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Publication date: 11/10/2021

Image shown hereRepeated Measures

The form of the repeated measures model is yijk = αij + sik + eijk, where

αij can be written as a treatment and time factorial

sik is the random effect of the kth subject assigned to the ith treatment

j = 1,…,m denotes the repeated measurements over time.

Assume that the sik are independent and identically distributed N(0, σs2) variables. Denote the number of treatment factors by t and the number of subjects by s. Then the distribution of eijk is N(0, Σ), where

Equation shown here


Equation shown here

Denote the block diagonal component of the covariance matrix Σ corresponding to the ikth subject within treatment by Σik. In other words, Σik = Var(yik|sik). Because observations over time within a subject are not typically independent, it is necessary to estimate the variance of yijk|sik. Failure to account for the correlation leads to distorted inference.

See Repeated Covariance Structures and Spatial and Temporal Variability for more information about the covariance structures available for Σik.

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