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[{"key": "dc.contributor.advisor", "value": "Taskinen, Sara", "language": "", "element": "contributor", "qualifier": "advisor", "schema": "dc"}, {"key": "dc.contributor.advisor", "value": "Niku, Jenni", "language": "", "element": "contributor", "qualifier": "advisor", "schema": "dc"}, {"key": "dc.contributor.author", "value": "Korhonen, Pekka", "language": "", "element": "contributor", "qualifier": "author", "schema": "dc"}, {"key": "dc.date.accessioned", "value": "2020-12-01T10:33:13Z", "language": null, "element": "date", "qualifier": "accessioned", "schema": "dc"}, {"key": "dc.date.available", "value": "2020-12-01T10:33:13Z", "language": null, "element": "date", "qualifier": "available", "schema": "dc"}, {"key": "dc.date.issued", "value": "2020", "language": "", "element": "date", "qualifier": "issued", "schema": "dc"}, {"key": "dc.identifier.uri", "value": "https://jyx.jyu.fi/handle/123456789/72890", "language": null, "element": "identifier", "qualifier": "uri", "schema": "dc"}, {"key": "dc.description.abstract", "value": "Yhteis\u00f6ekologian alalla tutkijat ovat usein kiinnostuneita yhden tai useamman kasvi- tai el\u00e4inlajin v\u00e4lisist\u00e4 esiintyvyyssuhteista eri mittauspaikoilla tai ekosysteemeiss\u00e4. T\u00e4m\u00e4nkaltaiset tutkimuskysymykset johtavat luonnostaan moniulotteisen runsausdatan ker\u00e4\u00e4miseen. Kasvi- tai el\u00e4inlajin ekologista runsautta tietyss\u00e4 ekosysteemiss\u00e4 voidaan kuvata esimerkiksi suoraan lajiyksil\u00f6iden lukum\u00e4\u00e4r\u00e4n\u00e4 tai bin\u00e4\u00e4risen\u00e4 esiintyvyysindikaattorina. Runsausvasteen tyyppi on otettava huomioon tilastollista mallia sovittaessa. Yleistetyt lineaariset latenttimuuttujamallit tarjoavat joustavan tavan mallintaa moniulotteista runsautta olettamalla yhden tai useamman latentin muuttujan olemassaolon. Latentit muuttujat ovat luonteeltaan satunnaisia ja havaitsemattomia. Niiden voidaan tulkita kuvaavan esimerkiksi havaitsematta j\u00e4\u00e4neit\u00e4 ymp\u00e4rist\u00f6tekij\u00f6it\u00e4. Latentit muuttujat ovat hy\u00f6dyllisi\u00e4, sill\u00e4 niiden avulla voidaan mallintaa eri lajien v\u00e4list\u00e4 korrelaatiorakennetta. Latenttimuuttujamallien sovittaminen ei kuitenkaan ole erityisen suoraviivaista latenttien muuttujien havaitsemattomuudesta johtuen. \n\nLatenttimuuttujamallia vastaava marginaalinen uskottavuusfunktio sis\u00e4lt\u00e4\u00e4 integraalin, jolla ei yleisess\u00e4 tapauksessa ole analyyttist\u00e4 ratkaisua. Mallin sovituksessa joudutaan t\u00e4m\u00e4n vuoksi k\u00e4ytt\u00e4m\u00e4\u00e4n jotakin approksimatiivista menetelm\u00e4\u00e4. Er\u00e4s varteenotettava vaihtoehto on niin sanottu variaatiomenetelm\u00e4, joka esitell\u00e4\u00e4n t\u00e4m\u00e4n tutkielman alussa. Menetelm\u00e4n etuna on sek\u00e4 estimointitarkkuus ett\u00e4 laskennallinen tehokkuus. Variaatiomenetelm\u00e4n selv\u00e4n\u00e4 heikkoutena on sen huono yleistyvyys, sill\u00e4 se ei suoraan sovellu k\u00e4ytett\u00e4v\u00e4ksi kaikkien tavanomaisten vastejakauma-linkkifunktio -parien yhteydess\u00e4. T\u00e4m\u00e4n vuoksi t\u00e4ss\u00e4 tutkielmassa esitet\u00e4\u00e4n nyt laajennettuksi variaatiomenetelm\u00e4ksi nimetty menetelm\u00e4. Esitetty\u00e4 laajennosta verrataan sek\u00e4 tavanomaiseen variaatiomenetelm\u00e4\u00e4n ett\u00e4 Laplace-approksimaatioon perustuvaan kilpailevaan menetelm\u00e4\u00e4n aineistopohjaisten simulointikokeiden avulla. Lis\u00e4ksi esitell\u00e4\u00e4n laajennetun variaatiomenetelm\u00e4n k\u00e4ytt\u00f6\u00e4 suoaineistolle teht\u00e4v\u00e4ss\u00e4 ordinaatiossa. Suoaineisto on per\u00e4isin Jyv\u00e4skyl\u00e4n yliopiston Bio- ja ymp\u00e4rist\u00f6tieteen laitokselta. Laajennettu variaatiomenetelm\u00e4 implementoitiin ohjelmointikieli\u00e4 R ja C++ k\u00e4ytt\u00e4en muutaman tyypillisimm\u00e4n latenttumuuttujamallin tapauksessa.", "language": "fi", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.abstract", "value": "Generalized Linear Latent Variable Models (GLLVM), a family of statistical models developed on recent years, has gained a lot of attraction in applications, in particular in the field of community ecology. Ecologists are often concerned with the relationships between two or more species across a multiple test sites. Such situations naturally lead to the collection of multivariate abundance data and call for appropriate statistical methods to analyze such data. GLLVMs offer a model-based approach for such analyses that is also flexible in the terms of the type of abundance response at question, i.e., species count, presence/absence, biomass, and such. As their namesake implies, GLLVMs generally assume the presence of some unobserved, latent variables as predictors. These latent variables are useful, for example in the modelling of the between-species correlation, but they also introduce some computational challenges into the model fitting.\n\nIn its general form, the GLLVM marginal likelihood involves an integral over the aforementioned latent variables. Under the standard assumptions this integral cannot be solved analytically, when dealing with other than normally distributed response variables. Thus some form of numerical approximation technique is often needed. This thesis starts by introducing a variational approximation (VA) approach for fitting GLLVMs, which has shown to be an attractive choice in terms of both the computational efficiency and estimation precision. From there we introduce a recently proposed method of extended variational approximation (EVA), which extends upon the standard VA approach by allowing a wider set of response distributions and link functions to be used in modelling. Then the comparative performance of these two approaches and a popular alternative, Laplace approximation (LA), is addressed in simulation studies. Additionally, an example study concerning the use of EVA in ordination of plant cover data is conducted. Lastly we discuss some ideas for further development regarding the EVA approach.\n\nThe VA and LA approaches to estimation of GLLVMs are readily available in the R package gllvm, which has been used in this thesis. An implementation of the EVA approach for a few types of common response distributions was developed as a part of this thesis in R and C++ using the package TMB.", "language": "en", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted by Paivi Vuorio (paelvuor@jyu.fi) on 2020-12-01T10:33:13Z\nNo. of bitstreams: 0", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Made available in DSpace on 2020-12-01T10:33:13Z (GMT). No. of bitstreams: 0\n Previous issue date: 2020", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.format.extent", "value": "46", "language": "", "element": "format", "qualifier": "extent", "schema": "dc"}, {"key": "dc.format.mimetype", "value": "application/pdf", "language": null, "element": "format", "qualifier": "mimetype", "schema": "dc"}, {"key": "dc.language.iso", "value": "eng", "language": null, "element": "language", "qualifier": "iso", "schema": "dc"}, {"key": "dc.rights", "value": "In Copyright", "language": "en", "element": "rights", "qualifier": null, "schema": "dc"}, {"key": "dc.subject.other", "value": "generalized linear latent variable models", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "variational inference", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "abundance data", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "ordination", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.title", "value": "Fitting Generalized Linear Latent Variable Models using the method of Extended Variational Approximation", "language": "", "element": "title", "qualifier": null, "schema": "dc"}, {"key": "dc.type", "value": "master thesis", "language": null, "element": "type", "qualifier": null, "schema": "dc"}, {"key": "dc.identifier.urn", "value": "URN:NBN:fi:jyu-202012016851", "language": "", "element": "identifier", "qualifier": "urn", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Pro gradu -tutkielma", "language": "fi", "element": "type", "qualifier": "ontasot", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Master\u2019s thesis", "language": "en", "element": "type", "qualifier": "ontasot", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Matemaattis-luonnontieteellinen tiedekunta", "language": "fi", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Faculty of Sciences", "language": "en", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Matematiikan ja tilastotieteen laitos", "language": "fi", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Department of Mathematics and Statistics", "language": "en", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "Jyv\u00e4skyl\u00e4n yliopisto", "language": "fi", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "University of Jyv\u00e4skyl\u00e4", "language": "en", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Tilastotiede", "language": "fi", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Statistics", "language": "en", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "yvv.contractresearch.funding", "value": "0", "language": "", "element": "contractresearch", "qualifier": "funding", "schema": "yvv"}, {"key": "dc.type.coar", "value": "http://purl.org/coar/resource_type/c_bdcc", "language": null, "element": "type", "qualifier": "coar", "schema": "dc"}, {"key": "dc.rights.accesslevel", "value": "openAccess", "language": null, "element": "rights", "qualifier": "accesslevel", "schema": "dc"}, {"key": "dc.type.publication", "value": "masterThesis", "language": null, "element": "type", "qualifier": "publication", "schema": "dc"}, {"key": "dc.subject.oppiainekoodi", "value": "4043", "language": "", "element": "subject", "qualifier": "oppiainekoodi", "schema": "dc"}, {"key": "dc.subject.yso", "value": "simulointi", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "tilastomenetelm\u00e4t", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "simulation", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "statistical methods", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.format.content", "value": "fulltext", "language": null, "element": "format", "qualifier": "content", "schema": "dc"}, {"key": "dc.rights.url", "value": "https://rightsstatements.org/page/InC/1.0/", "language": null, "element": "rights", "qualifier": "url", "schema": "dc"}, {"key": "dc.type.okm", "value": "G2", "language": null, "element": "type", "qualifier": "okm", "schema": "dc"}]
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