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EN
The paper focuses on latent class models and their application for quantitative data. Latent class modeling is one of multivariate analysis techniques of the contingency table and can be viewed as a special case of model-based clustering, for multivariate discrete data. It is assumed that each observation comes from one of the numbers of subpopulations, with its own probability distribution. We used latent class analysis for grouping and detecting homogeneity of Silesian people using poLCA package of R. We analyzed data collected by the Department of Social Pedagogy, University of Silesia in Katowice.
EN
Small area estimation (SAE) under a linear mixed model may not be efficient if data contain substantial proportion of zeros than would be expected under standard model assumptions (hereafter zero-inflated data). We discuss the SAE for zero-inflated data under a mixture model (Fletcher et al., 2005 and Karlberg, 2000) that account for excess zeros in the data. Our results from simulation studies show that mixture model based approach for SAE works well and produces an efficient set of small area estimates. An application to real survey data from the National Sample Survey Organisation of India demonstrates the satisfactory performance of the approach.
PL
W pracy omówiono semiparametryczny model mieszany, w którym pewne współczynniki są parametryzowane za pomocą wspólnego parametru euklidesowego, natomiast inne są zupełnie nieznane. Wprowadzono metodę estymacji parametrów opartą na podejściu GEE (uogólnionych równań estymujących)  oraz adaptacyjnym podejściu GEE. Proponowane estymatory zostały przeanalizowane w badaniu symulacyjnym.
EN
We discuss semiparametric mixture model where some components are parametrized with common Euclidean parameter and others are fully unknown. We introduce GEE approach and adaptive GEE-based approach for parameter estimation. Proposed estimators are tested on simulated sample.
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