loess regression on each group with dplyr::group_by()

This is a neat Tidyverse way to make it work:

library(dplyr)
library(tidyr)
library(purrr)
library(ggplot2)

models <- fems %>%
        tidyr::nest(-CpG) %>%
        dplyr::mutate(
                # Perform loess calculation on each CpG group
                m = purrr::map(data, loess,
                               formula = Meth ~ AVGMOrder, span = .5),
                # Retrieve the fitted values from each model
                fitted = purrr::map(m, `[[`, "fitted")
        )

# Apply fitted y's as a new column
results <- models %>%
        dplyr::select(-m) %>%
        tidyr::unnest()

# Plot with loess line for each group
ggplot(results, aes(x = AVGMOrder, y = Meth, group = CpG, colour = CpG)) +
        geom_point() +
        geom_line(aes(y = fitted))

You may have already figured this out -- but if not, here's some help.

Basically, you need to feed the predict function a data.frame (a vector may work too but I didn't try it) of the values you want to predict at.

So for your case:

fems <- fems %>% 
  group_by(CpG) %>% 
  arrange(CpG, AVGMOrder) %>% 
  mutate(Loess = predict(loess(Meth ~ AVGMOrder, span = .5, data=.),
    data.frame(AVGMOrder = seq(min(AVGMOrder), max(AVGMOrder), 1))))

Note, loess requires a minimum number of observations to run (~4? I can't remember precisely). Also, this will take a while to run so test with a slice of your data to make sure it's working properly.