Vispārinātie lineārie modeļi skaita tipa datu analīzei

6533b7cefe1ef96bd12574d5

RESEARCH PRODUCT

Vispārinātie lineārie modeļi skaita tipa datu analīzei

Emīls Siliņš

subject

vispārinātie lineārie modeļi Matemātika Puasona regresija GLM negatīvā binomiālā regresija skaita tipa dati

description

Bakalaura darbs ir veltīts vispārināto lineāro modeļu, kas piemēroti skaita tipa datu analīzei, teorijas apskatam. Darbā apskatīts Puasona regresijas modelis, kā arī modeļi, kas piemēroti pārāk lielas dispersijas gadījumā (kvazi-Puasona un negatīvā binomiālā sadalījuma regresijas modeļi). Skaita tipa datos var būt situācijas, kad liels datu daudzums ir 0, tāpēc šādu datu analīzei aprakstīti īpaši piemēroti modeļi, jo iepriekšminētie modeļi šādiem datiem nevar sniegt korektus novērtējumus. Atsevišķi tika aprakstīta arī empīriskās ticamības funkcijas metode vispārināto lineāro modeļu koeficientu novērtēšanai un ticamības intervālu konstruēšanai, kuru var izmantot Puasona modeļa gadījumā. Darbā veiktas simulācijas, lai salīdzinātu dažādu modeļu sniegtos koeficientu novērtējumus, ticamības intervālu pārklājumu precizitātes un iegūto ticamības intervālu garumus. Simulāciju analīzes rezultātā ilustrētas atšķirības starp modeļu veidiem. Sniegta arī praktiska skaitu datu piemēra analīze, kas dod ieskatu piemērotākā modeļa izvēlē un iegūto regresijas koeficientu interpretācijā.

year	journal	country	edition	language
2022-01-01

https://dspace.lu.lv/dspace/handle/7/60122

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