Why is there a difference in the output of PLSREGRESS when using the 'cv' option with an integer 'k' and using a cvpartition object of type kfold of the same integer 'k' in Statistics Toolbox 8.1 (R2012b)?

I am computing a partial least-squares regression using PLSREGRESS function in two different ways:

1. Directly adding the option 'cv' with a particular integer k =10:

k = 10;

[XL, YL, XS, YS, BETA, PCTVAR, MSE] = plsregress(X, Y, ncomp, 'cv', k);

2. Creating a cvpartition of type k-fold with the same integer 10:

k = 10;

C = cvpartition(length(X), 'kfold', k);

[XL, YL, XS, YS, BETA, PCTVAR, MSE] = plsregress(X, Y, ncomp, 'cv', C);

However, the results I obtain in MSE are different. Why is that?

Answer 1

[MathWorks Support Team]

Using 'cv' option with an integer 'k' and using a cvpartition object of type kfold of 'k' are conceptually the same. Both commands compute the mean-squared error, MSE, using k-fold cross-validation.

However, the cross-validated MSE values from two runs of k-fold cross-validation may not be exactly the same, as the data will probably be partitioned into k folds in different ways. Contrarily, passing a cvpartition object of type k-fold of 'k' into PLSREGRESS will reproduce the same MSE values every time.

In the same way, using 'cv' option with 'resubstitution' and using a cvpartition object created with 'resubstitution' will get the same results. In both cases, PLSREGRESS uses X and Y both to fit the model and to estimate the mean-squared errors, without cross-validation.