Simple reparameterization to improve convergence in linear mixed models

Gorjanc, Gregor (author), Flisar, Tina (author), Martínez-Ávila, Jose Carlos (author), García-Cortés, Luis Alberto (author)

Slow convergence and mixing are one of the main problems of Markov chain Monte Carlo (McMC) algorithms applied to mixed models in animal breeding. Poor convergence is to a large extent caused by high posterior correlation between variance components and solutions for the levels of associated effects. A simple reparameterization of the conventional model for variance component estimation is presented which improves McMC sampling and provides the same posterior distributions as the conventional model. Reparameterization is based on the rescaling of hierarchical (random) effects in a model, which alleviates posterior correlation. The developed model is compared against the conventional model using several simulated data sets. Results show that presented reparameterization has better behaviour of associated sampling methods and is several times more efficient for the low values of heritability.

• Language: English
• Keywords: statistics, mixed model, Bayesian analysis, McMC, reparameterization, convergence
• Work type: Not categorized
• Typology: 1.01 - Original Scientific Article
• Organization: BF - Biotechnical Faculty
• Year: 2010
• Number of pages: Str. 69-73
• Numbering: Letn. 96, št. 2
• PID: 20.500.12556/RUL-15711
• UDC: 519.2
• ISSN on article: 1581-9175
• COBISS.SI-ID: 2792328
• Publication date in RUL: 11.07.2014

Record is a part of a journal

• Title: Acta agriculturae Slovenica
• Shortened title: Acta agric. Slov.
• Publisher: Biotehniška fakulteta
• ISSN: 1581-9175
• COBISS.SI-ID: 213840640

Secondary language

• Language: Slovenian

Abstract

Počasna konvergenca je eden največjih problemov uporabe metode Monte Carlo z Markovimi verigami (McMC) za mešane modele na področju genetike in selekcije domačih živali. Slaba konvergenca je v veliki meri posledica visoke posteriorne korelacije med komponentami variance in rešitvami za ravni pripadajočih vplivov. Predstavljamo enostavno reparametrizacijo običajnega modela, ki izboljša lastnosti metode McMC in daje enake posteriorne porazdelitve parametrov modela kot standardni pristop. Reparametrizacija temelji na standardizaciji hierarhičnih (naključnih) vplivov v modelu, kar posledično spremeni posteriorne korelacije med parametri. Oba pristopa smo primerjali na večjem setu simuliranih podatkov. Rezultati kažejo, da reparametrizacija vodi do bolj učinkovitih metod McMC vzorčenja in je nekajkrat bolj učinkovita za analizo lastnosti z nizko heritabilitet.

• Keywords: statistika, mešani model, bayesovska analiza, McMC, reparametrizacija, konvergenca