# Thread: Restricted Maximum Likelihood (REML) Estimate of Variance Component.

1. ## Restricted Maximum Likelihood (REML) Estimate of Variance Component.

Let,

where

is a vector of response for individual at time points, is a matrix, is a vector of fixed effect parameters, is a matrix, is a vector of random effects, is a vector of within errors, is a covariance matrix of between-subject, is a scalar.

Note that, , , and do NOT involve .

Now I have to find out the Restricted Maximum Likelihood (REML) Estimate of , that is,

where .

So first I wrote the Restricted Maximum Log-Likelihood :

Then I have to differentiate log-likelihood, , with respect to and equate it to zero, i.e.,

But basically I can't differentiate,

and

.

How can I differentiate the above derivatives and get the REML estimate in equation ?

2. ## Re: Restricted Maximum Likelihood (REML) Estimate of Variance Component.

Originally Posted by tnkvrbox
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.

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