Interpreting margin and marginplot

[Marc Pelow]

Hi everyone,

I'm working on estimating a negative binomial regression model with the following (simplified) specification:

Y=β0+β1Narcissism+β2Celebrity+β3(Narcissism×Celebr ity)+β4Controls

• Y is a count variable ranging from 0 to 4.
• Narcissism is a continuous variable ranging from -1.5 to 6.
• Celebrity is a binary variable (1 if the individual is a celebrity, 0 if not).

I'm primarily interested in the moderating effect of Celebrity on the relationship between Narcissism and Y. Specifically, I want to know if the impact of an individual's narcissism on Y differs between celebrities and non-celebrities.

Regression output

Negative binomial regression                            Number of obs =    648
                                                        Wald chi2(39) = 113.89
Dispersion: mean                                        Prob > chi2   = 0.0000
Log pseudolikelihood = -410.97166                       Pseudo R2     = 0.0868

-------------------------------------------------------------------------------------------------------
                                      |               Robust
                                    Y | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
--------------------------------------+----------------------------------------------------------------
                          1.Celebrity |   .1967454   .2577428     0.76   0.445    -.3084212    .7019121
                           Narcissism |   -.111148   .1610676    -0.69   0.490    -.4268346    .2045386
                                      |
               Celebrity#c.Narcissism |
                                   1  |   .9446963   .3442989     2.74   0.006     .2698828     1.61951

The interaction term between Narcissism and Celebrity is highly significant. Now, I would like to break down and visualize this interaction. Here's what I've done so far:

1. Differences in Slopes by Celebrity Status:

margins Celebrity, dydx(Narcissism)

Output:

Average marginal effects                                   Number of obs = 648
Model VCE: Robust

Expression: Predicted number of events, predict()
dy/dx wrt:  Narcissism

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
Narcissism   |
   Celebrity |
          0  |  -.0322268   .0472799    -0.68   0.495    -.1248936    .0604401
          1  |   .5637967   .7154872     0.79   0.431    -.8385325    1.966126
------------------------------------------------------------------------------

As you can see, the slopes I obtained are:
For non-celebrities: − 0.0322268
For celebrities: 0.5637967

Does this imply that a one-unit increase in Narcissism is associated with a decrease in Y for non-celebrities, and an increase in Y for celebrities when all covariates are at their average level? Or is such a conclusion not valid given the non-significant results? I want to make sure I am interpreting the direction of these effects correctly.

Next, I wanted to visualize the interaction term and its implications. I used the following commands:

margins Celebrity at(Narcissism=(0 1 2 3 4 5))
marginsplot

Output:




From the plot, it seems that the influence of Celebrity status on the effect of Narcissism becomes more pronounced at higher levels of Narcissism. Could you help confirm whether this interpretation is accurate? Are there any nuances in the plot that I might be missing? I am especially curious about the large CI at narcissism = 5.

Thank you!