Interpretation of coefficients with polynomials

#1
Dear Talk Stats Users,
I want to interpret my regression output of my fixed effects model. I am looking at political interest and the independet variables I include are period and cohort. All terms I included are nonlinear, I included cohort as cubic in my model. My independent variables are standardised. (I will include a picture of my margins plot and regression table).
I have a question concering the interpretation the coefficients of my model. While my marginsplot shows me that my margins for cohort increase, my term for the linear effect is negative. How I understood it, it is convex, and as I understood it so far, my linear effect shows me my effect if x is 0? How do I then interpret the linear term or
do I not interpret it att all and only look at the margins? I there a way to transform the data so that the coeffients makes sense? What is the common way to do this?
(ok in the marginsplot is the variablename for cohort)
I am Thankful for any help!
Sarah
stattalktable.PNG margstattalk.png
 

hlsmith

Less is more. Stay pure. Stay poor.
#2
I didn't follow. Perhaps if you describe the variable and you provide a toy data frame, we can better follow along.

Your issues are that you used polynomials of standardized terms in the model? Many times in GAMs you just present the figure and perhaps if really needed pieceswise estimates of certain sections of the fitted spline.