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Design‐Based Inference in a Mixture Model for Ordinal Variables for a Two Stage Stratified Design
Author(s) -
Gambacorta R.,
Iannario M.,
Valliant R.
Publication year - 2014
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/anzs.12072
Subject(s) - mathematics , statistics , estimator , ordinal data , inference , sampling design , linearization , statistical inference , stratified sampling , variance (accounting) , sampling (signal processing) , goodness of fit , negative binomial distribution , ordinal regression , econometrics , poisson distribution , computer science , artificial intelligence , population , physics , demography , accounting , filter (signal processing) , nonlinear system , quantum mechanics , sociology , business , computer vision
Summary In this paper we present methods for inference on data selected by a complex sampling design for a class of statistical models for the analysis of ordinal variables. Specifically, assuming that the sampling scheme is not ignorable, we derive for the class of cub models (Combination of discrete Uniform and shifted Binomial distributions) variance estimates for a complex two stage stratified sample. Both Taylor linearization and repeated replication variance estimators are presented. We also provide design‐based test diagnostics and goodness‐of‐fit measures. We illustrate by means of real data analysis the differences between survey‐weighted and unweighted point estimates and inferences for cub model parameters.