It is a two-tailed test. There is a literature on testing variances against zero. See, for example,
Stoel, R.D., Garre, F.G., Donal, C., and van den Wittenboer, G. (2006) On the likelihood ratio test in structural equation modeling when parameters are subject to boundary constraints. Psychological Methods,11, 439-455.
C. Lechner posted on Wednesday, May 15, 2013 - 6:57 am
Dear Linda and Bengt,
I have a multilevel model involving a cross-level interaction between a level-1 predictor x and a level-2 predictor w:
%within% x_slope | y ON x; %between% y x_slope ON w; y WITH x_slope ;
I noticed that the p-value of the residual variance of the slope depends strongly on centering option. Specifically, if I center x, the residual variance of x_slope is n.s. However, if I do not center x, the residual variance is highly significant. How does this come about? Should x not be centered if it gets a random slope?
Note: In a model without w, x_slope does have a significant level-2 variance.