Κατεύθυνση Στατιστική και Επιχειρησιακή Έρευνα
Library of the School of Science

2017-04-05

2017

Karalekas Eleftherios

Σάμης Τρέβεζας, Λέκτορας, Τμήμα Μαθηματικών, ΕΚΠΑ

Κριτήρια Τύπου BIC για την επιλογή μοντέλων με μικτές επιδράσεις και επεκτάσεις

Greek

Bayesian Information Criteria for the selection of mixed effects models and extensions.

This thesis aspires to fulfill the following : (1) To present and classify various types of Mixed Effects Models, but to also justify why these models outperform their Fixed Effects counterparts, (2) to summarize and prove the general features of these models (i.e. Likelihood functions, Maximum Likelihood Estimators, Predictors etc.), so that any interested party can immediately retrieve these explicit results, (3) to build a notional bridge across various sorts of Mixed Effects Models and show that there are no significant differences among them (despite the differences in conventions that these models adopt), essentially they are equivalent from a mathematical point of view, (4) to compare three Bayesian Information Criteria (BIC_N,BIC_n_tot,BIC_h), in terms of their performance in choosing correct models, (5) to give a relatively rigorous proof of the hybrid Bayesian Information Criterion (BIC_h).
Ultimately we arrive at the conclusion that for relatively great number of clusters (N) and observations (n), BIC_h outperforms the other two Bayesian Information Criteria (BIC_N and BIC_n_tot) as far as the correct model selection is concerned.
The greatest bulk of technical proofs is located in Appendix A'.

Science

Mathematics

Mixed Effects Models, Hierarchical Models, Regularity Conditions, Longitudinal Data.

Yes

2

Yes

16

145

File access is restricted only to the intranet of UoA.

https://pergamos.lib.uoa.gr/uoa/dl/object/1449584