How Can I simulate Data for Least-Squares Variance Component Estimation (LS-VCE) for Multiple regression?

Hello

I Have a muliple regression:

y=a1*x1+a2*x2+a3*x3+a4*x4+a5 and i want simulate data for Least-Squares Variance component Estimation (LS-VCE). How I can Simulate data for this problem?

Answer 1

[Jeff Miller]

You could use mvnrnd to generate random values of x1-x4. Is that what you need?

[Mary Tavoosi]

Hello Tnx for your answer I simulated data for dependent and independent variables with mvnrnd but I need covariance matrix of dependent and independent variables and for this problem need cofactor matrix and factor variance for each variables and cofactor matrixes must be independent How can is simulate data for this?

[Jeff Miller]

Sorry, I'm not familiar with LS-VCE, so I don't really understand what you want. As you probably know, though, the inputs to mvnrnd uniquely determine the joint distribution of the generated random numbers, so I am pretty sure that your only option is to vary those inputs until you get the outputs that you want (cofactors etc).

You can generate very large sample with mvnrnd to get close to the "true" underlying output values, and then generate any desired smaller samples with the same parameters for your simulation.

[Mary Tavoosi]

Thanks for your help