## Finite Mixture Models for Small Area Estimation in Cases of Unobserved Heterogeneity

- A basic assumption of standard small area models is that the statistic of interest can be modelled through a linear mixed model with common model parameters for all areas in the study. The model can then be used to stabilize estimation. In some applications, however, there may be different subgroups of areas, with specific relationships between the response variable and auxiliary information. In this case, using a distinct model for each subgroup would be more appropriate than employing one model for all observations. If no suitable natural clustering variable exists, finite mixture regression models may represent a solution that „lets the data decide“ how to partition areas into subgroups. In this framework, a set of two or more different models is specified, and the estimation of subgroup-specific model parameters is performed simultaneously to estimating subgroup identity, or the probability of subgroup identity, for each area. Finite mixture models thus offer a fexible approach to accounting for unobserved heterogeneity. Therefore, in this thesis, finite mixtures of small area models are proposed to account for the existence of latent subgroups of areas in small area estimation. More specifically, it is assumed that the statistic of interest is appropriately modelled by a mixture of K linear mixed models. Both mixtures of standard unit-level and standard area-level models are considered as special cases. The estimation of mixing proportions, area-specific probabilities of subgroup identity and the K sets of model parameters via the EM algorithm for mixtures of mixed models is described. Eventually, a finite mixture small area estimator is formulated as a weighted mean of predictions from model 1 to K, with weights given by the area-specific probabilities of subgroup identity.

Author: | Charlotte Articus |
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URN: | urn:nbn:de:hbz:385-1-9884 |

DOI: | https://doi.org/10.25353/UBTR-7631-5471-06XX |

Referee: | Ralf Münnich |

Advisor: | Ralf Münnich |

Document Type: | Doctoral Thesis |

Language: | English |

Date of completion: | 2018/11/27 |

Publishing institution: | Universität Trier |

Granting institution: | Universität Trier, Fachbereich 4 |

Date of final exam: | 2018/06/29 |

Release Date: | 2018/12/12 |

Tag: | rental prices; small area estimation; survey statistics |

GND Keyword: | Erhebungsverfahren; Mietpreis; Schätzung |

Number of pages: | 159 |

Institutes: | Fachbereich 4 |

Dewey Decimal Classification: | 3 Sozialwissenschaften / 33 Wirtschaft / 330 Wirtschaft |

Licence (German): | CC BY: Creative-Commons-Lizenz 4.0 International |