st: Obtaining (and testing difference among) coefficients of nonlinear interaction of continuous variables at specific values with xtmelogit

[Matthew Elba <matthew.elba@gmail.com>]

Dear Statalist members,

I have two questions about an analysis of a logistic multilevel
(random-intercept) model, which I’m running in xtmelogit in Stata.

In a nutshell, my question is (1) how obtain the actual coefficients -
rather than probabilities - for some variable X at specific values of
X and specific values of some other variable Z, and (2) how to test if
the difference between pairs of coefficients is significantly
different from zero.

Some background:
The model aims to show that there is a curvilinear by linear
interaction between independent variable X and moderator Z in
predicting Y. The nonlinear interaction emerges because Z moderates
the relationship between X and Y at low levels of X but not at high
levels of X. In other words, at low values of X, the slope of X is
much steeper for high values of Z than for low values of Z, whereas at
high values of X, the slope of X is more or less equally steep for
each value of Z. In yet other words, when Z is low, the relationship
of X to Y is curvilinear (i.e., a slope that is increasingly steep).
As Z increases, the relationship of X to Y becomes increasingly
linear.

Question 1:
I very much would like to show the dynamics of the nonlinear
interaction in a table, with in it, the coefficients for all values of
X (say, 1, 2, 3, 4, and 5) at specific values of Z (say, Zlow and
Zhigh). This way, I can show that the coefficients for the interaction
effect (i.e., the slopes) differ quite strongly at low values of X,
but not so much anymore at high values of X (because at that point,
all slopes are almost equally steep). The problem is that I don’t know
how to obtain these coefficients. Therefore, my question is: what
Stata command I should use to obtain them?

As an aside, this is the command I use to run the full model including
the curvilinear by linear interaction term (X2Z). The model
appropriately includes the linear by linear interaction term (XZ) as
well as the quadratic term for X (X2):

 . xtmelogit  y x z xz x2 x2z cov1 cov2 cov3 … || clustervariable:

In order to obtain coefficients at specific values of X and Z, it may
be that I will need to run a model that does not include the three
terms necessary to demonstrate the interaction (XZ, X2, X2Z). So I
would also like to know which model to run before using the command
that allows me to get the coefficients I want.

Question 2:
Supposing it is possible to obtain the coefficients as requested per
Question 1, is there a way to assess whether the coefficients for
specific values of X (1, .., 5) are statistically different from one
another at Zlow and Zhigh? If so, what Stata command do I need to use
to assess the statistical significance of the difference between two
coefficients (for Zlow and Zhigh) for specific values of X?

Any help is greatly appreciated. Many thanks in advance.

Best,
Matt

*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/