An Alternative Procedure to Produce a P-Spline Small Area Estimation Model Based on Partial Residual Plot and Significance Test of Spline Term

Abstract

This study provides an alternative procedure to produce the penalized spline small area estimation (P-Spline SAE) model by plotting each of auxiliary variable and variable interest as a simple nonlinearity identification and performing the iterative procedure: by estimating the model, producing partial residual plots to check model adequacy and also identify the nonlinearity, and testing the significance of spline term using Restricted Likelihood Ratio Test (RLRT). These procedures are applied to estimate the monthly average per-capita expenditure of district level in the Province of Bali, 2014 using direct survey estimates from the National Socio-Economic Survey (Susenas 2014) and auxiliary variables from the administrative record of village data (PODES 2014). The Fay-Herriot (FH) model (M1) as a benchmark and four P-Spline SAE model, i.e. the P-Spline SAE with spline term: x2 and x3 (M2), x3 and x4 (M3), x2, x3 and x4 (M4), and x1, x2, x3 and x4 (M5), are obtained. From RLRT, the spline term of M3, M4, and M5 are statistically significant. According to the parametric bootstrap of mean squared prediction error (MSPE) and coefficient of variation (CV), the M4 and M5 show a significant improvement with the CV values range from about 1%-6% compared to M1 with a range from about 4%-17%, shows that these two models more efficient. The M3 model shows the opposite performance even though has the smallest AIC value. More detail, the MSPE and CV produced by M4 are slightly better than M5 makes the M4 is the best model in this study.