Bias_Correction/README.md
In John-R-Wallace-NOAA/FishNIRS: NIRS on fish structures.
Bias Correction for Older NN Predicted Ages
Since the NN prediction bias in older ages is consistently in one direction it can be adjusted for.
The bias correction needs to be done not only when a TMA (Traditional Method of Aging) age is given, but also when there is no corresponding TMA for a given age structure. Hence, the goal of a bias corrected prediction from scans and/or metadata without the need for a traditional age can be achieved.
A functional form (model) is needed that predicts the difference between TMA and the NN predicted age given a new value of the NN predicted age. Below a LOWESS (locally weighted scatterplot smoothing) non-parametric model is used with R's splinefun() function for prediction. The mgcv R package's gam() with the s() smoother is also looked at for standard errors of the bias adjustment.
First some functions are needed:
File.ASCII <- tempfile()
for(Func in c("predict.lowess.R", "lowess.line.R", "browsePlot.R", "headTail.R")) {
download.file(paste0("https://raw.githubusercontent.com/John-R-Wallace-NOAA/JRWToolBox/master/R/", Func), File.ASCII)
source(File.ASCII)
}
for(Func in c("agreementFigure.R", "Cor_R_squared_RMSE_MAE_SAD_APE.R")) {
download.file(paste0("https://raw.githubusercontent.com/John-R-Wallace-NOAA/FishNIRS/master/R/", Func), File.ASCII)
source(File.ASCII)
}
nul <- file.remove(File.ASCII); rm(File.ASCII, Func, nul)
" "
Download an example dataset with missing TMA in the last 10 rows:
download.file("https://raw.githubusercontent.com/John-R-Wallace-NOAA/FishNIRS/main/Bias_Correction/TMA_Pred.RData",
"TMA_Pred.RData")
load("TMA_Pred.RData")
headTail(TMA_Pred, 3, 12)
" "
Plot the data to create this agreement figure.
My toolbox function browsePlot() was downloaded above and will be used for viewing the figures directly in browser and (optionally) saved into a file.
browsePlot('agreementFigure(TMA_Pred$TMA, TMA_Pred$NN_Pred_BIASED, xlim = c(0, 18.5), ylim = c(0, 18.5),
main = "NN Predicted Ages with Bias at Older Ages")', file = 'NN_Pred_vs_TMA_Agreement_Fig.png')
" "
The difference between TMA and NN_Pred is fitted against the biased NN_Pred using lowess(). A prediction of the bias adjustment given a new value of NN_Pred is done with predict.lowess() from my toolbox [which uses stats::splinefun()]. The resulting bias adjustment is added to NN_Pred and plotted along with lowess smoothed lines using lowess.line() with 3 different values of the smoothing parameter (all in green). The original biased data is plotted in black and only one smoothed line for the biased data is shown.
(Bias_Adjustment <- predict.lowess(lowess(TMA_Pred$NN_Pred_BIASED[!is.na(TMA_Pred$TMA)],
TMA_Pred$TMA[!is.na(TMA_Pred$TMA)] - TMA_Pred$NN_Pred_BIASED[!is.na(TMA_Pred$TMA)], f = 2/3),
newdata = TMA_Pred$NN_Pred_BIASED))[1:10]
# Note the need to use double quotes inside the plotting code when using browsePlot()
browsePlot('
plot(TMA_Pred$TMA, TMA_Pred$NN_Pred_BIASED, xlim = c(0, 16), ylim = c(0, 16)); abline(0, 1, col = "grey")
lowess.line(TMA_Pred$TMA, TMA_Pred$NN_Pred_BIASED)
points(TMA_Pred$TMA + 0.15, TMA_Pred$NN_Pred_BIASED + Bias_Adjustment, col = "green")
lowess.line(TMA_Pred$TMA, TMA_Pred$NN_Pred_BIASED + Bias_Adjustment, col = "green", smoothing.param = 0.1)
lowess.line(TMA_Pred$TMA, TMA_Pred$NN_Pred_BIASED + Bias_Adjustment, col = "green", smoothing.param = 1/3, lty = 2)
lowess.line(TMA_Pred$TMA, TMA_Pred$NN_Pred_BIASED + Bias_Adjustment, col = "green", smoothing.param = 2/3, lty = 3)
', file = 'NN_Pred_Bias_Adj_Lowess_vs_TMA.png')
Cor_R_squared_RMSE_MAE_SAD_APE(TMA_Pred$TMA, round(TMA_Pred$NN_Pred_BIASED + Bias_Adjustment), digits = 4)
" "
The stats for the lowess biased adjusted NN_Pred plotted against TMA figure, where the NN_pred is rounded to the newest integer (no Delta added) are:
Correlation R_squared RMSE MAE SAD APE N
0.9649 0.931 0.7732 0.4725 2589 5.699 5479
The lowess based adjustment above does not move the older ages sufficiently (perhaps it will for other data), so a bias adjustment factor was implemented. First, older ages where bias still existed, and where there was sufficient data is defined (ages 9-15 in the example below). For each of these TMA ages, the difference between each age and the average of the biased NN predicted ages which have that particular TMA value was calculated (Ages_Diff below). Next those differences were divided by the lowess predicted ages at each TMA value, and the average taken (Bias_Increase_Factor below). Note that the "Bias_Increase_Factor" cannot depend on TMA, since predictions need to made when TMA is unknown, hence the need for a single scalar value. One plus the Bias_Increase_Factor divided by 2 is then multiplied by the lowess predictions looked at above and added to biased NN predictions to create less biased estimates (NN_Pred below). Another value (age 8 in the example below) is selected below which the unbiased younger ages remain unchanged. (Note that the code below repeats the lowess predictions and does not depend on the code looking only at the lowess predictions above.)
A bias adjustment figure and an
agreement figure are created.
Smoothers are fickle and caution is needed when using them, looking past the smoothers and only at the data should also be done. One of the smoothers being right on the 1-1 line for older ages, as seen in this bias adjustment figure, is atypical. Although, that smoothed line is based on the lowess() function’s smoothing parameter default value of 2/3.
# TMA_Pred_SAVE <- TMA_Pred
# TMA_Pred_SAVE -> TMA_Pred
Bias_Adj_Factor_Ages <- c(8, 9:15)
Ages_Diff <- Bias_Adj_Factor_Ages[-1] - apply(matrix(Bias_Adj_Factor_Ages[-1], ncol = 1), 1, function(x) mean(TMA_Pred$NN_Pred_BIASED[TMA_Pred$TMA == x],na.rm = T))
Bias_Increase_Factor <- mean(Ages_Diff/predict.lowess(lowess(TMA_Pred$NN_Pred_BIASED[!is.na(TMA_Pred$TMA)], TMA_Pred$TMA[!is.na(TMA_Pred$TMA)] -
TMA_Pred$NN_Pred_BIASED[!is.na(TMA_Pred$TMA)], f = 2/3), newdata = Bias_Adj_Factor_Ages[-1]))
TMA_Pred$Bias_Adjustment <- (1 + Bias_Increase_Factor/2) * predict.lowess(lowess(TMA_Pred$NN_Pred_BIASED[!is.na(TMA_Pred$TMA)], TMA_Pred$TMA[!is.na(TMA_Pred$TMA)] -
TMA_Pred$NN_Pred_BIASED[!is.na(TMA_Pred$TMA)], f = 2/3), newdata = TMA_Pred$NN_Pred_BIASED)
TMA_Pred$NN_Pred <- TMA_Pred$NN_Pred_BIASED + TMA_Pred$Bias_Adjustment
TMA_Pred$Bias_Adj <- TRUE
TMA_Pred$Bias_Adj[TMA_Pred$NN_Pred_BIASED < Bias_Adj_Factor_Ages[1]] <- FALSE
TMA_Pred$NN_Pred[!TMA_Pred$Bias_Adj] <- TMA_Pred$NN_Pred_BIASED[!TMA_Pred$Bias_Adj]
# assign('TMA_Pred', TMA_Pred, pos = 1) # These assignments to ".GlobalEnv" would be needed if browsePlot() was inside a function
# assign('Bias_Adj_Factor_Ages', Bias_Adj_Factor_Ages, pos = 1)
browsePlot('
plot(TMA_Pred$TMA, TMA_Pred$NN_Pred_BIASED, xlim = c(0, 16), ylim = c(0, 16),
xlab = "TMA; Bias corrected points staggered to the right (Lowess line is not moved over.)", ylab = "NN Predicted Median",
main = paste0("Lowess Bias Corr using ", Bias_Adj_Factor_Ages[2], ":", Bias_Adj_Factor_Ages[length(Bias_Adj_Factor_Ages)],
" NN_Pred, Starting at ", Bias_Adj_Factor_Ages[1], "; No Bias Correction is Black, Bias Corrected is Green"))
abline(0, 1, col = "grey")
lowess.line(TMA_Pred$TMA, TMA_Pred$NN_Pred_BIASED, smoothing.param = 2/3)
points(TMA_Pred$TMA + 0.25, TMA_Pred$NN_Pred, col = "green")
lowess.line(TMA_Pred$TMA, TMA_Pred$NN_Pred, col = "green", lwd = 1.2, smoothing.param = 0.1)
lowess.line(TMA_Pred$TMA, TMA_Pred$NN_Pred, col = "green", lwd = 1.2, smoothing.param = 1/3, lty = 2)
lowess.line(TMA_Pred$TMA, TMA_Pred$NN_Pred, col = "green", lwd = 1.2, smoothing.param = 2/3, lty = 3)
', file = 'NN_Pred_Bias_Adj_Lowess_Factor_vs_TMA.png')
headTail(TMA_Pred, 3, 12)
browsePlot('agreementFigure(TMA_Pred$TMA, TMA_Pred$NN_Pred, xlim = c(0, 18.5), ylim = c(0, 18.5),
main = "NN Predicted Ages with Corrected Bias at Older Ages")', file = 'NN_Pred_Bias_Corrected_vs_TMA_Agreement_Fig.png')
" "
First and last values rows TMA_Pred are below. Row 5,485 shows that the older aged biased prediction was adjusted with TMA being unknown.
# TMA NN_Pred_BIASED Bias_Adjustment NN_Pred Bias_Adj
# 1 1 0.9643 0.5370134 0.964300 FALSE
# 2 1 0.7074 0.5261169 0.707400 FALSE
# 3 1 0.8265 0.5315790 0.826500 FALSE
# 5478 4 2.4962 0.5018800 2.496200 FALSE
# 5479 8 5.8144 0.5208765 5.814400 FALSE
# 5480 NA 0.7195 0.5267396 0.719500 FALSE
# 5481 NA 7.3813 0.6889761 7.381300 FALSE
# 5482 NA 4.8665 0.3319816 4.866500 FALSE
# 5483 NA 2.3780 0.5240816 2.378000 FALSE
# 5484 NA 4.8340 0.3305552 4.834000 FALSE
# 5485 NA 8.9714 0.9309345 9.902334 TRUE
# 5486 NA 2.8856 0.4943580 2.885600 FALSE
# 5487 NA 4.9158 0.3341453 4.915800 FALSE
# 5488 NA 2.0576 0.5446515 2.057600 FALSE
# 5489 NA 5.1654 0.3648089 5.165400 FALSE
If standard errors for the bias adjustment are wanted, then the mgcv R package could be
tried:
# mgcv R package's gam() with mgcv's s() smoother (Trevor Hastie's 'gam' package also has a s() smoother.)
if(!any(installed.packages()[, 1] %in% "mgcv")) install.packages('mgcv')
library(mgcv)
Bias_Adjustment <- predict(mgcv::gam(TMA - NN_Pred_BIASED ~ s(NN_Pred_BIASED), data = TMA_Pred),
newdata = TMA_Pred[, 'NN_Pred_BIASED', drop = F], type = "response", se.fit = TRUE)
browsePlot('
plot(TMA_Pred$TMA, TMA_Pred$NN_Pred_BIASED); abline(0, 1, col = "grey")
lowess.line(TMA_Pred$TMA, TMA_Pred$NN_Pred_BIASED)
points(TMA_Pred$TMA + 0.2, TMA_Pred$NN_Pred_BIASED + Bias_Adjustment$fit, col = "red")
lowess.line(TMA_Pred$TMA, TMA_Pred$NN_Pred_BIASED + Bias_Adjustment$fit, col = "red")
', file = 'mgcv_gam_bias_adjustment.png')
headTail(data.frame(fit = Bias_Adjustment$fit, se.fit = Bias_Adjustment$se.fit), 3, 12)
# fit se.fit
# 1 0.22295098 0.02120150
# 2 0.12220316 0.03037579
# 3 0.16982558 0.02552071
# 5478 0.18421369 0.02034234
# 5479 -0.12689477 0.03405727
# 5480 0.12706570 0.02984933
# 5481 0.53932923 0.03583973
# 5482 0.21001997 0.03085982
# 5483 0.20315991 0.01932915
# 5484 0.22857269 0.03103718
# 5485 0.24260078 0.04077792
# 5486 0.19955985 0.02355215
# 5487 0.18167853 0.03066340
# 5488 0.28256894 0.01940362
# 5489 0.04279344 0.03102674
# Dimension: 5489 2
" "
John-R-Wallace-NOAA/FishNIRS documentation built on April 12, 2025, 12:59 a.m.
R Package Documentation
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Note that we can't provide technical support on individual packages. You should contact the package authors for that.
Bias Correction for Older NN Predicted Ages
Since the NN prediction bias in older ages is consistently in one direction it can be adjusted for.
The bias correction needs to be done not only when a TMA (Traditional Method of Aging) age is given, but also when there is no corresponding TMA for a given age structure. Hence, the goal of a bias corrected prediction from scans and/or metadata without the need for a traditional age can be achieved.
A functional form (model) is needed that predicts the difference between TMA and the NN predicted age given a new value of the NN predicted age. Below a LOWESS (locally weighted scatterplot smoothing) non-parametric model is used with R's splinefun() function for prediction. The mgcv R package's gam() with the s() smoother is also looked at for standard errors of the bias adjustment.
First some functions are needed:
File.ASCII <- tempfile()
for(Func in c("predict.lowess.R", "lowess.line.R", "browsePlot.R", "headTail.R")) {
download.file(paste0("https://raw.githubusercontent.com/John-R-Wallace-NOAA/JRWToolBox/master/R/", Func), File.ASCII)
source(File.ASCII)
}
for(Func in c("agreementFigure.R", "Cor_R_squared_RMSE_MAE_SAD_APE.R")) {
download.file(paste0("https://raw.githubusercontent.com/John-R-Wallace-NOAA/FishNIRS/master/R/", Func), File.ASCII)
source(File.ASCII)
}
nul <- file.remove(File.ASCII); rm(File.ASCII, Func, nul)
" "
Download an example dataset with missing TMA in the last 10 rows:
download.file("https://raw.githubusercontent.com/John-R-Wallace-NOAA/FishNIRS/main/Bias_Correction/TMA_Pred.RData",
"TMA_Pred.RData")
load("TMA_Pred.RData")
headTail(TMA_Pred, 3, 12)
" "
Plot the data to create this agreement figure. My toolbox function browsePlot() was downloaded above and will be used for viewing the figures directly in browser and (optionally) saved into a file.
browsePlot('agreementFigure(TMA_Pred$TMA, TMA_Pred$NN_Pred_BIASED, xlim = c(0, 18.5), ylim = c(0, 18.5),
main = "NN Predicted Ages with Bias at Older Ages")', file = 'NN_Pred_vs_TMA_Agreement_Fig.png')
" "
The difference between TMA and NN_Pred is fitted against the biased NN_Pred using lowess(). A prediction of the bias adjustment given a new value of NN_Pred is done with predict.lowess() from my toolbox [which uses stats::splinefun()]. The resulting bias adjustment is added to NN_Pred and plotted along with lowess smoothed lines using lowess.line() with 3 different values of the smoothing parameter (all in green). The original biased data is plotted in black and only one smoothed line for the biased data is shown.
(Bias_Adjustment <- predict.lowess(lowess(TMA_Pred$NN_Pred_BIASED[!is.na(TMA_Pred$TMA)],
TMA_Pred$TMA[!is.na(TMA_Pred$TMA)] - TMA_Pred$NN_Pred_BIASED[!is.na(TMA_Pred$TMA)], f = 2/3),
newdata = TMA_Pred$NN_Pred_BIASED))[1:10]
# Note the need to use double quotes inside the plotting code when using browsePlot()
browsePlot('
plot(TMA_Pred$TMA, TMA_Pred$NN_Pred_BIASED, xlim = c(0, 16), ylim = c(0, 16)); abline(0, 1, col = "grey")
lowess.line(TMA_Pred$TMA, TMA_Pred$NN_Pred_BIASED)
points(TMA_Pred$TMA + 0.15, TMA_Pred$NN_Pred_BIASED + Bias_Adjustment, col = "green")
lowess.line(TMA_Pred$TMA, TMA_Pred$NN_Pred_BIASED + Bias_Adjustment, col = "green", smoothing.param = 0.1)
lowess.line(TMA_Pred$TMA, TMA_Pred$NN_Pred_BIASED + Bias_Adjustment, col = "green", smoothing.param = 1/3, lty = 2)
lowess.line(TMA_Pred$TMA, TMA_Pred$NN_Pred_BIASED + Bias_Adjustment, col = "green", smoothing.param = 2/3, lty = 3)
', file = 'NN_Pred_Bias_Adj_Lowess_vs_TMA.png')
Cor_R_squared_RMSE_MAE_SAD_APE(TMA_Pred$TMA, round(TMA_Pred$NN_Pred_BIASED + Bias_Adjustment), digits = 4)
" "
The stats for the lowess biased adjusted NN_Pred plotted against TMA figure, where the NN_pred is rounded to the newest integer (no Delta added) are:
Correlation R_squared RMSE MAE SAD APE N
0.9649 0.931 0.7732 0.4725 2589 5.699 5479
The lowess based adjustment above does not move the older ages sufficiently (perhaps it will for other data), so a bias adjustment factor was implemented. First, older ages where bias still existed, and where there was sufficient data is defined (ages 9-15 in the example below). For each of these TMA ages, the difference between each age and the average of the biased NN predicted ages which have that particular TMA value was calculated (Ages_Diff below). Next those differences were divided by the lowess predicted ages at each TMA value, and the average taken (Bias_Increase_Factor below). Note that the "Bias_Increase_Factor" cannot depend on TMA, since predictions need to made when TMA is unknown, hence the need for a single scalar value. One plus the Bias_Increase_Factor divided by 2 is then multiplied by the lowess predictions looked at above and added to biased NN predictions to create less biased estimates (NN_Pred below). Another value (age 8 in the example below) is selected below which the unbiased younger ages remain unchanged. (Note that the code below repeats the lowess predictions and does not depend on the code looking only at the lowess predictions above.) A bias adjustment figure and an agreement figure are created.
Smoothers are fickle and caution is needed when using them, looking past the smoothers and only at the data should also be done. One of the smoothers being right on the 1-1 line for older ages, as seen in this bias adjustment figure, is atypical. Although, that smoothed line is based on the lowess() function’s smoothing parameter default value of 2/3.
# TMA_Pred_SAVE <- TMA_Pred
# TMA_Pred_SAVE -> TMA_Pred
Bias_Adj_Factor_Ages <- c(8, 9:15)
Ages_Diff <- Bias_Adj_Factor_Ages[-1] - apply(matrix(Bias_Adj_Factor_Ages[-1], ncol = 1), 1, function(x) mean(TMA_Pred$NN_Pred_BIASED[TMA_Pred$TMA == x],na.rm = T))
Bias_Increase_Factor <- mean(Ages_Diff/predict.lowess(lowess(TMA_Pred$NN_Pred_BIASED[!is.na(TMA_Pred$TMA)], TMA_Pred$TMA[!is.na(TMA_Pred$TMA)] -
TMA_Pred$NN_Pred_BIASED[!is.na(TMA_Pred$TMA)], f = 2/3), newdata = Bias_Adj_Factor_Ages[-1]))
TMA_Pred$Bias_Adjustment <- (1 + Bias_Increase_Factor/2) * predict.lowess(lowess(TMA_Pred$NN_Pred_BIASED[!is.na(TMA_Pred$TMA)], TMA_Pred$TMA[!is.na(TMA_Pred$TMA)] -
TMA_Pred$NN_Pred_BIASED[!is.na(TMA_Pred$TMA)], f = 2/3), newdata = TMA_Pred$NN_Pred_BIASED)
TMA_Pred$NN_Pred <- TMA_Pred$NN_Pred_BIASED + TMA_Pred$Bias_Adjustment
TMA_Pred$Bias_Adj <- TRUE
TMA_Pred$Bias_Adj[TMA_Pred$NN_Pred_BIASED < Bias_Adj_Factor_Ages[1]] <- FALSE
TMA_Pred$NN_Pred[!TMA_Pred$Bias_Adj] <- TMA_Pred$NN_Pred_BIASED[!TMA_Pred$Bias_Adj]
# assign('TMA_Pred', TMA_Pred, pos = 1) # These assignments to ".GlobalEnv" would be needed if browsePlot() was inside a function
# assign('Bias_Adj_Factor_Ages', Bias_Adj_Factor_Ages, pos = 1)
browsePlot('
plot(TMA_Pred$TMA, TMA_Pred$NN_Pred_BIASED, xlim = c(0, 16), ylim = c(0, 16),
xlab = "TMA; Bias corrected points staggered to the right (Lowess line is not moved over.)", ylab = "NN Predicted Median",
main = paste0("Lowess Bias Corr using ", Bias_Adj_Factor_Ages[2], ":", Bias_Adj_Factor_Ages[length(Bias_Adj_Factor_Ages)],
" NN_Pred, Starting at ", Bias_Adj_Factor_Ages[1], "; No Bias Correction is Black, Bias Corrected is Green"))
abline(0, 1, col = "grey")
lowess.line(TMA_Pred$TMA, TMA_Pred$NN_Pred_BIASED, smoothing.param = 2/3)
points(TMA_Pred$TMA + 0.25, TMA_Pred$NN_Pred, col = "green")
lowess.line(TMA_Pred$TMA, TMA_Pred$NN_Pred, col = "green", lwd = 1.2, smoothing.param = 0.1)
lowess.line(TMA_Pred$TMA, TMA_Pred$NN_Pred, col = "green", lwd = 1.2, smoothing.param = 1/3, lty = 2)
lowess.line(TMA_Pred$TMA, TMA_Pred$NN_Pred, col = "green", lwd = 1.2, smoothing.param = 2/3, lty = 3)
', file = 'NN_Pred_Bias_Adj_Lowess_Factor_vs_TMA.png')
headTail(TMA_Pred, 3, 12)
browsePlot('agreementFigure(TMA_Pred$TMA, TMA_Pred$NN_Pred, xlim = c(0, 18.5), ylim = c(0, 18.5),
main = "NN Predicted Ages with Corrected Bias at Older Ages")', file = 'NN_Pred_Bias_Corrected_vs_TMA_Agreement_Fig.png')
" "
First and last values rows TMA_Pred are below. Row 5,485 shows that the older aged biased prediction was adjusted with TMA being unknown.
# TMA NN_Pred_BIASED Bias_Adjustment NN_Pred Bias_Adj
# 1 1 0.9643 0.5370134 0.964300 FALSE
# 2 1 0.7074 0.5261169 0.707400 FALSE
# 3 1 0.8265 0.5315790 0.826500 FALSE
# 5478 4 2.4962 0.5018800 2.496200 FALSE
# 5479 8 5.8144 0.5208765 5.814400 FALSE
# 5480 NA 0.7195 0.5267396 0.719500 FALSE
# 5481 NA 7.3813 0.6889761 7.381300 FALSE
# 5482 NA 4.8665 0.3319816 4.866500 FALSE
# 5483 NA 2.3780 0.5240816 2.378000 FALSE
# 5484 NA 4.8340 0.3305552 4.834000 FALSE
# 5485 NA 8.9714 0.9309345 9.902334 TRUE
# 5486 NA 2.8856 0.4943580 2.885600 FALSE
# 5487 NA 4.9158 0.3341453 4.915800 FALSE
# 5488 NA 2.0576 0.5446515 2.057600 FALSE
# 5489 NA 5.1654 0.3648089 5.165400 FALSE
If standard errors for the bias adjustment are wanted, then the mgcv R package could be tried:
# mgcv R package's gam() with mgcv's s() smoother (Trevor Hastie's 'gam' package also has a s() smoother.)
if(!any(installed.packages()[, 1] %in% "mgcv")) install.packages('mgcv')
library(mgcv)
Bias_Adjustment <- predict(mgcv::gam(TMA - NN_Pred_BIASED ~ s(NN_Pred_BIASED), data = TMA_Pred),
newdata = TMA_Pred[, 'NN_Pred_BIASED', drop = F], type = "response", se.fit = TRUE)
browsePlot('
plot(TMA_Pred$TMA, TMA_Pred$NN_Pred_BIASED); abline(0, 1, col = "grey")
lowess.line(TMA_Pred$TMA, TMA_Pred$NN_Pred_BIASED)
points(TMA_Pred$TMA + 0.2, TMA_Pred$NN_Pred_BIASED + Bias_Adjustment$fit, col = "red")
lowess.line(TMA_Pred$TMA, TMA_Pred$NN_Pred_BIASED + Bias_Adjustment$fit, col = "red")
', file = 'mgcv_gam_bias_adjustment.png')
headTail(data.frame(fit = Bias_Adjustment$fit, se.fit = Bias_Adjustment$se.fit), 3, 12)
# fit se.fit
# 1 0.22295098 0.02120150
# 2 0.12220316 0.03037579
# 3 0.16982558 0.02552071
# 5478 0.18421369 0.02034234
# 5479 -0.12689477 0.03405727
# 5480 0.12706570 0.02984933
# 5481 0.53932923 0.03583973
# 5482 0.21001997 0.03085982
# 5483 0.20315991 0.01932915
# 5484 0.22857269 0.03103718
# 5485 0.24260078 0.04077792
# 5486 0.19955985 0.02355215
# 5487 0.18167853 0.03066340
# 5488 0.28256894 0.01940362
# 5489 0.04279344 0.03102674
# Dimension: 5489 2
" "
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