Plotting cross validated regression coefficients across folds

Question

Given a cross validated generalised linear model with about 5-10 coefficients across 10 folds, is it appropriate to plot all the coefficients on one graph using multiple line charts? That is:

1. Have the folds numbered 1 to 10 on the x-axis.
2. Plot a line chart for each model covariate, so that the y-value is the model coefficient for that covariate on the respective fold.

I would like to do this as it shows:

1. How the model coefficients compare to each other in scale.
2. The flatness of the line shows the stability of the coefficients to some extent.

What I do not like is:

1. There is no linear relationship between the folds so a line chart would not be usually suitable; in other cases like this a scatterplot or bar plot would be preferred.
2. The horizontal width of the plot artificially affects the flatness of the line.

Does anyone have any comments on this methodology or can recommend other ways of showing the cross validated coefficients?

Answer 1

First, to add one more point to your list of drawbacks of the proposed plot: as the folds are (usually) drawn at random and interpreted to be random, there is no reason why fold 2 should be in between folds 1 and 3: the order along the x axis is also random.

Here is what I do:

source: C. Beleites, K. Geiger, M. Kirsch, S. B. Sobottka, G. Schackert and R. Salzer: Raman spectroscopic grading of astrocytoma tissues: using soft reference information, Anal. Bioanal. Chem., 400 (2011), 2801 - 2816. DOI: 10.1007/s00216-011-4985-4
AAM version

Note that the data are spectra, so there is an inherent relationship between the variates that makes a line plot of the coefficients a sensible and common choice.
Also, that plot was produced from 125$\times$ repeated/iterated $8$-fold cross validation. An overlay plot of 1000 lines would have been a mess, so I plotted median and quartiles instead.

• If the model (co)variates do not have such an inherent relationship lines are clearly not indicated. I'd preferrably go for facets unless that makes the plot too crowded.
• If only few surrogate models were calculated, I'd go for a dot plot, with many surrogate models for a box plot or something similar.

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• If you facet (co)variates, and have an idea how the coefficient values are distributed, you could put QQ-plots into the facets.