By Bruce Schneier
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Extra resources for Applied Cryptography: Protocols, Algorithms and Source Code in C. 20th Anniversary Edition
Then we could write the correlation between the residuals as corr(eij , eij ) = ρ, j=j. Alternatively, it is possible that the correlation between pairs of measurements decays as they become more widely separated in time. We could then write corr(eij , eij ) = ρ |j −j| , j=j. In the extreme, we can set a separate correlation for each pair of visits and may write corr(eij , eij ) = ρj,j , j = j . A covariance pattern model can be used to fit any of these covariance (or correlation) patterns. This type of model forms another class of mixed models.
4 25 Mixed models in medicine Frequently, there are advantages to be gained from using mixed models in medical applications. Data in medical studies are often clustered; for example, data may be recorded at several centres, hospitals or general practices. This design can be described as hierarchical and wider inferences can be made by fitting the clustering effect as random. Repeated measures designs are also often used in medicine and it is not uncommon for some of the observations to be missing.
Thus, the treatment estimates will be identical whether the patient effect is fitted as fixed or random, but these estimates will (in general) differ from the raw means. The above definition has been applied in the context of one particular type of mixed model; namely, the random effects model. In random coefficients models, the random coefficient blocking effect (usually patients) can be substituted for ‘random effect’ in the definition. In covariance pattern models the blocking effect within which the covariance pattern is defined (again usually patients) can be substituted for ‘random effect’.
Applied Cryptography: Protocols, Algorithms and Source Code in C. 20th Anniversary Edition by Bruce Schneier
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