GENERALIZED VARIANCE FUNCTIONS FOR BINOMIAL VARIABLES IN STRATIFIED TWO-STAGE SAMPLING

Abstract

      This empirical study evaluates the application of Generalized Variance Functions (GVFs) for binomial variables in the 1998 Indonesian Labor Force Survey. The survey employs stratified two-stage cluster sampling for selecting samples from a population of households. The study covers all provinces in Java to produce estimates at the level of Java Island. The relative variance estimates resulted from the GVF models are compared to the relative variance estimates which are computed directly.

The results illustrate that  model  expressed by logarithmic model  log = log c + d log () gives a good approximation to estimate the variances for the nonagricultural employment group, especially for working male category both in urban and rural areas. It is also good for the total employment group differentiated by age group, educational attainment, and employment status. On the other hand, the model gives poor results for the agricultural employment group.

Based on the empirical results, the GVF models may not perform particularly well for the common characteristics which have relatively dissimilar deff values to majority of characteristics in the same group, since these characteristics usually come out among all persons in the sample household and often among all households in the sample cluster as well. The success of the GVF technique depends critically on the grouping of the estimates total () and amount of characteristics involved as the observations for fitting the model. Furthermore, observations with relatively large residuals will also determine the performance of goodness-of-fit of the model.

Application of GVF technique to obtain an approximate standard error on numerous binomial characteristics in large scale survey should be carried out further using extensive data. The better performance of GVF model may also be accomplished by utilizing, for examples, weighted least squares procedure or robust regression method. Additionally, the data users should be warned that there will inevitably be survey characteristics for which GVF's will give poor results or even no GVF will be appropriate.

Keywords :  Generalized Variance Functions, Stratified Two-Stage Sampling