Wednesday, June 13, 2012

Concordance, Correlation, Agreement -- Plots

Stata Command
Frequency Table Plot
Created by the prolific Nicholas Cox (Durham University, UK), this command “plots a table of frequencies, fractions or percents in graphical form” (Stata help file).  Well over a dozen options exist to sex up the plots.  A handy graphic to visually assess concordance between two categorical variables. 
(Cumulative) Distribution Plot
Also authored by Nick Cox, these plots chart the cumulative distribution of one or more variables.  Although the two plots are subtly different, they essentially produce plots of cumulative distributions as the proportion or frequency ≤ to each value.  The first command, -distplot-, appears to be a succession of the latter command, -ordplot-, although –ordplot- explicitly specifies that the variable be ordinal.  
Paired Observation Plot
Again, credit goes to Nick Cox.  This plot is ideally suited for paired data sharing a time component (e.g. before/after).  The barebones command requires two y-variables where the difference or ratio between the two is plotted on the y-axis and the observation number on the x-axis.  Helpful for visualizing change between two finite points by subject.
Two-dimensional Biplot
This official Stata command plots the relationship between observations and variables.  The graph returned plots the observations as points and the relative position of the variables as arrows.  This command seems helpful in visualizing where observations and variables cluster as well as correlation between the variables.
Bland-Altman Plot
First published by Bland and Altman in 1983, this graph assesses measure of agreement between two variables.  The authors used continuous variables in their paper but note that categorical variables can also be analyzed.  The plot is intended as a replacement to using the correlation coefficient to assess agreement.  The graph plots the difference of two (paired) variables versus their average and state that with this plot “it is much easier to assess the magnitude of disagreement (both error and bias), spot outliers, and see whether there is any trend” (Altman & Bland, 1983).  Another Brit, Paul Seed, wrote the Stata programs for these plots. 

Although I'm no longer planning to use any of these concordance plots or tests for my dissertation, I figured I'd post them anyway since I went to the trouble of jotting them down on my whiteboard.  (I also need the whiteboard space and wanted to move the information online before unceremoniously erasing my table.) 

This isn't intended to be an exhaustive list of all the tests and techniques for assessing concordance but I think I managed to get a fair number of them.  If nothing else, this can be used as a good jumping off point for further research.

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