Why the observations within a treatment of a Random-effects model are correlated? (1998)
- Authors:
- USP affiliated authors: In both the fixed- and the random-effects designs, a random sample of observations is taken within each level of a factor. However, for the fixed-effects model, the observations within each level are uncorrelated whereas those in the random-effects model are correlated. The appearance of the correlation among the observations in the random-effects models seems mysterious to the students. In the textbooks (for example, Neter, Kutner, Nachtsheim, and Wasserman, 1996, pages 960-961 ), the correlation between observations within the same level for the random-effects model is usually derived from the assumptions of the model. This explains the existence of the correlation but fails to clarify why it occurs. The proof does not completely exploit the two-stage random sampling involved in the planning of a random-effects design. Using the properties of the multivariate normal distribution, we show that if we perform the conditional analysis for the random-effects model, i. e., given the levels of the factor that are included in the experiment, the observations within each level are uncorrelated. This helps the students understand better how the first stage of random sampling in the random-effects model results in the appearance of the correlation between the observations within each level. - ; PERES, CLOVIS DE ARAUJO - IME ; ANDRE, CARMEN DIVA SALDIVA DE - IME
- Unidade: IME
- Subjects: ANÁLISE DE VARIÂNCIA; DISTRIBUIÇÕES (PROBABILIDADE)
- Language: Inglês
- Imprenta:
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ABNT
PERES, Clovis de Araujo e ANDRÉ, Carmen Diva Saldiva de e NARULA, Subhash Chander. Why the observations within a treatment of a Random-effects model are correlated?. . São Paulo: IME-USP. Disponível em: https://repositorio.usp.br/directbitstream/48fd1958-9005-46ed-ab24-34849c9a03e2/1019228.pdf. Acesso em: 19 abr. 2024. , 1998 -
APA
Peres, C. de A., André, C. D. S. de, & Narula, S. C. (1998). Why the observations within a treatment of a Random-effects model are correlated? São Paulo: IME-USP. Recuperado de https://repositorio.usp.br/directbitstream/48fd1958-9005-46ed-ab24-34849c9a03e2/1019228.pdf -
NLM
Peres C de A, André CDS de, Narula SC. Why the observations within a treatment of a Random-effects model are correlated? [Internet]. 1998 ;[citado 2024 abr. 19 ] Available from: https://repositorio.usp.br/directbitstream/48fd1958-9005-46ed-ab24-34849c9a03e2/1019228.pdf -
Vancouver
Peres C de A, André CDS de, Narula SC. Why the observations within a treatment of a Random-effects model are correlated? [Internet]. 1998 ;[citado 2024 abr. 19 ] Available from: https://repositorio.usp.br/directbitstream/48fd1958-9005-46ed-ab24-34849c9a03e2/1019228.pdf - Variação de quantidade de fase 'Y IND.2', em função do tempo decorrido após o preparo de amalgamas feitos com seis ligas diferentes, para corpos de prova integros ou triturados
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