Testing for the presence of a U-shape in multilevel model (xtmixed)

[Sophie Dibbern]

Dear all,

I am testing an inverted u-shaped relationship in a multilevel model. I am using the xtmixed estimation command.

To test for the actual presence of my hypothesized inverted u-shaped relationship, I wanted to follow the procedure as suggested by Lind & Mehlum (2010) and I was happy to find the utest module. However, it seems that the utest command does not work after xtmixed (to check, I also estimated my model with "regress" and thereafter, the utest command worked perfectly).

Are there any other post estimation commands I could use for testing for the presence of the u-shape that also work after xtmixed/mixed? Alternatively, does anyone have an advice on how to estimate the slopes at the high and low end of x and the location of the turning point "manually"?

Thank you very much in advance.

Sophie

[Clyde Schechter]

Probably the simplest way to do this is to run -mixed- (-xtmixed is the old names; it has been called -mixed- since at least version 14) with a linear and quadratic term. I assume that you are fitting a single overall quadratic model, not a quadratic model whose parameters are themselves random effects at the group level. Thus

mixed y c.x##c.x /*perhaps other variables as well*/ || group:

Whether there is an effect of x at all in this model can be tested with

 test x x#x

If you want to contrast quadratic and simple linear models, I would recommend running the model both ways and the looking at the AIC and BIC (-estat ic- after each estimation).

To locate the turning point, assuming you stay with your quadratic model, it's

nlcom -_b[x]/(2*_b[x#x])

For slopes at high and low ends of x, I would pick representative high and low values of x, call them `x_high' and `x_low' and then run

margins, dydx(x) at(x = (`x_low' `x_high'))

[Sophie Dibbern]

Thank you very much!

I also learned that the results in the coefficient matrix are saved with the DV as a prefix when I use mixed. I need to indicate that when using utest --> utest x xsquared, pre(y)