In the second edition of the book by Snijders and Bosker, it is explained on pages 98/99 how to test for a random intercept and a random slope.

My model has a random intercept and two random slopes.

Testing for the significance of each of the two the random slopes is clearly described on page 99: a mixture of two chisquare distributions should be used, chisquare(df=2) and chisquare(df=3), both weighted by 0.5.

But what about testing the random intercept? It appears to me that a similar procedure should be followed and the same mixture of chisquare(2) and chisquare(3) should be applied. Is this indeed the right way to proceed?

And does this mean that the procedutre described on page 98 about testing a random intercept, only applies to a model with no random slopes in it?

Thanks for any advice!!