First, you should not be looking at statistical significance. The American Statistical Association has recommended that this concept be abandoned and has devoted a full issue of its journal, The American Statistician to the topic. See https://www.tandfonline.com/doi/full...5.2019.1583913 for the lead summary article, and
https://www.tandfonline.com/toc/utas20/73/sup1 for the full issue (43 articles).
Your question about interpreting the -margins- output cannot be answered as stated because you have omitted crucial information. There are two different cases.
If your original regression included separate variables, one for the linear term and another for the quadratic, then the output of -margins- is simply incorrect and you have to go back and do it over using correct factor variable notation. The use of factor variable notation is absolutely required in order for -margins- to do correct calculations for models with interactions or with quadratic and higher order terms.
If you did use correct factor variable notation (c.Leverage##c.Leverage) to incorporate linear and quadratic leverage into your regression, then the output of -margins- correctly shows you the average marginal effect of Leverage taking into account both the linear and quadratic terms.
Do bear in mind that with non-linearities, such as quadratic terms, it is not meaningful to speak of "the" marginal effect of the variable: there is a different marginal effect corresponding to each value of the variable. So you can speak of marginal effects conditional on specific values of the variable (which you would have to specify using the -at()- option in -margins-) or you can speak of the average marginal effect, which is what you get from the code you show. But there is no such thing as "the marginal effect" of a variable that enters the model in a non-linear way.
That's right. In fact, not only do you not need to mention them in isolation, you can't do so in any meaningful way. Only their joint effect is meaningful.
https://www.tandfonline.com/toc/utas20/73/sup1 for the full issue (43 articles).
Your question about interpreting the -margins- output cannot be answered as stated because you have omitted crucial information. There are two different cases.
If your original regression included separate variables, one for the linear term and another for the quadratic, then the output of -margins- is simply incorrect and you have to go back and do it over using correct factor variable notation. The use of factor variable notation is absolutely required in order for -margins- to do correct calculations for models with interactions or with quadratic and higher order terms.
If you did use correct factor variable notation (c.Leverage##c.Leverage) to incorporate linear and quadratic leverage into your regression, then the output of -margins- correctly shows you the average marginal effect of Leverage taking into account both the linear and quadratic terms.
Do bear in mind that with non-linearities, such as quadratic terms, it is not meaningful to speak of "the" marginal effect of the variable: there is a different marginal effect corresponding to each value of the variable. So you can speak of marginal effects conditional on specific values of the variable (which you would have to specify using the -at()- option in -margins-) or you can speak of the average marginal effect, which is what you get from the code you show. But there is no such thing as "the marginal effect" of a variable that enters the model in a non-linear way.
Do I even need to mention the impact of these variables in isolation at all? I guess not!!
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