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Feasible computation of generalized linear mixed models with application to credit risk modelling
Örebro University, Swedish Business School at Örebro University.
2010 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis deals with developing and testing feasible computational procedures to facilitate the estimation of and carry out the prediction with the generalized linear mixed model (GLMM) with a scope of applying them to large data sets. The work of this thesis is motivated from an issue arising incredit risk modelling. We have access to a huge data set, consisting of about one million observations, on credit history obtained from two major Swedish banks. The principal research interest involved with the data analysis is to model the probability of credit defaults by incorporating the systematic dependencies among the default events. In order to model the dependent credit defaults we adopt the framework of GLMM which is apopular approach to model correlated binary data. However, existing computational procedures for GLMM did not offer us the flexibility to incorporate the desired correlation structure of defaults events.For the feasible estimation of the GLMM we propose two estimation techniques being the fixed effects (FE) approach and the two-step pseudolikelihood approach (2PL). The preciseness of the estimation techniques and their computational advantages are studied by Monte-Carlo simulations and by applying them to the credit risk modelling. Regarding the prediction issue, we show how to apply the likelihood principle to carryout prediction with GLMM. We also provide an R add-in package to facilitate the predictive inference for GLMM.

Place, publisher, year, edition, pages
Örebro: Örebro universitet , 2010. , p. 29
Series
Örebro Studies in Statistics, ISSN 1651-8608 ; 5
Keywords [en]
Credit risk, cluster correlation, GLMM, large data, two-step pseudo likelihood estimation, defaults contagion, predictive likelihood
National Category
Social Sciences Probability Theory and Statistics
Research subject
Statistics
Identifiers
URN: urn:nbn:se:oru:diva-12390ISBN: 978-91-7668-771-0 (print)OAI: oai:DiVA.org:oru-12390DiVA, id: diva2:360110
Public defence
2010-12-21, Hörsal M, Örebro universitet, Fakultetsgatan 1, 701 82 Örebro, 15:15 (English)
Opponent
Available from: 2010-11-04 Created: 2010-11-02 Last updated: 2017-10-17Bibliographically approved
List of papers
1. Computationally feasible estimation of the covariance structure in generalized linear mixed models 
Open this publication in new window or tab >>Computationally feasible estimation of the covariance structure in generalized linear mixed models 
2008 (English)In: Journal of Statistical Computation and Simulation, ISSN 0094-9655, E-ISSN 1563-5163, Vol. 78, no 12, p. 1229-1239Article in journal (Refereed) Published
Abstract [en]

In this paper, we discuss how a regression model, with a non-continuous response variable, which allows for dependency between observations, should be estimated when observations are clustered and measurements on the subjects are repeated. The cluster sizes are assumed to be large.We find that the conventional estimation technique suggested by the literature on generalized linear mixed models(GLMM) is slow and sometimes fails due to non-convergence and lack of memory on standard PCs.We suggest to estimate the random effects as fixed effects by generalized linear model and to derive the covariance matrix from these estimates.A simulation study shows that our proposal is feasible in terms of mean-square error and computation time.We recommend that our proposal be implemented in the software of GLMM techniques so that the estimation procedure can switch between the conventional technique and our proposal, depending on the size of the clusters.

Place, publisher, year, edition, pages
London: Taylor & Francis, 2008
Keywords
Monte Carlo simulations, Large sample, Interdependence, Cluster errors
National Category
Probability Theory and Statistics Social Sciences
Research subject
Statistics
Identifiers
urn:nbn:se:oru:diva-14060 (URN)10.1080/00949650701688547 (DOI)
Note
Mr Alam is also affiliated to Dalarna University, SE 781 88 Borlange, SwedenAvailable from: 2011-01-19 Created: 2011-01-19 Last updated: 2017-12-11Bibliographically approved
2. Feasible estimation of generalized linear mixed models (GLMM) with weak dependency between groups
Open this publication in new window or tab >>Feasible estimation of generalized linear mixed models (GLMM) with weak dependency between groups
2010 (English)Manuscript (preprint) (Other academic)
Abstract [en]

This paper presents a two-step pseudo likelihood estimation for generalized linear mixed models with the random effects being correlated between groups. The core idea is to deal with the random intractable integrals in  the likelihood function by multivariate Taylor's approximation. The accuracy of the estimation technique is assessed in a Monte-Carlo study: An application of it with binary response variable is presented using a real dara set on credit defaults from two Swedish banks. Thanks to   the use of two-step estimation technique, the proposed algorithm outperforms conventional likelihood algoritms in terms of computational time.

Keywords
PQL, Laplace approximation, interdependence, cluster errrors, credit risk model
National Category
Social Sciences Probability Theory and Statistics
Research subject
Statistics
Identifiers
urn:nbn:se:oru:diva-14061 (URN)
Note

Mr Alam is also affiliated to Dalarna University, SE 781 88 Borlange, Sweden

Available from: 2011-01-19 Created: 2011-01-19 Last updated: 2017-10-17Bibliographically approved
3. Industry shocks and empirical evidences on defaults comovements
Open this publication in new window or tab >>Industry shocks and empirical evidences on defaults comovements
(English)Manuscript (preprint) (Other academic)
Abstract [en]

It is commonly agreed that the credit defaults are correlated. However, the structure and magnitude of such dependence is not yet fully understood. This paper contributes to the current understanding about the defaults comovement in the following way. Assuming that the industries provides the basis of defaults comovement it provides empirical evidence as to how such comovements can be modeled using correlated industry shocks. Generalized linear mixed model (GLMM) with correlated random effects is used to model the defaults comovement. It is also demonstrated as to how a GLMM with complex correlation structure can be estimated through a very simple way. Empirical evidences are drawn through analyzing quarterly individual borrower level credit history data obtained from two major Swedish banks between the period 1994 and 2000. The results show that, conditional on the borrower level accounting data and macro business cycle variables, the defaults are correlated both within and between industries but not over time (quarters). A discussion has also been presented as to how a GLMM for defaults correlation can be explained.

Keywords
Credit risk, defaults contagion, GLMM, cluster correlation
National Category
Social Sciences Probability Theory and Statistics
Research subject
Statistics
Identifiers
urn:nbn:se:oru:diva-14072 (URN)
Note

Mr Alam is also affiliated to Dalarna University, SE 781 88 Borlange, Sweden

Available from: 2011-01-19 Created: 2011-01-19 Last updated: 2017-10-17Bibliographically approved
4. Likelihood prediction for generalized linear mixed models under covariate uncertainty
Open this publication in new window or tab >>Likelihood prediction for generalized linear mixed models under covariate uncertainty
2010 (English)Manuscript (preprint) (Other academic)
Abstract [en]

This paper presents the techniques of likelihood prediction for the generalized linear mixed models. Methods of likelihood prediction is explained through a series of examples; from a classical one to more complicated ones. The examples show, in simple cases, that the likelihood prediction (LP) coincides with already known best frequentist practice such as the best linear unbiased predictor. The paper outlines a way to deal with the covariate uncertainty while producing predictive inference. Using a Poisson error-in-variable general-ized linear model, it has been shown that in complicated cases LP produces better results than already know methods.

Keywords
Predictive likelihood, Pro…le predictive likelihood, Stochastic covariate, Coverage interval, Future value prediction, Credit risk prediction
National Category
Social Sciences Probability Theory and Statistics
Research subject
Statistics
Identifiers
urn:nbn:se:oru:diva-14079 (URN)
Note

Mr Alam is also affiliated to Dalarna University, SE 781 88 Borlange, Sweden

Available from: 2011-01-19 Created: 2011-01-19 Last updated: 2017-10-17Bibliographically approved
5. Computation and application of likelihood prediction with generalized linear and mixed models
Open this publication in new window or tab >>Computation and application of likelihood prediction with generalized linear and mixed models
(English)Manuscript (preprint) (Other academic)
Abstract [en]

This paper presents the computation of likelihood prediction with the generalized linear and mixed models. The method of likelihood prediction is briefy discussed and approximate formulae are provided to make easy computation of the likelihoodprediction with generalized linear models. For complicated prediction problems, simulation methods are suggested. An R add-in package is accompanied to carryout the computation of the predictive inference with the generalized linear and mixed models. The likelihood prediction is applied to the prediction of the credit defaults using a real data set. Results show that the predictive likelihood can be a useful tool to predict portfolio credit risk.

Keywords
Predictive likelihood, Pro…le predictive likelihood, Coverage inter- val, Future value prediction, Credit risk prediction, R-package.
National Category
Social Sciences Probability Theory and Statistics
Research subject
Statistics
Identifiers
urn:nbn:se:oru:diva-14081 (URN)
Note

Mr Alam is also affiliated to Dalarna University, SE 781 88 Borlange, Sweden

Available from: 2011-01-19 Created: 2011-01-19 Last updated: 2017-10-17Bibliographically approved

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