Interpreting results of npregress series (polynomial)

[Navya Kumar]

Hello Everyone,

Am working on Stata 17.

Following are my code and output:
Please note that Y is a binary outcome (0 and 1).
Am using the polynomial option, not allowing the Xs to interact with each other, and including a factor control asis.

. npregress series Y X1 X2 X3 X4 X5 X6 X7 X8 X9, nointeract(X1 X2 X3 X4 X5 X6 X7 X8 X9) asis(i.gender) polynomial

Computing approximating function

Minimizing cross-validation criterion

Iteration 0:  Cross-validation criterion =  .2065269

Computing average derivatives

Polynomial-series estimation               Number of obs      =            301
Criterion: cross-validation                Polynomial order   =                2
------------------------------------------------------------------------------
             |               Robust
           Y |     Effect   std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
          X1 |   -.090843    .042029    -2.16   0.031    -.1732184   -.0084676
          X2 |   .0012329   .0459111     0.03   0.979    -.0887512    .0912171
          X3 |   .0515722   .0271503     1.90   0.057    -.0016414    .1047858
          X4 |  -.0221318    .034087    -0.65   0.516     -.088941    .0446775
          X5 |   .1323169   .0408576     3.24   0.001     .0522375    .2123964
          X6 |     .02101   .0362033     0.58   0.562    -.0499472    .0919672
          X7 |   .0310251   .0384144     0.81   0.419    -.0442657    .1063159
          X8 |   .0662618    .024961     2.65   0.008     .0173391    .1151846
          X9 |   .0710502   .0317508     2.24   0.025     .0088197    .1332807
             |
      gender |
   (1 vs 0)  |   -.135051    .056472    -2.39   0.017    -.2457342   -.0243678
------------------------------------------------------------------------------

The effect for X1 is negative and significant.

Had this been a logistic regression, I may have interpreted that unit increase in X1 reduces the likelihood of Y being = 1 by ...

But here, I must interpret it as unit increase in X1 reduces Y by 0.09. Am I correct?

Also, I drew up the marginsplot for X1 for the actual range of X1 in the dataset.

margins, at(X1=(1(0.25)7))
marginsplot

This is the output:


So while the effect of X1 simply showed negative (-.091) in the output, the plot shows diminishing returns.
"Mean function" on y=axis and values of X1 on the x-axis

How am I to finally interpret the results?

Simply say increase in X1 reduces Y or that there is a diminishing returns relationship?

Please advise.

[Henrik Carlhoff]

From my understanding the shown effect for X1 is only an average derivative and does not describe the nature of the mean function. This can only be seen in the marginsplot.