PaoloH PaoloH - 3 months ago 12
R Question

R plot with ggplot2 linear regression with a transformed dependent variable

So my problem is quite simple, I want to plot the exponential regression of my data, so far what I've done was plot the polynomial regression :

ggplot(data = mydataANOVA, aes(x = TpsenJour, y = PrptionJourAuDelaDe, color = Type_Contrat))+
geom_point()+
geom_smooth(method ="lm", formula = y ~ poly(x,2))


I got the following plot :
enter image description here

The regression isn't exactly a good fit for the actual data but the data looked a lot like an exponential function so I used the logarithm of my data, I used the same code with the log of my data to get the following plot:

enter image description here

Which seemed to be an very accurate fit, so I wanted to compare the two regression models directly by plotting the exponential regression, but when i used the formula
formula = y ~ exp(poly(x,2))
, I didn't get the same accurate regression and instead I got something else :
enter image description here

Which is even less accurate than the first one. How am I supposed to get that polynomial exponential regression plotted with the confidence intervals. I managed to get the good regression on the regular plot function but not with the confidence intervals and not in ggplot2. Here is what I got for only one of the two curves:

enter image description here

How can I get the good regression on ggplot2 with the confidence intervals ?
Here is the data that I used on one of the 2 curves.

TpsenJour PrptionJourAuDelaDe fact
1 1 0.955669 a
3 3 0.877947 a
5 5 0.815058 a
7 7 0.764725 a
9 9 0.721070 a
11 11 0.681675 a
13 13 0.646490 a
15 15 0.614689 a
17 17 0.585664 a
19 19 0.558905 a
21 21 0.534362 a
23 23 0.511791 a
25 25 0.490651 a
27 27 0.470923 a
29 29 0.452498 a
31 31 0.435190 a
33 33 0.419160 a
35 35 0.404359 a
37 37 0.390519 a
40 40 0.371018 a
40.1 40 0.371018 a
43 43 0.352960 a
46 46 0.336170 a
49 49 0.320631 a
52 52 0.306194 a
55 55 0.292584 a
58 58 0.279858 a
62 62 0.264096 a
65 65 0.253316 a
68 68 0.243120 a
71 71 0.233544 a
74 74 0.224474 a
77 77 0.215905 a
81 81 0.205180 a
84 84 0.197623 a
87 87 0.190440 a
90 90 0.183609 a
93 93 0.177278 a
96 96 0.171358 a
100 100 0.163951 a


Thank you.

I had a smal problem with the answer of @Roland, where it would return an error, I think I've solved it. I simply had to add two lines : (I hope that by fixing my error I did not alter the originally predicted outcome)

fact<-DF$fact
fit <- lm(log(PrptionJourAuDelaDe) ~ poly(TpsenJour, 2) * fact, data = mydataANOVA)
fact<-c(rep('a',1000),rep('b',1000))
pred <- expand.grid(TpsenJour = seq(min(mydataANOVA$TpsenJour), max(mydataANOVA$TpsenJour), length.out = 1e3),
fact = unique(mydataANOVA$fact))

pred <- cbind(pred,
exp(predict(fit,
newdata = data.frame(TpsenJour = pred$TpsenJour),
interval = "confidence")))

ggplot(data = DF, aes(x = TpsenJour, y = PrptionJourAuDelaDe, color = fact)) +
geom_point() +
geom_ribbon(data = pred, aes(y = fit, ymin = lwr, ymax = upr, fill = fact), alpha = 0.3) +
geom_line(data = pred, aes(y = fit, color = fact))


I then get the following plot:

enter image description here

Answer

Do the fit outside of ggplot2:

fit <- lm(log(PrptionJourAuDelaDe) ~ poly(TpsenJour, 2) * fact, data = DF)
pred <- expand.grid(TpsenJour = seq(min(DF$TpsenJour), max(DF$TpsenJour), length.out = 1e3), 
                    fact = unique(DF$fact))
pred <- cbind(pred, 
              exp(predict(fit, 
                          newdata = data.frame(TpsenJour = pred$TpsenJour), 
                          interval = "confidence")))

library(ggplot2)
ggplot(data = DF, aes(x = TpsenJour, y = PrptionJourAuDelaDe, color = fact)) +
  geom_point() +
  geom_ribbon(data = pred, aes(y = fit, ymin = lwr, ymax = upr, fill = fact), alpha = 0.3) +
  geom_line(data = pred, aes(y = fit, color = fact))

Note that I wouldn't call this exponential regression. It's linear regression with a transformed dependent variable (in contrast to a non-linear model, which would need to be fitted with nls). And its probably not the model I would use.