TY - JOUR
T1 - Response probability estimation
AU - Niyonsenga, Théophile
PY - 1997/12/1
Y1 - 1997/12/1
N2 - This paper extends the ideas in Giommi (Proc. 45th Session of the Internat. Statistical Institute, Vol. 2 (1985) 577-578; Techniques d'enquête 13(2) (1987) 137-144) and, in Särndal and Swenson (Bull Int. Statist. Inst. 15(2) (1985) 1-16; Int. Statist. Rev. 55 (1987) 279-294). Given the parallel between a 'three-phase sampling' and a 'sampling with subsequent unit and item nonresponse', we apply results from three-phase sampling theory to nonresponse situation. To handle the practical problem of unknown distributions at the second and the third phases of selection (the response mechanisms) in the nonresponse case, we use two approaches of response probability estimation: response homogeneity groups (RHG) model (Särndal and Swenson, 1985, 1987) and the nonparametric estimation (Giommi, 1985, 1987). To motivate the three-phase selection, imputation procedures for item nonresponse are used with the RHG model for unit nonresponse. By means of a Monte Carlo study, we find that the regression-type estimators are the most precise of those studied under the two approaches of response probability estimation in terms of lower bias, mean square error and variance; variance estimator close to the true variance and achieved coverage rates closer to the nominal levels. The simulation study shows how poor the variance estimators are under the single imputation approach currently used to handle the problem of missing values.
AB - This paper extends the ideas in Giommi (Proc. 45th Session of the Internat. Statistical Institute, Vol. 2 (1985) 577-578; Techniques d'enquête 13(2) (1987) 137-144) and, in Särndal and Swenson (Bull Int. Statist. Inst. 15(2) (1985) 1-16; Int. Statist. Rev. 55 (1987) 279-294). Given the parallel between a 'three-phase sampling' and a 'sampling with subsequent unit and item nonresponse', we apply results from three-phase sampling theory to nonresponse situation. To handle the practical problem of unknown distributions at the second and the third phases of selection (the response mechanisms) in the nonresponse case, we use two approaches of response probability estimation: response homogeneity groups (RHG) model (Särndal and Swenson, 1985, 1987) and the nonparametric estimation (Giommi, 1985, 1987). To motivate the three-phase selection, imputation procedures for item nonresponse are used with the RHG model for unit nonresponse. By means of a Monte Carlo study, we find that the regression-type estimators are the most precise of those studied under the two approaches of response probability estimation in terms of lower bias, mean square error and variance; variance estimator close to the true variance and achieved coverage rates closer to the nominal levels. The simulation study shows how poor the variance estimators are under the single imputation approach currently used to handle the problem of missing values.
KW - Imputation
KW - Nonparametric estimation
KW - Response homogeneity group
KW - Response mechanisms
KW - Response probabilities
KW - Three-phase selection
KW - Variance estimation
UR - http://www.scopus.com/inward/record.url?scp=0031498447&partnerID=8YFLogxK
U2 - 10.1016/S0378-3758(96)00094-8
DO - 10.1016/S0378-3758(96)00094-8
M3 - Article
AN - SCOPUS:0031498447
SN - 0378-3758
VL - 59
SP - 111
EP - 126
JO - Journal of Statistical Planning and Inference
JF - Journal of Statistical Planning and Inference
IS - 1
ER -