Test Nonlinear/Squared/Quadratic/Curvilinear Moderating Effect with utest

[Johannes Szczepanski]

Hi everyone,

currently I am investigating a regression model with nonlinear moderating effect (XZ²):

The significance of b₅ indicates a nonlinear moderating effect between X and Y (see Dawson 2014).

Given the significance of this effect, I am wondering if the effect can be tested using the "utest.ado" by typing the follwoing:

utest XZ XZ², fieller level(90)

Furthermore I am wondering if the curve can be plotted as follows:

sum Z
margins, dydx(X) at (Z = (min (.1)max))
marginsplot, recast(line) noci

Can anyone help in that regard?

Best Regards
Johannes

[Clyde Schechter]

The significance of b₅ indicates a nonlinear moderating effect between X and Y (see Dawson 2014).

References like (Dawson 2014) are not helpful. If you feel the need to provide a reference, provide a full one that will enable people to actually find it. Dawson 2014 may be folklore in your circles, but I assure you many others on the Forum have not heard of it and have no idea where to find it.

That said, I wouldn't make much, if anything, of that. It would make absolutely no sense at all to have a model that omitted the XZ² term but retained the Z, Z², and XZ terms. If you keep both Z and Z² in the model, then the effect of Z is represented by both of those terms jointly and neither one alone can be considered the effect of Z. Any effect moderation would only be properly specified if it interacted X with both of those variables. It does not matter whether the coefficient of one or the other were individually "not significant." In fact, it wouldn't matter if both of them were "not significant"--the only meaningful test for interaction here would be a joint test of b4 and b5.

And all of that is predicated on still believing in the concept of statistical significance, which the American Statistical Assocation has recommended be abandoned. See https://www.tandfonline.com/doi/full...5.2019.1583913.

I am not terribly familiar with the -utest- command, as, when dealing with quadratic models, I tend to just hand code whatever estimations or tests I need. But to the best of my knowledge, it would not apply to this kind of situation.

Furthermore I am wondering if the curve can be plotted as follows:

There are several curves that might be of interest after fitting this type of model. I don't know which one you have in mind. The code you show would give you a plot of the marginal effect of X as a function of Z.

[Phil Bromiley]

First, you need to specify the estimation using factor variable notation. Otherwise, you have to specify values for z and z squared in the margins statement - factor variable notation is much easier so something like:
reg y x z c.z#c.z c.x#c.z c.x#c.z#c.z


You also are likely to want to use margins without the dydx - you probably want to plot predicted values not derivatives. I don't know if the margins syntax takes min/max or not. But you also want to set the value of the interacting variable. Something like:

margins, at(Z = (1 (.1)5) X=(0 1))
marginsplot

By giving a lot of values for z and only two for x, marginsplot knows you want to plot the predicted value vs X at different values of x.

At least some U-tests just run linear models for values of the non-linear variable on subsamples where one subsample is observations corresponding to the full estimate's up slope and the second the values that look like the down slope.