quality in high school level (SMA/MA) in Sumenep Regency with structural equation modeling approach partial least square with three schemes estimation of score factors.This paper is a result of explanatory research using secondary data from Sumenep Education Department and Badan Pusat Statistik (BPS) Sumenep which was data of Sumenep in the Figures and the District of Sumenep in the Figures for the year 2015. The unit of observation in this study were districts in Sumenep that consists of 18 districts on the mainland and 9 districts in the islands. There were two endogenous variables and one exogenous variable. Endogenous variables are the quality of education level of SMA/MA (Y1) and school infrastructure (Y2), whereas exogenous variable is socioeconomic condition (X1). In this study, There is one improved model which represented by model from path scheme because this model is a consistent , all of its indicators are valid and its the value of Rsquare increased which is: Y 1 =0.651Y 2. In this model, the quality of education influenced only by the school infrastructure (0.651). The socioeconomic condition did not affect neither the school infrastructure nor the quality of education. If the school infrastructure increased 1 point, then the quality of education increased 0.651 point. The quality of education had an R 2 of 0.418, which indicates that 41.8 percent of variance in the quality of education is explained by the school infrastructure, the remaining 58.2% is explained by the other factors which were not investigated in this work.

The application of a structural equation modeling (SEM) assumes that all data follow only one model. This assumption may be inaccurate in certain cases because individuals tend to differ in their responses, and failure to consider heterogeneity may threaten the validity of the SEM results. This study focuses on unobservable heterogeneity, where the difference between two or more data sets does not depend on observable characteristics. In this study, we propose a new method for estimating SEM parameters containing unobserved heterogeneity within the data and assume that the heterogeneity arises from the outer model and inner model. The method combines partial least squares (PLS) and modified fuzzy clustering. Initially, each observation was randomly assigned weights in each selected segment. These weights continued to be iteratively updated using a specific objective function. The sum of the weighted residual squares resulting from the outer and inner models of PLS-SEM is an objective function that must be minimized. We then conducted a simulation study to evaluate the performance of the method by considering various factors, including the number of segments, model specifications, residual variance of endogenous latent variables, residual variance of indicators, population size, and distribution of latent variables. From the simulation study and its application to the actual data, we conclude that the proposed method can classify observations into correct segments and precisely predict SEM parameters in each segment.

This study investigates the impact of resident empowerment on support for sustainable tourism, with technology adoption as a moderating factor. Using the Social Exchange Theory (SET) and Technology Acceptance Model (TAM), it examined how psychological, social, and political empowerment influenced community participation in tourism development. A cross-sectional survey was conducted, involving 328 respondents from tourism villages in East Java, Indonesia. The data was analyzed using Structural Equation Modeling (SEM). The results revealed that psychological empowerment has the strongest effect on support for tourism, followed by social and political empowerment. Technology adoption significantly moderates these relationships, enhancing the positive effects of empowerment on community support. The findings highlight the need for integrating digital transformation with resident empowerment to strengthen tourism sustainability. Policymakers should focus on improving digital literacy, infrastructure, and participatory governance to maximize community involvement.

• We present MAGWGPRS, a new model that is a combination and development of count response MARS and spatial regression. • Selecting the optimal bandwidth using an adaptive Gaussian kernel function based on the CV method. • Grouping districts/cities in Java Indonesia based on inter-regional disaggregating variables in modeling DHF cases.

Partial Least Squares Structural Equation Modelling (PLS-SEM) struggles with nonlinear relationships between latent variables, leading to biased results. To address this limitation, this study proposes a new model, Multivariate Adaptive Regression Splines Partial Least Square (MARSPLS), which is based on Multivariate Adaptive Regression Splines (MARS) using the PLS-SEM framework. The innovation lies in its ability to capture nonlinear and interaction effects between latent variables by leveraging the flexibility of MARS while retaining the latent structure estimation through PLS. The article elaborates the steps of Maximum Likelihood Estimator (MLE) and Ordinary Least Squares (OLS) to estimate values of MARSPLS parameters. The model is evaluated using both simulated and empirical data on e-wallet behavioural intention from 385 Indonesian respondents. Results show that MARSPLS with interaction achieves superior predictive accuracy, as indicated by higher R² value 54.08 % and lower AIC, AICc, and RMSE values. The primary characteristics of the recommended method involve the following:•A novel approach to PLS-SEM that assumes the relationship between latent is nonlinear or unknown.•The model involves four exogenous and one endogenous latent variable, without moderation and mediation effects.