Development of Semiparametric Truncated Spline Logistic Path Analysis

Logistic path analysis extends logistic regression by incorporating intervening variables, addressing the limitations of linearity assumptions through nonparametric models like spline regression. However, this study develops a semiparametric truncated spline logistic path analysis to accommodate linear and nonlinear relationships, considering direct and indirect effects of intervening variables. The model is applied to analyze the impact of price volatility and human resource quality on farmer welfare, with farmer productivity as an intervening variable. It assumes a nonlinear relationship between price volatility and productivity/welfare, while other relationships are linear. This development was applied to secondary data collected through questionnaires from farmer group members in Bali Province, which were analyzed using a semiparametric truncated spline logistic path model. Optimal knots were determined using the lowest GCV value. The results show that the model effectively captures changes in data patterns, providing robust parameter estimates. Hypothesis testing highlights significant differences in the effectiveness of linear and nonlinear relationships. The use of truncated splines offers critical insights into variable interactions and enhances model reliability, making it a valuable tool for analyzing complex agricultural systems and informing policies to improve farmer welfare and productivity.