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How to obtain variance-Covariance matrix in Mixture Design analysis (regression) after it is completed?

Hi Team,

One of the professors who is teaching DOE using JMP is using the book Experiments with Mixtures: Designs, Models and Analysis of Mixture data. from Wiley publication. He is trying to replicate the output and Analysis from the book.

I have attached the dataset here. 

Please advice

thanks

Murali

Re: How to obtain variance-Covariance matrix in Mixture Design analysis (regression) after it is completed?

I assume he is asking for the correlations between parameter estimates in the regression. I added a table script for the Fit Model launch dialog and the Fit Least Squares platform. Click the red triangle at the top and select Estimates > Correlation of Estimates.

We don't usually ask about the correlations between the components.

See the attached data table that I modified.

Note that you can also open the data table for the experiment and then select DOE > Design Diagnostics > Evaluate Design. This command will produce the design diagnostics, including the correlations between estimates.

(11/10/23) I reached out to Ryan Lekivetz to check my explanation. He provided a script demonstrating the difference between the correlations reported in the Design Evaluation section in Custom Design and the Correlation of Estimates table in Fit Least Squares. The former reports the pair-wise correlations between the columns in the model matrix. The latter takes into account the regression procedure.

Names Default To Here( 1 );

// use the open data table for example
xmat = Current Data Table() << Get As Matrix;

// make another empty, conforming matrix
xmatint = Matrix( N Row( xmat ), 6 );

// copy factor levels
xmatint[0, 1 :: 3] = xmat[0, 1 :: 3];

// create cross terms
xmatint[0, 4] = xmat[0, 1] :*</img> xmat[0, 2];
xmatint[0, 5] = xmat[0, 1] :*</img> xmat[0, 3];
xmatint[0, 6] = xmat[0, 2] :*</img> xmat[0, 3];


//evaluate design version (Color Map on Correlations)
Show( Correlation( xmatint ) );

//Fit Model version
V = Sqrt( Diag( Inverse( Transpose( xmatint ) * xmatint ) ) );
Show( Inverse( V ) * Inverse( Transpose( xmatint ) * xmatint ) * Inverse( V ) );

 

Re: How to obtain variance-Covariance matrix in Mixture Design analysis (regression) after it is completed?

Thanks a lot @Mark_Bailey . 

The professor was  interested in actual (X'X)-1 sigma^2 matrix.  I think JMP (The professor also thinks the same) has provisions for X'X matrix which however needs to be inverted. 

Please advice

 

thanks

murali