emmip (emmeans) with quadratic term - r

Question

Is it possible to plot with emmip the marginal (log odds) means from a geeglm model when you have a quadratic term? I have repeated measures data and the model fits better with a treatment x time squared term in addition to an interaction term with linear time.
I just want to be able to visualise the predicted curve in the data. If it's possible I don't know how to specify it. I've tried:
mod3 <- geeglm(outcome ~ treatment*time + treatment*time_sq, data = dat, id = id, family = "binomial", corstr = "exchangeable"))
mod3a.rg <- ref_grid(mod3, at = list(time = c(1,2,3,4,5,6), time_sq = c(1,4,9,16,25,36)))
emmip(mod3a.rg, treatment ~ time)

Answer 1

I don't think your mod3 is including your quadratic term correctly (hard to tell since you did not include reproducible code). This will let you include your squared term for time correctly:
mod3 <- geeglm(outcome ~ treatment*time + treatment*I(time^2), data =
dat, id = id, family = "binomial", corstr = "exchangeable"))
The add plotit = TRUE to your call to emmip():
emmip(mod3a.rg, treatment ~ time, plotit = TRUE)
Here's a simple reproducible example with the savings dataset in the MASS, faraway package for comparison
library(MASS)
data(savings, package="faraway")
#fit model with polynomial term
mod <- lm(sr ~ ddpi+I(ddpi^2))
summary(mod)
The summary produces this output, note the additonal coefficient for your quadratic term
> Call: lm(formula = sr ~ ddpi + I(ddpi^2), data = savings)
>
> Residuals:
> Min 1Q Median 3Q Max
> -8.5601 -2.5612 0.5546 2.5735 7.8080
>
> Coefficients:
> Estimate Std. Error t value Pr(>|t|)
>(Intercept) 5.13038 1.43472 3.576 0.000821 ***
>ddpi 1.75752 0.53772 3.268 0.002026 **
>I(ddpi^2) -0.09299 0.03612 -2.574 0.013262 *
> --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>
> Residual standard error: 4.079 on 47 degrees of freedom Multiple
> R-squared: 0.205, Adjusted R-squared: 0.1711 F-statistic: 6.059 on
> 2 and 47 DF, p-value: 0.004559
If you don't enclose the quadratic term with I() your summary will only include the term for ddpi.
mod2 <- lm(sr ~ ddpi+ddpi^2)
summary(mod2)
produces the following summary with a coefficient only for ddpi
> lm(formula = sr ~ ddpi + ddpi^2, data = savings)
>
> Residuals:
> Min 1Q Median 3Q Max
> -8.5535 -3.7349 0.9835 2.7720 9.3104
>
> Coefficients:
> Estimate Std. Error t value Pr(>|t|)
>(Intercept) 7.8830 1.0110 7.797 4.46e-10 ***
>ddpi 0.4758 0.2146 2.217 0.0314 *
> --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>
> Residual standard error: 4.311 on 48 degrees of freedom Multiple
> R-squared: 0.0929, Adjusted R-squared: 0.074 F-statistic: 4.916 on
> 1 and 48 DF, p-value: 0.03139