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I have the following data, which I'm trying to model via GLM, using Gamma function. It works, except that abline won't show any line. What am I doing wrong?

y <- c(0.00904977380111,0.009174311972687,0.022573363475789,0.081632653008122,0.005571030584803,1e-04,0.02375296916921,0.004962779106823,0.013729977117333,0.00904977380111,0.004514672640982,0.016528925619835,1e-04,0.027855153258277,0.011834319585449,0.024999999936719,1e-04,0.026809651528869,0.016348773841071,1e-04,0.009345794439034,0.00457665899303,0.004705882305772,0.023201856194357,1e-04,0.033734939711656,0.014251781472007,0.004662004755245,0.009259259166667,0.056872037917387,0.018518518611111,0.014598540145986,0.009478673032951,0.023529411811211,0.004819277060357,0.018691588737881,0.018957345923721,0.005390835525461,0.056179775223141,0.016348773841071,0.01104972381185,0.010928961639344,1e-04,1e-04,0.010869565271444,0.011363636420778,0.016085790883856,0.016,0.005665722322786,0.01117318441372,0.028818443860841,1e-04,0.022988505862069,0.01010101,1e-04,0.018083182676638,0.00904977380111,0.00961538466323,0.005390835525461,0.005763688703004,1e-04,0.005571030584803,1e-04,0.014388489208633,0.005633802760722,0.005633802760722,1e-04,0.005361930241431,0.005698005811966,0.013986013986014,1e-04,1e-04)
x <- c(600,600,600,600,600,600,600,600,600,600,600,600,600,600,600,600,600,600,600,600,3500,3500,3500,3500,3500,3500,3500,3500,3500,3500,3500,3500,3500,3500,3500,3500,3500,3500,3500,3500,3500,3500,3500,3500,3500,3500,3500,3500,3500,3500,3500,3500,3500,3500,3500,3500,744.47,744.47,744.47,744.47,744.47,744.47,744.47,630.42,630.42,630.42,630.42,630.42,630.42,630.42,630.42,630.42)
hist(y,breaks=15)
plot(y~x)
fit <- glm(y~x,family='Gamma'(link='log'))
abline(fit)

Histogram

Plot

Rodrigo
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2 Answers2

2

abline plots linear functions, from a simple linear regression, say. A GLM with a Gamma family and a log link is nonlinear on the original scale. To visualize the fit of such a model, you could use predict (an example is given below). Several packages (e.g. effects or visreg) for R exist that feature functions that allow you to directly plot the fit on the original scale including confidence intervals.

Here is an example using visreg using your data and model:

library(visreg)

y <- c(0.00904977380111,0.009174311972687,0.022573363475789,0.081632653008122,0.005571030584803,1e-04,0.02375296916921,0.004962779106823,0.013729977117333,0.00904977380111,0.004514672640982,0.016528925619835,1e-04,0.027855153258277,0.011834319585449,0.024999999936719,1e-04,0.026809651528869,0.016348773841071,1e-04,0.009345794439034,0.00457665899303,0.004705882305772,0.023201856194357,1e-04,0.033734939711656,0.014251781472007,0.004662004755245,0.009259259166667,0.056872037917387,0.018518518611111,0.014598540145986,0.009478673032951,0.023529411811211,0.004819277060357,0.018691588737881,0.018957345923721,0.005390835525461,0.056179775223141,0.016348773841071,0.01104972381185,0.010928961639344,1e-04,1e-04,0.010869565271444,0.011363636420778,0.016085790883856,0.016,0.005665722322786,0.01117318441372,0.028818443860841,1e-04,0.022988505862069,0.01010101,1e-04,0.018083182676638,0.00904977380111,0.00961538466323,0.005390835525461,0.005763688703004,1e-04,0.005571030584803,1e-04,0.014388489208633,0.005633802760722,0.005633802760722,1e-04,0.005361930241431,0.005698005811966,0.013986013986014,1e-04,1e-04)
x <- c(600,600,600,600,600,600,600,600,600,600,600,600,600,600,600,600,600,600,600,600,3500,3500,3500,3500,3500,3500,3500,3500,3500,3500,3500,3500,3500,3500,3500,3500,3500,3500,3500,3500,3500,3500,3500,3500,3500,3500,3500,3500,3500,3500,3500,3500,3500,3500,3500,3500,744.47,744.47,744.47,744.47,744.47,744.47,744.47,630.42,630.42,630.42,630.42,630.42,630.42,630.42,630.42,630.42)

fit <- glm(y~x,family='Gamma'(link='log'))

visreg(fit, scale = "response")

Gamma_fit

An here is the example using R base graphics and predict:

pred_frame <- data.frame(
  x = seq(min(x), max(x), length.out = 1000)
)

pred_frame$fit <- predict(fit, newdata = pred_frame, type = "response")

plot(y~x, pch = 16, las = 1, cex = 1.5)
lines(fit~x, data = pred_frame, col = "steelblue", lwd = 3)

Gamma_fit_base

COOLSerdash
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1

You are not being consistent here since you chose to model on the log scale but you are plotting on the raw scale. Mind you many, many published plots do the same. You need to plot the points in log space or transform the coefficients and pass them to abline() explicitly.