What is the intercept term in a mixed effects model using orthogonal polynomials to model time? I'm using a mixed effects model (lmer) in R to model eye-tracking data using orthogonal polynomials (poly(time,3)) for time. The response variable is log(looks to target/looks to competitor). The fixed effects are condition, talker gender, accuracy, like so:
lmer(looks~(poly1+poly2+poly3)*condition*gender*accuracy+(1|stimulus)+(1|subject)

The polynomial time variables are of course, continuous (and centered), while the other factors are treatment coded so that each coefficient is compared to the baseline of the cells (where condition=0, gender=0, accuracy=0 (actually accuracy is recoded so that accurate trials are the baseline)). All of this is pretty much irrelevant because my question is more of a matter of mathematical interpretation.
I understand that the intercept reflects the estimate for the base level of each cell, but my question is-- what is the base level of the time polynomials? Mirman (2014) claims "For natural polynomials, the intercept term corresponds to the y-intercept [...] For orthogonal polynomials, the intercept term corresponds to the overall average [...] 'area under the curve'" (p. 48). While I don't claim to thoroughly understand mixed effects modeling (because matrix algebra!), it seems to me that the intercept should estimate a value for the zero points of the polynomials (so, at the midpoint of the linear time, at two points for the quadratic, and three points for the cubic, one of which is also the midpoint of the linear). 
While it would be very convenient for me to pretend that this is the average, I can't make this claim while I am still confused about the math.
Is there anyone who can explain to me whether my "5-point snapshot" hypothesis is correct, or if the intercept reflects the mean over time? I have no stake in which hypothesis is more accurate, but I don't want to misreport my results, and I would very much like to understand how mixed effects models work. Also, this is my first time posting a question here (though I've found many useful answers over the years), so please be kind even if you think I am completely stupid.
(Ref: Mirman, D. 2014. Growth Curve Analysis and Visualization Using R. CRC Press.)
 A: After some searching outside of my field, I came across Hedecker and Gibbons 2006 (http://rtksa.com/library1/wp-content/uploads/2015/11/523.pdf), who suggest that using a sufficiently large number of polynomials to model time will effectively yield an average over time for the intercept, but this is not the same thing as the mean over all the time values, but, as I suspected, the mean over the x-zero crossings (um, y-intercept, if you like), which will be evenly spaced for each orthogonal polynomial. If you have very many polynomial terms, this is likely very similar to a mean, but for the only three terms that I am interested in, it is too susceptible to random fluctuations, and will change based on which timepoint the zero-crossings happen to be at (such as I observe if I shift the center to the right or left by 20 ms). They suggest, in order to get a mean over time, to create an orthogonal constant (1*sqrt(n)) over all time, to replace the intercept term, which must be held to zero, so as to not have two factors predicting the same thing (and in fact, lmer will not run with both, but always drops one). So I have changed my analyses to reflect that, as such:
    lmer(looks~0+constant+(poly1+poly2+poly3)*condition*gender*accuracy+(1|stimulus)+(1|subject) 

and the result gives me essentially the same effects in the interactions, but additionally significant effects where they ought to have appeared for main effect coefficients, if they had represented a mean over time.
Does anyone know if this seems right, or am I just taking it upon myself to revise my field's understanding of mixed effects models using orthogonal polynomials? Any additional citions would be helpful, as I feel I am stepping out into uncharted territory, at least as far as my field has gotten.
