2
$\begingroup$

I have fit parabolas to two groups in a growth curve analysis (GCA) of eye tracking data using orthogonal polynomials (essentially by following Dan Mirman's example for his paper with Magnuson in 2009, Dynamics of activation of semantically similar concepts during spoken word recognition, which is also carried out similarly in this growth curve analysis vignette from http://www.eyetracking-r.com, which is what I used). The interaction between the orthogonal quadratic term and variable of interest, Sex, is significant, which can be seen on the graph below: The parabolas are indeed slightly different across the two sexes.

However, the main effect for Sex has a very large p-value (0.949), which makes sense to me, as I don't think these two groups are actually statistically different, despite the significant interaction term (again, conclusion supported by the plot).

I'm wondering if those experienced in GCAs can help me interpret the output in terms of the interactions and main effects in this instance. Is it appropriate to look at the main effect's p-value alone, despite the significant interaction term? Any peer-reviewed sources that specifically discuss this would be much appreciated.

Here is the plot:

GCA plot

And here are the hypothesis test results associated with this plot. They were obtained via the drop1() function, employing likelihood ratio tests. Note the variable Sex was coded with deviation coding (-0.5, 0.5), then subsequently centered. ot1 and ot2 are the orthogonal linear and quadratic terms, respectively.

                       npar   AIC     LRT   Pr(Chi)    
<none>                      44701                      
Sex_c_centered            1 44699   0.004  0.948733    
ot1                       1 44836 136.551 < 2.2e-16 ***
ot2                       1 44815 116.134 < 2.2e-16 ***
Sex_c_centered:ot1        1 44703   4.249  0.039285 *  
Sex_c_centered:ot2        1 44707   7.971  0.004752 **
Improve this question
$\endgroup$
16
  • $\begingroup$ It's standard practice when introducing an interaction into a regression to focus on the interaction, ignoring the main effect parameters used to create it. $\endgroup$
    – user78229
    Commented Aug 12, 2020 at 14:56
  • 1
    $\begingroup$ What is your hypothesis you really want to test? Your table of p-values just gives tests of model coefficients, it is not obvious that those are your real interest! That the Sex main effect is insignificant just says that on average, there is no sex difference. If that is your hypothesis, fine. $\endgroup$
    – kjetil b halvorsen ♦
    Commented Aug 12, 2020 at 15:18
  • $\begingroup$ @MikeHunter Unless you want to interpret simple effects, which is what I am trying to do here. $\endgroup$
    – Meg
    Commented Aug 12, 2020 at 17:45
  • $\begingroup$ 1/2 Thanks, @kjetil b halvorsen. You're correct that I'm not truly interested in the magnitude of the estimates here, but obviously their size plays in the associated hypothesis test's results. You're also correct that yes, what I'm trying to get at here is whether or not there is evidence of a difference in sex. My understanding was the same as what you wrote - on average, there is no evidence of a difference in sex. This seems obvious when you look at the plot, and thus the p-value makes sense in this way. However, I wasn't sure about how to deal with the interaction term. $\endgroup$
    – Meg
    Commented Aug 12, 2020 at 17:45
  • $\begingroup$ 2/2 Namely, I'm trying to reconcile the "on average" interpretation of the test of the Sex_c_centered predictor mathematically. Presumably, it has to be interpreted when ot1 and ot2 are set to 0, so would it be correct that this is then a test of the simple effect of Sex? Further, setting the orthogonal polynomials to 0 equates to ignoring the change over the time-course, which then equates to pooling the data together for each group (male and female), and hence is a test of male vs. female (Sex), on average (over the time-course)? Is this wording/interpretation reasonable? $\endgroup$
    – Meg
    Commented Aug 12, 2020 at 17:46

1 Answer 1

Reset to default
1
$\begingroup$

I think this is essentially the answer I was looking for: In Barr (2008): Analyzing ‘visual world’ eyetracking data using multilevel logistic regression, it is stated: "With orthogonal polynomials, the interpretation of each term in the equation is independent of all other terms (i.e., inclusion of a higher-order term does not change its interpretation). Thus, the intercept term gives the mean height of the curve over the entire analysis window..."

So, according to Barr (2008), it seems the p-value associated with the Sex_c_centered term could independently compare the mean outcome of the two sexes over the entire time-course (despite the other terms in the model). In light of this, it seems the associated p-value should indeed be a test of whether or not these two groups are different on average with respect to the outcome (which, here, is proportions that have been transformed with the empirical logit transformation (this is what Elog means on the y-axis of the plot)).

I was a little concerned about how to interpret the deviation (-0.5/0.5) coding here, but I think because there are only two groups, it doesn't matter. Namely, according to https://stats.idre.ucla.edu/spss/faq/coding-systems-for-categorical-variables-in-regression-analysis-2/#DEVIATION%20EFFECT%20CODING, it says, "DEVIATION CODING: This coding system compares the mean of the dependent variable for a given level to the mean of the dependent variable for the other levels of the variable. In our example below, the first comparison compares level 1 (hispanics) to all 3 other groups, the second comparison compares level 2 (Asians) to the 3 other groups, and the third comparison compares level 3 (African Americans) to the 3 other groups." Since in this study, Sex is composed of only males and females, comparing "level 1" (e.g.) to "all other groups" would just be comparing males to females here.

I am leaving this here as a tentative answer in case it is helpful, but am still open for feedback if something about this seems amiss.

Improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.