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I'm wondering if there is a name for one to one line graphs. Is it qq-plots? Is the qq-plots applicable on all types of variables or only quantiles? In other words, what's the name of the graph that compare two variables to assess if one variable is overestimating the other in relation to a 1:1 line?

If I want to built a one to one line plot, how should I standardized my variables so that the are comparable on the one to one line?

For example, here is a one to one line graph. 

plot(x= 1:100, y = c(12*(1:100)^(1/2) + rnorm(1,1,1)), 
     asp = 1, xlim = c(0,100),ylim = c(0,100)) ; abline(a=0, b = 1, col = "red")

enter image description here

In that case, we could say that the y variable is alway overestimated in comparison of the x variable.

gung - Reinstate Monica
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M. Beausoleil
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  • I don't understand, what would like to do exactly? A qq plot is used to compare if two distributions are identical or, if not, where they differ – Repmat Sep 12 '16 at 18:55
  • For example, I would like to see if two different models are estimating similar some parameters in the same way. So my approach was to compare the parameter output of one model (y axis) and the parameter output of the second model (x axis) and see if the are identical (would sit on a 1-1 line graph perfectly) or different (could be overestimated consistently if above the 1-1 line or underestimate if below the 1-1 line). I could also look at the shape of the distribution of the parameters in the 1-1 line graph. It's a way I found useful to compare models. It's graphical. – M. Beausoleil Sep 12 '16 at 19:09
  • Sorry this question is still completely unclear to me. Do you want am official name for this kind of plot? Do you want advice on how to standardize? If so please clarify on data, and model information etc – Repmat Sep 12 '16 at 19:17
  • 1. I want a name if possible 2. If you have advices on how to make this kind of graph, you're welcome! 3. this is fake data, it's only to show my argument. – M. Beausoleil Sep 12 '16 at 19:35
  • Even if this has a name, it might not be so useful, because there are better ways to compare two sets of data. Ordinarily one computes *residuals*--usually either their differences or ratios--to compare each pair of results, and then plots the residuals against some other quantity to see how the differences in the data vary with that quantity. To get a sense of how important and ubiquitous residuals are, [search our site](http://stats.stackexchange.com/search?q=residual): five percent of all posts mention them. – whuber Sep 12 '16 at 20:03
  • A name I've seen here and there is _calibration plot_ whenever there is some question of plotting observed versus fitted or predicted or other observed, and equality is a benchmark level. – Nick Cox Nov 03 '20 at 17:43

2 Answers2

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The official name of the line is 'identity line' or 'line of equality'. And if you are comparing measured data with predicted data, or two different models, you should standardize the axis. The starting and ending point of both axes should be the same. You can also plot the trend line in the scatter plot (measured ~ predicted) to better visualize the difference between the 1:1 line and the actual trend in the model.

Mathematically, it can be written as the line where: $$y = x$$

M. Beausoleil
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Daniel Augusto da Silva
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    I don't know in what sense that term is "official". Also known as line of equality. – Nick Cox Nov 03 '20 at 17:42
  • "Identity line", or "line of equality", is the name of the *1:1 line*, but not of the *plot*. I would advise against standardizing the data, as that can obscure some of what you'd like to be able to see. Otherwise, this is good. – gung - Reinstate Monica Nov 03 '20 at 21:01
  • Thanks! As I understand it now, the name of the plot will change depending what you are doing. But I didn't know that there was a name for the line. So now I can say "the regression plot is shown with a line of equality" or something similar. – M. Beausoleil Nov 04 '20 at 00:02
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Based on your comment, I think what you are ultimately after is to assess agreement (see Wikipedia, or John Uebersax's website). I don't think there is a name for the plot you have in mind. I would just call it a scatterplot with a 1:1 reference line plotted. I think that's probably fine to do. I would not standardize your variables first, as that would prevent the plot from showing what you want to discover. If you wanted a quantitative value to describe the level of agreement, you could compute Lin's concordance coefficient to pair with your plot.

However, note that it is typically more difficult for people to assess agreement in this way. You might prefer to create a Bland-Altman plot (also called Tukey's mean-difference plot). You can see if the differences diverge from mean $0$ (and test them with a $t$-test), if the differences vary more at higher levels, if there is any residual curvature, etc.

If you just want to see if the distributional shapes differ, you can do a qq-plot as well, but I don't think that's what you're after.

gung - Reinstate Monica
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  • Bland-Altman is a common term in medical statistics. Neither Martin Bland nor Doug Altman claim to have invented that plot. Some earlier users include Neyman and Tukey. – Nick Cox Nov 03 '20 at 17:45