Displaying nominal data with a line graph Recently I stumbled across a line graph displaying a contingency table which I found was a very powerfull visualization. In my opinion it is very seldom that nominal data is displayed this way; usually plots like a bar plot, mosaic plot etc. are used (see here or here for example).
To illustrate I provide a) a bar plot, b) a mosaic plot and c) a line plot for the same data. The Titanic data shows the frequencies for the variables Survived (yes vs. no), Sex (males vs. females) and class (1st, 2nd, 3rd and crew). I only included adults in the plots.
a) Bar plot

b) Mosaic plot

c) Line plot

The line graph seems to clearly display what is going on, e.g. more males than females in total, class has a big effect on survival and so does sex, etc. Drawbacks of the line graph I can think of:

*

*The line goes through area were no category exists, e.g. there is nothing between first and second class. But: this seems to highlight what the changes between the categories are. It`s kind of like a piecewise regression which shows the slope between two adjacent categories.

*It is confusing if we would include confidence intervalls here because the ci must not follow the line. But: Mosaic plots can not display ci either.

What are other drawbacks of the line graph here? Considering the rare use of the line graph in this case I guess there must be more. Or am I wrong and line graphs are a legitim/ common way to display nominal data?

Beforehand: 2 groups
For binary nominal variables the line plot provides a clear representation where the slope shows how the frequency changes if we go from one group to the other. Consider the following line plot for the frequencies of sex:

Here the slope shows the change of the frequency between males and females.
The problem: >2 groups
Consider the line plot for the nominal variable hair colour, which in the following data has four groups:

Here, the lines shows changes between two adjacent groups, e.g. the line goes up from Black to Brown, meaning that there are more people with black hair than with brown.
For a nominal variable with k groups there are (k^2 + k)/ 2 possible comparisons. But the line plot only depicts the changes between two adjacent groups, i.e. k-1 slopes. Since nominal data has no natural order, the placement of the groups on the x axis is arbitrary. Thus, depicting nominal data with a line plot means highlighting the k-1 changes which are arbitrary choosen from (k^2 +k)/ 2 possible group comparisons. We can see this in the second plot: The plot shows the frequency increasment while we go from black to brown hair colour but the plot does not display the slope between black and red neither the one between black and blonde hair colour.
We can connect all possible group combinations with the line graph to provide complete information of the data but this is quite overhelming:

To sum up
For ordinal, interval and ratio variables the line plot makes sense because it displays the trend of the data. For nominal data the location of the groups is arbitrary placed on the x axis and the lines of the line plot connect only two adjacent groups, i.e. groups that by coincidence lay next to each other. This is missleading. On the other hand, connecting all possible group comparisons results in an overhelming plot.
