Interpretation of the linear term in a quadratic estimation

[Dapeng Cheng]

Hello Stata Experts,

I am running a GEE model. I expect that the independent variable has a non-linear relationship with the dependent variable.

So I first run the linear model:

xtgee DV IV control, i(id) family(nb 3.2) corr(independent) vce(robust)

the coefficient of IV is insignificant (b=-0.226)

then I run the quadratic model:

xtgee DV IV IV^2 control i(id) family(nb 3.2) corr(independent) vce(robust)

the coefficient of linear IV is significant (b1=-0.567, p < 0.05) and that of quadratic IV is insignificant (b2=0.094).

My question is how I should interpret the significance of the linear term in a quadratic equation when the coefficient of the quadratic term is insignificant? Thanks.

[Phil Bromiley]

You will increase your chances of useful answer by following the FAQ on asking questions.

Part of what you're seeing is the problem in using the magic .05 as a decision criterion. Your training .05 significance is important but .09 as irrelevant. I would assume that if you do a likelihood test you'll find that the nonlinear model is better than the linear. The second set of results clearly indicate the variable influences the outcome and it has a positive linear influence. It's not clear what you are telling us about the squared term – are you actually giving us the parameter or you giving us the parameters statistical probability level?