I am using linear mixed models to investigate change over time on the score on a questionnaire, which was administered at 5 points in time. While I hypothesized a decline, I had no a priori assumptions as to how this decline would look (whether it's linear or not). After visually checking the trajectory, I did see the slope become steeper after the second time point, and thus I thought I'd need to add polynomials and see what model fits the data better—but correct me if I'm wrong.
I created an initial model (Model 1) with just the variable Time as a predictor of Score. Here, Time was a significant predictor (β = -3.8, p < .001).
Next, I wanted to know whether a quadratic or cubic slope model fitted my data better, so I added a second-order polynomial (Time * Time), along with Time, in Model 2. Model fit significantly increased (comparing -2LL between Models 1 and 2 with a chi square test). Here, the polynomial was significant (β = -4.6, p = .007), which I believe suggests a non-linear slope for decline in Score over time. However, Time was no longer significant (β = 0.2, p = .905), yet in all examples I could find, both the linear and quadratic predictors were significant.
My question is, how should I interpret the fact that Time is not a significant predictor in this model? Can I still conclude that a quadratic slope best represents my data, even if the linear slope is no longer significant?