R ggplot double y-axis, log10 and continuous

Question

This question was closed for no reason, the provided link to a similar question does NOT provide an answer for this specific problem.

How can I have two different plots in one graph, with two separate y-axis, and with different scales?

   df <- data.frame(x=3:22,
                   y1=c(3, 4, 5, 7, 9, 13, 15, 19, 23, 24, 29,
                       38, 40, 50, 56, 59, 70, 89, 104, 130),
                   y2=c(1,2,3,4,4,5,5,6,6,7,6,5,5,5,4,4,3,3,2,1))
  
  
  
  ylim.prim <- c(min(df$y1), max(df$y1))
  ylim.sec <- c(min(df$y2), max(df$y2))
  b <- diff(ylim.prim)/diff(ylim.sec)
  a <- ylim.prim[1] - b*ylim.sec[1] 
  
  
  ggplot(df, aes(x=x)) +
    geom_line(aes(y=y1))+
    geom_line(aes(y = a + y2*b))+
    scale_y_continuous(sec.axis = sec_axis(~ (. - a)/b))

So with this, I can plot a double y-axis, but I would like either the left or the right one to be in log-scale. Does anyone have an idea how to do that? I would like to highlight, that each axis belongs to one of the two geom_lines.

exemplary real data:

df<-structure(list(x = c(0.3499125, 8.347913, 16.34591, 24.34391, 
                     32.34191, 40.33992, 48.33792, 56.33592, 64.33392, 72.33192, 80.32992, 
                     88.32792, 96.32592, 104.3239, 112.3219, 120.3199, 128.3179, 136.3159, 
                     144.3139, 152.3119, 160.3099, 168.3079, 176.3059, 184.3039, 192.3019, 
                     200.2999, 208.2979, 216.2959, 224.2939, 232.2919, 240.2899, 248.2879, 
                     256.2859, 264.2839, 272.2819, 280.2799, 288.2779, 296.2759, 304.2739, 
                     312.2719, 320.2699, 328.2679, 336.2659, 344.2639, 352.2619, 360.2599, 
                     368.2579, 376.2559, 384.2539, 392.2519, 400.2451, 408.0882, 415.9314, 
                     423.7745, 431.7164, 439.6766, 447.6368, 455.597, 463.5572, 471.5174, 
                     479.4776, 487.4378, 495.398, 503.3582, 511.3184, 519.2786, 527.2465, 
                     535.234, 543.2215, 551.209, 559.1966, 567.1841, 575.1716, 583.1591, 
                     591.1466, 599.1342, 607.1217, 615.1092, 623.0967, 631.0842, 639.0718, 
                     647.0593, 655.0468, 663.0343, 671.0218, 679.0094, 686.9969, 694.9844, 
                     702.9719, 710.9594, 718.947, 726.9345, 734.922, 742.9095, 750.897, 
                     758.8846, 766.8721, 774.8596, 782.8471, 790.8346, 798.8222, 806.8097, 
                     814.7972, 822.7847, 830.7722, 838.7598, 846.7413, 854.7015, 862.6617, 
                     870.6219, 878.5821, 886.5423, 894.5025, 902.4627, 910.4229, 918.3831, 
                     926.3433, 934.3035, 942.2637, 949.9737, 957.7313, 965.6915, 973.6517, 
                     981.6119, 989.5721, 997.5323, 1005.493, 1013.453, 1021.413, 1029.373, 
                     1037.333, 1045.294, 1053.254, 1060.905, 1068.657, 1076.5, 1084.343, 
                     1092.245, 1100.232, 1108.22, 1116.207, 1124.195, 1132.183, 1140.17, 
                     1148.158, 1156.145, 1164.133, 1172.12, 1180.108, 1188.095, 1196.083, 
                     1204.07, 1212.058, 1220.045, 1228.033, 1236.02, 1244.008, 1251.995, 
                     1259.983, 1267.97, 1275.958, 1283.945, 1291.933, 1299.92, 1307.908, 
                     1315.895, 1323.883, 1331.871, 1339.858, 1347.846, 1355.833, 1363.821, 
                     1371.808, 1379.796, 1387.783, 1395.771, 1403.758, 1411.683, 1419.488, 
                     1427.293, 1435.234, 1443.214, 1451.195, 1459.175, 1467.155, 1475.135, 
                     1483.115, 1491.095, 1499.075, 1507.055, 1515.035, 1523.015, 1530.995, 
                     1538.975, 1546.955, 1554.935, 1562.915, 1570.895, 1578.875, 1586.855, 
                     1594.835, 1602.815, 1610.796, 1618.776, 1626.756), y2 = c(2.27, 
                                                                               2.27, 2.27, 2.27, 2.27, 2.27, 2.27, 2.27, 2.27, 2.27, 2.27, 2.27, 
                                                                               2.27, 2.27, 2.27, 2.27, 2.27, 2.27, 2.27, 2.27, 2.27, 2.27, 2.27, 
                                                                               2.27, 2.27, 2.27, 2.27, 2.27, 2.27, 2.27, 2.27, 2.27, 2.27, 2.27, 
                                                                               2.27, 2.27, 2.27, 2.27, 2.27, 2.27, 2.27, 2.27, 2.27, 2.27, 2.27, 
                                                                               2.27, 2.27, 2.27, 2.27, 2.27, 2.300344, 2.300344, 2.300344, 2.300344, 
                                                                               2.356774, 2.356774, 2.356774, 2.356774, 2.356774, 2.356774, 2.356774, 
                                                                               2.356774, 2.356774, 2.356774, 2.356774, 2.356774, 2.35672, 2.35672, 
                                                                               2.35672, 2.35672, 2.35672, 2.35672, 2.35672, 2.35672, 2.35672, 
                                                                               2.35672, 2.35672, 2.35672, 2.35672, 2.35672, 2.35672, 2.35672, 
                                                                               2.35672, 2.35672, 2.35672, 2.35672, 2.35672, 2.35672, 2.35672, 
                                                                               2.35672, 2.35672, 2.35672, 2.35672, 2.35672, 2.35672, 2.35672, 
                                                                               2.35672, 2.35672, 2.35672, 2.35672, 2.35672, 2.35672, 2.35672, 
                                                                               2.35672, 2.35672, 2.35672, 2.436441, 2.436441, 2.436441, 2.436441, 
                                                                               2.436441, 2.436441, 2.436441, 2.436441, 2.436441, 2.436441, 2.436441, 
                                                                               2.436441, 2.436441, 2.593907, 2.436372, 2.436372, 2.436372, 2.436372, 
                                                                               2.436372, 2.436372, 2.436372, 2.436372, 2.436372, 2.436372, 2.436372, 
                                                                               2.436372, 2.436372, 2.32186, 2.362217, 2.362217, 2.362217, 2.356666, 
                                                                               2.356666, 2.356666, 2.356666, 2.356666, 2.356666, 2.356666, 2.356666, 
                                                                               2.356666, 2.356666, 2.356666, 2.356666, 2.356666, 2.356666, 2.356666, 
                                                                               2.356666, 2.356666, 2.356666, 2.356666, 2.356666, 2.356666, 2.356666, 
                                                                               2.356666, 2.356666, 2.356666, 2.356666, 2.356666, 2.356666, 2.356666, 
                                                                               2.356666, 2.356666, 2.356666, 2.356666, 2.356666, 2.356666, 2.356666, 
                                                                               2.356666, 2.356666, 2.356666, 2.356666, 2.6, 2.6, 2.6, 1.38, 
                                                                               1.38, 1.38, 1.38, 1.38, 1.38, 1.38, 1.38, 1.38, 1.38, 1.38, 1.38, 
                                                                               1.38, 1.38, 1.38, 1.38, 1.38, 1.38, 1.38, 1.38, 1.38, 1.38, 1.38, 
                                                                               1.38, 1.38), y1 = c(1.0121711505181e-12, 1.36703949435522e-12, 
                                                                                                   1.84632494858934e-12, 2.49364868526704e-12, 3.36792573591631e-12, 
                                                                                                   4.54872499912722e-12, 6.14351261535188e-12, 8.29743536886833e-12, 
                                                                                                   1.12065270336094e-11, 1.5135549574501e-11, 2.04420900737953e-11, 
                                                                                                   2.76091094527446e-11, 3.7288908764166e-11, 5.03624430409839e-11, 
                                                                                                   6.80195634790675e-11, 9.1867308143082e-11, 1.24076096081818e-10, 
                                                                                                   1.67577290537946e-10, 2.26330068874485e-10, 3.05681854075198e-10, 
                                                                                                   4.12854243103824e-10, 5.57601379152127e-10, 7.53097024416113e-10, 
                                                                                                   1.01713383727135e-09, 1.37374208059794e-09, 1.85537854367786e-09, 
                                                                                                   2.50587585968424e-09, 3.38443865549292e-09, 4.57102650080046e-09, 
                                                                                                   6.17363418887535e-09, 8.33811836170825e-09, 1.12614720154805e-08, 
                                                                                                   1.52097587979964e-08, 2.05423179929812e-08, 2.77444811472099e-08, 
                                                                                                   3.74717262176886e-08, 5.06093638045714e-08, 6.83530636095683e-08, 
                                                                                                   9.23177269923811e-08, 1.24684445803943e-07, 1.68399029805712e-07, 
                                                                                                   2.2743990730289e-07, 3.07180534936803e-07, 4.14878418164378e-07, 
                                                                                                   5.60335245682253e-07, 7.56789448222779e-07, 1.02212079550612e-06, 
                                                                                                   1.38047758295943e-06, 1.86447536195262e-06, 2.51816121915984e-06, 
                                                                                                   3.40041627253216e-06, 4.54641422109325e-06, 6.03834395349185e-06, 
                                                                                                   7.97982308417383e-06, 1.04817057864209e-05, 1.35489394526282e-05, 
                                                                                                   1.72865813618296e-05, 2.18309175451225e-05, 2.73477089217644e-05, 
                                                                                                   3.40380929265256e-05, 4.21460976943755e-05, 5.1967369819244e-05, 
                                                                                                   6.38600965206997e-05, 7.82579725998248e-05, 9.56860600237062e-05, 
                                                                                                   0.000116779922497502, 0.000142335963852117, 0.000173355233081032, 
                                                                                                   0.000210921169220437, 0.00025641423771755, 0.000311506843394084, 
                                                                                                   0.000378223660039666, 0.000459016772258694, 0.000556855446703318, 
                                                                                                   0.000675335852469291, 0.000818812559327979, 0.000992558463515475, 
                                                                                                   0.00120295979079978, 0.00145774933544351, 0.00176629223196222, 
                                                                                                   0.00213992675332361, 0.00259238540452746, 0.00314030080012767, 
                                                                                                   0.00380380663276417, 0.00460729241649197, 0.00558028623723877, 
                                                                                                   0.00675855195676351, 0.00818539089553454, 0.00991324940277193, 
                                                                                                   0.0120056289887936, 0.0145394320140841, 0.0176077795085524, 0.0213234607142798, 
                                                                                                   0.0258230276512022, 0.0312718588796218, 0.0378702107462816, 0.0458605985746323, 
                                                                                                   0.0555366906666179, 0.0672541473478419, 0.0814435879234418, 0.0986265500083953, 
                                                                                                   0.119434540978074, 0.144632361864515, 0.175146169178876, 0.212097172372404, 
                                                                                                   0.256843809691636, 0.310804466617569, 0.369842684226363, 0.431179045399307, 
                                                                                                   0.493945429064933, 0.557253598745863, 0.620207670785615, 0.681916748818428, 
                                                                                                   0.741507890725135, 0.7981374131588, 0.85100435722966, 0.899360296843544, 
                                                                                                   0.942521141956581, 0.979876115698495, 0.999812477868897, 0.972735811573507, 
                                                                                                   0.932054481163834, 0.885815978946983, 0.834672310063189, 0.779345135479752, 
                                                                                                   0.720614966194481, 0.659310357439126, 0.596295772938628, 0.532460446628508, 
                                                                                                   0.468704750726898, 0.405928059993783, 0.345016117261179, 0.286827900234236, 
                                                                                                   0.237623456225718, 0.19790417419609, 0.164452220923679, 0.136482929335078, 
                                                                                                   0.112955983834528, 0.0932654285994524, 0.0770066613579728, 0.0635815895825471, 
                                                                                                   0.0524963384973958, 0.0433430973402779, 0.0357851408660264, 0.0295444442412585, 
                                                                                                   0.0243914258497928, 0.0201365021470287, 0.0166231553258446, 0.0137221430720713, 
                                                                                                   0.0113267390267136, 0.00934882441245559, 0.00771563465768068, 
                                                                                                   0.00636709119593569, 0.00525358045912998, 0.00433414349100376, 
                                                                                                   0.00357495316102798, 0.00294808230359634, 0.00243046968641578, 
                                                                                                   0.00200307217108402, 0.00165016998349207, 0.00135877837976224, 
                                                                                                   0.00111817834219132, 0.000919518759694046, 0.000755491588934199, 
                                                                                                   0.000620062540625639, 0.000508249477581297, 0.000415939214900695, 
                                                                                                   0.000339735906332031, 0.000276836029518111, 0.000224925814050528, 
                                                                                                   0.000182095460069257, 0.000146769499059896, 0.000117648326182113, 
                                                                                                   9.36606547647744e-05, 7.39240003391358e-05, 5.77123463706654e-05, 
                                                                                                   4.44292627620613e-05, 3.35069132161542e-05, 2.30948965054054e-05, 
                                                                                                   1.35498521268301e-05, 6.6480335943903e-06, 3.22817353776792e-06, 
                                                                                                   1.56754636933548e-06, 7.6117394173847e-07, 3.69613102610182e-07, 
                                                                                                   1.79477797412926e-07, 8.71511930430619e-08, 4.23189904393637e-08, 
                                                                                                   2.05492170784783e-08, 9.97819224010812e-09, 4.84507812590914e-09, 
                                                                                                   2.3525233197402e-09, 1.1421808424864e-09, 5.54459053511967e-10, 
                                                                                                   2.69071150351853e-10, 1.30491713616467e-10, 6.32000285938001e-11, 
                                                                                                   3.05246463595271e-11, 1.46586964219514e-11, 6.95585084010912e-12, 
                                                                                                   3.218335275606e-12, 1.40934851021314e-12, 5.43057275709068e-13, 
                                                                                                   1.47366028903012e-13, 6.63775977550542e-15)), class = c("tbl_df", 
                                                                                                                                                           "tbl", "data.frame"), row.names = c(NA, -205L))

plot:

ylim.prim <- c(min(df$y1), max(df$y1))
 ylim.sec <- c(min(df$y2), max(df$y2))
 b <- diff(ylim.prim)/diff(ylim.sec)
 a <- ylim.prim[1] - b*ylim.sec[1] 
 
 
 
 ggplot(df, aes(x=x)) +
   geom_line(aes(y=y1, color = "y1"))+
   geom_line(aes(y = 10^(a+ y2*b), color = "y2")) +
   scale_y_log10(sec.axis = sec_axis(~ (log(., 10.0) - a)/b, 
                                     breaks = 1:6 * 0.5, name = "y2")) +
   coord_cartesian(
     xlim = c(),
     ylim=c(1e-10,3))+
   scale_color_brewer(palette = "Set1", name = NULL) +
   theme_minimal(base_size = 16) +
   theme(axis.line.y.left = element_line(color = "#E41A1C"),
         axis.line.y.right = element_line(color = "#377EB8"),
         axis.line.x.bottom = element_line("gray"),
         axis.text.y.left = element_text(color = "#E41A1C"),
         axis.text.y.right = element_text(color = "#377EB8"))

I've reopened this question because the linked duplicate did not deal with one of the axes being a log axis — Allan Cameron, Jun 21 '22 at 13:09

Allan Cameron · Accepted Answer · 2022-06-21T13:05:44.793

Showing which line belongs to which axis is simple enough by using colored theme elements and mapping each line to a color aesthetic.

The y1 series is approximately linear if we switch to scale_y_log10, which is also easy to do.

The difficult part is trying to get the second series mapped to a linear continuous axis when the primary axis is log scaled. To do this, we need to use the value of the second series as an exponent of some small number, chosen so that the scales of the two lines are approximately equal on your plot. We then need to take the log to the same base as part of our transformation in the secondary axis. In your case, 1.03 gives reasonable results:

ggplot(df, aes(x=x)) +
  geom_line(aes(y=y1, color = "y1"))+
  geom_line(aes(y = 1.05^(a + y2*b), color = "y2")) +
  scale_y_log10(sec.axis = sec_axis(~ (log(., 1.03) - a)/b, 
                                    breaks = 1:4 * 2.5, name = "y2")) +
  scale_color_brewer(palette = "Set1", name = NULL) +
  theme_minimal(base_size = 16) +
  theme(axis.line.y.left = element_line(color = "#E41A1C"),
        axis.line.y.right = element_line(color = "#377EB8"),
        axis.line.x.bottom = element_line("gray"),
        axis.text.y.left = element_text(color = "#E41A1C"),
        axis.text.y.right = element_text(color = "#377EB8"))

You can see that y1 is plotted on a log axis, but y2 is on a normal continuous axis.

As a caveat here, secondary axes are often frowned upon in data visualization, and having one axis on a log scale with the other being non-log is likely to make the plot very difficult for your audience to interpret.

Edit

A more general approach would be to log transform the series on the primary axis and transform its labels too. This allows using a continuous axis rather than log axis:

a <- range(log10(df$y1))
b <- range(df$y2)

 ggplot(df, aes(x=x)) +
   geom_line(aes(y=(log10(y1) - a[1])/diff(a), color = "y1"))+
   geom_line(aes(y = (y2 - b[1])/diff(b) , color = "y2")) +
   scale_y_continuous(
     labels = ~ 10^(. * diff(a) + a[1]),
     breaks = (pretty(log10(df$y1)) - a[1])/diff(a), name = "y1",
     sec.axis = sec_axis(~ diff(b) * . + b[1], name = "y2")) +
   scale_color_brewer(palette = "Set1", name = NULL) +
   theme_minimal(base_size = 16) +
   theme(axis.line.y.left = element_line(color = "#E41A1C"),
         axis.line.y.right = element_line(color = "#377EB8"),
         axis.line.x.bottom = element_line("gray"),
         axis.text.y.left = element_text(color = "#E41A1C"),
         axis.text.y.right = element_text(color = "#377EB8"))

Thank you for your answer @Allan Cameron , I have tried to apply your solution to my real data and I don't think that is a reasonable way to do it, even if it works in this case. 1) That means you would need to tweak the 1.05 and 1.03 values every time depending on your data, which seems to be extremely sensitive. 2) it becomes a huge mess if one of your curves starts at for example 0.001 and the otherone at 1 — Manfred Manfredo, Jun 21 '22 at 08:30
@ManfredManfredo but these are mathematically unavoidable consequences of trying to plot a log axis and non-log axis on the same plot. It's a dubious concept, and as with any secondary axis, requires manual tweaking to get the parameters right. If you want to post your real data then I'm sure I could get it working satisfactorily, but you will need to do this each time with a new data set. I suppose it would be possible to calculate the optimal value based on the ranges in the data, but this would be complex and, dare I say it, not worth the effort. — Allan Cameron, Jun 21 '22 at 08:41
I don't doubt that you can make it work but I have tried around for more than one hour changing the values of 1.05 and 1.03 without any success. With some software, it is possible to have completely independent y-axis. I wouldn't call it a dubious concept because sometimes the focus is to evaluate the overlap of different curves. I will mark this question as answered, even though it is not really satisfactory, but I guess that's the best R can do. Thank you for your time! — Manfred Manfredo, Jun 21 '22 at 10:37
@ManfredManfredo thanks for marking as accepted, but I would like to give a more general solution if you feel one is required. It is possible to achieve what you want in several different ways, and it would be possible to write some code to do it. It's just that the code would be relatively complex, and I don't think anyone has yet written a package that will do it, most likely because this is an unusual way to plot data. — Allan Cameron, Jun 21 '22 at 10:43

R ggplot double y-axis, log10 and continuous

1 Answers1