pcrboot: Bootstrapping and jackknifing qPCR data
In qpcR: Modelling and Analysis of Real-Time PCR Data
Description
Usage
Arguments
Details
Value
Author(s)
References
Examples
Description
Confidence intervals for the estimated parameters and goodness-of-fit measures are calculated for a nonlinear qPCR data fit by either
a) boostrapping the residuals of the fit or
b) jackknifing and refitting the data.
Confidence intervals can also be calculated for all parameters obtained from the efficiency analysis.
Usage
1
2
Arguments
object
an object of class 'pcrfit'.
type
either bootstrapping or jackknifing.
B
numeric. The number of iterations.
njack
numeric. In case of type = "jack", how many datapoints to exclude. Defaults to leave-one-out.
plot
should the fitting and final results be displayed as a plot?
do.eff
logical. If TRUE, efficiency analysis will be performed.
conf
the confidence level.
verbose
logical. If TRUE, the iterations will be printed on the console.
...
other parameters to be passed on to the plotting functions.
Details
Non-parametric bootstrapping is applied using the centered residuals.
1) Obtain the residuals from the fit:
\hat{\varepsilon}_t = y_t - f(x_t, \hat{θ})
2) Draw bootstrap pseudodata:
y_{t}^{\ast} = f(x_t, \hat{θ}) + ε_{t}^{\ast}
where ε_{t}^{\ast} are i.i.d. from distribution \hat{F}, where the residuals from the original fit are centered at zero.
3) Fit \hatθ^\ast by nonlinear least-squares.
4) Repeat B times, yielding bootstrap replications
\hatθ^{\ast 1}, \hatθ^{\ast 2}, …, \hatθ^{\ast B}
One can then characterize the EDF and calculate confidence intervals for each parameter:
θ \in [EDF^{-1}(α/2), EDF^{-1}(1-α/2)]
The jackknife alternative is to perform the bootstrap on the data-predictor vector, i.e. eliminating a certain number of datapoints.
If the residuals are correlated or have non-constant variance the latter is recommended. This may be the case in qPCR data,
as the variance in the low fluorescence region (ground phase) is usually much higher than in the rest of the curve.
Value
A list containing the following items:
ITER
a list containing each of the results from the iterations.
CONF
a list containing the confidence intervals for each item in ITER.
Each item contains subitems for the coefficients (coef), root-mean-squared error (rmse), residual sum-of-squares (rss), goodness-of-fit measures (gof) and the efficiency analysis (eff). If plot = TRUE, all data is plotted as boxplots including confidence intervals.
Author(s)
Andrej-Nikolai Spiess
References
Nonlinear regression analysis and its applications.
Bates DM & Watts DG.
Wiley, Chichester, UK, 1988.
Nonlinear regression.
Seber GAF & Wild CJ.
Wiley, New York, 1989.
Boostrap accuracy for non-linear regression models.
Roy T.
J Chemometics (1994), 8: 37-44.
Examples
1
2
3
4
5
6
7
8
9
10
Example output
Loading required package: MASS
Loading required package: minpack.lm
Loading required package: rgl
Loading required package: robustbase
Loading required package: Matrix
Warning messages:
1: In rgl.init(initValue, onlyNULL) : RGL: unable to open X11 display
2: 'rgl_init' failed, running with rgl.useNULL = TRUE
3: .onUnload failed in unloadNamespace() for 'rgl', details:
call: fun(...)
error: object 'rgl_quit' not found
.........10.........20
fitting converged in 100% of iterations.
$ITER
$ITER$coef
b c d e
[1,] -12.21118 0.09686212 11.33265 17.55819
[2,] -12.07278 0.07016143 11.31772 17.61487
[3,] -11.81028 0.03597171 11.33150 17.53671
[4,] -11.97491 0.05733131 11.31543 17.61115
[5,] -11.83458 0.08998748 11.30267 17.57865
[6,] -11.76470 0.07215907 11.34185 17.63384
[7,] -12.02630 0.03820658 11.32024 17.56343
[8,] -12.16614 0.08235887 11.33595 17.57804
[9,] -12.01651 0.06370201 11.34809 17.62744
[10,] -11.90387 0.06401986 11.31160 17.59889
[11,] -12.01525 0.07762558 11.32354 17.57681
[12,] -12.05149 0.09601110 11.32681 17.63113
[13,] -12.09255 0.05652215 11.32326 17.60491
[14,] -12.33257 0.03743030 11.30060 17.53166
[15,] -12.02775 0.07860079 11.34630 17.61969
[16,] -12.34194 0.06200407 11.32437 17.58958
[17,] -12.33862 0.02339232 11.29593 17.57953
[18,] -12.41745 0.07225319 11.32995 17.62079
[19,] -12.12952 0.08079887 11.32357 17.61310
[20,] -12.43329 0.07113203 11.30092 17.54731
$ITER$rmse
[1] 0.07920127 0.08121134 0.07748896 0.08615544 0.08283411 0.08588817
[7] 0.08066167 0.08314796 0.07672933 0.07404001 0.08109171 0.08366045
[13] 0.09358520 0.07718795 0.09334495 0.08065552 0.08228887 0.08582896
[19] 0.08984434 0.08746631
$ITER$rss
[1] 0.2822778 0.2967877 0.2702042 0.3340242 0.3087671 0.3319550 0.2927838
[8] 0.3111112 0.2649325 0.2466865 0.2959140 0.3149582 0.3941185 0.2681091
[15] 0.3920976 0.2927391 0.3047156 0.3314974 0.3632402 0.3442660
$ITER$gof
Rsq Rsq.ad AIC AICc BIC resVar
[1,] 0.9997701 0.9997548 -103.62153 -102.71244 -94.16243 0.006272841
[2,] 0.9997587 0.9997426 -101.16540 -100.25631 -91.70630 0.006595281
[3,] 0.9997811 0.9997665 -105.76350 -104.85441 -96.30440 0.006004538
[4,] 0.9997286 0.9997105 -95.37376 -94.46467 -85.91466 0.007422761
[5,] 0.9997465 0.9997296 -99.22646 -98.31737 -89.76736 0.006861490
[6,] 0.9997303 0.9997123 -95.67825 -94.76916 -86.21915 0.007376778
[7,] 0.9997630 0.9997472 -101.83095 -100.92185 -92.37184 0.006506306
[8,] 0.9997474 0.9997306 -98.85585 -97.94676 -89.39675 0.006913583
[9,] 0.9997859 0.9997717 -106.72894 -105.81985 -97.26984 0.005887390
[10,] 0.9997990 0.9997856 -110.22542 -109.31633 -100.76632 0.005481923
[11,] 0.9997590 0.9997429 -101.30986 -100.40077 -91.85076 0.006575866
[12,] 0.9997432 0.9997261 -98.25368 -97.34459 -88.79458 0.006999070
[13,] 0.9996807 0.9996594 -87.26730 -86.35821 -77.80819 0.008758189
[14,] 0.9997829 0.9997684 -106.14492 -105.23583 -96.68582 0.005957980
[15,] 0.9996823 0.9996611 -87.51920 -86.61011 -78.06009 0.008713280
[16,] 0.9997632 0.9997475 -101.83842 -100.92933 -92.37932 0.006505313
[17,] 0.9997539 0.9997375 -99.87366 -98.96457 -90.41456 0.006771458
[18,] 0.9997321 0.9997142 -95.74584 -94.83675 -86.28674 0.007366610
[19,] 0.9997046 0.9996850 -91.26507 -90.35598 -81.80597 0.008072005
[20,] 0.9997200 0.9997013 -93.89391 -92.98482 -84.43481 0.007650355
RMSE
[1,] 0.07589975
[2,] 0.07782603
[3,] 0.07425882
[4,] 0.08256404
[5,] 0.07938116
[6,] 0.08230791
[7,] 0.07729928
[8,] 0.07968192
[9,] 0.07353085
[10,] 0.07095364
[11,] 0.07771139
[12,] 0.08017305
[13,] 0.08968408
[14,] 0.07397036
[15,] 0.08945386
[16,] 0.07729338
[17,] 0.07885864
[18,] 0.08225116
[19,] 0.08609916
[20,] 0.08382026
$ITER$eff
eff cpD1 cpD2 cpE cpR cpT Cy0 cpCQ cpMR fluo init1
[1,] 1.951465 17.32 15.43 NA NA NA NA NA NA 2.019437 0.09686212
[2,] 1.959912 17.37 15.45 NA NA NA NA NA NA 1.986170 0.07016143
[3,] 1.974724 17.29 15.33 NA NA NA NA NA NA 1.951952 0.03597171
[4,] 1.962987 17.37 15.43 NA NA NA NA NA NA 1.974902 0.05733131
[5,] 1.921363 17.33 15.38 NA NA NA NA NA NA 2.002992 0.08998748
[6,] 1.927840 17.38 15.41 NA NA NA NA NA NA 1.987541 0.07215907
[7,] 1.990264 17.32 15.40 NA NA NA NA NA NA 1.963729 0.03820658
[8,] 1.959224 17.34 15.44 NA NA NA NA NA NA 2.007911 0.08235887
[9,] 1.960054 17.38 15.45 NA NA NA NA NA NA 1.984079 0.06370201
[10,] 1.950148 17.35 15.41 NA NA NA NA NA NA 1.983360 0.06401986
[11,] 1.949860 17.33 15.41 NA NA NA NA NA NA 1.997155 0.07762558
[12,] 1.931297 17.39 15.47 NA NA NA NA NA NA 2.020715 0.09601110
[13,] 1.974865 17.37 15.45 NA NA NA NA NA NA 1.982575 0.05652215
[14,] 2.023581 17.30 15.43 NA NA NA NA NA NA 1.969434 0.03743030
[15,] 1.946897 17.38 15.45 NA NA NA NA NA NA 2.002206 0.07860079
[16,] 1.994929 17.36 15.48 NA NA NA NA NA NA 1.990702 0.06200407
[17,] 2.033439 17.35 15.48 NA NA NA NA NA NA 1.965828 0.02339232
[18,] 1.987763 17.39 15.53 NA NA NA NA NA NA 2.013588 0.07225319
[19,] 1.955118 17.37 15.46 NA NA NA NA NA NA 1.998582 0.08079887
[20,] 1.997717 17.32 15.46 NA NA NA NA NA NA 1.997721 0.07113203
init2 cf
[1,] 6.682891e-05 NA
[2,] 6.066808e-05 NA
[3,] 5.759138e-05 NA
[4,] 5.968018e-05 NA
[5,] 8.704935e-05 NA
[6,] 8.042139e-05 NA
[7,] 4.896194e-05 NA
[8,] 6.208216e-05 NA
[9,] 6.053679e-05 NA
[10,] 6.721389e-05 NA
[11,] 6.783592e-05 NA
[12,] 7.645722e-05 NA
[13,] 5.384865e-05 NA
[14,] 3.723064e-05 NA
[15,] 6.778884e-05 NA
[16,] 4.530312e-05 NA
[17,] 3.327559e-05 NA
[18,] 4.681311e-05 NA
[19,] 6.297804e-05 NA
[20,] 4.511079e-05 NA
$CONF
$CONF$coef
2.5% 97.5%
b -12.42576604 -11.78634898
c 0.02936753 0.09645788
d 11.29814443 11.34723989
e 17.53405721 17.63255581
$CONF$rmse
2.5% 97.5%
x 0.07531743 0.09347108
$CONF$rss
2.5% 97.5%
x 0.2553534 0.3931586
$CONF$gof
2.5% 97.5%
Rsq 0.99968145 0.999792775
Rsq.ad 0.99966021 0.999778960
AIC -108.56459595 -87.386948870
AICc -107.65550505 -86.477857961
BIC -99.10549446 -77.927847379
resVar 0.00567452 0.008736857
RMSE 0.07217782 0.089574725
$CONF$eff
2.5% 97.5%
eff 1.924440e+00 2.028757e+00
cpD1 1.729475e+01 1.739000e+01
cpD2 1.535375e+01 1.550625e+01
cpE NA NA
cpR NA NA
cpT NA NA
Cy0 NA NA
cpCQ NA NA
cpMR NA NA
fluo 1.957546e+00 2.020108e+00
init1 2.936753e-02 9.645788e-02
init2 3.515424e-05 8.390107e-05
cf NA NA
.........10.........20
fitting converged in 100% of iterations.
$ITER
$ITER$coef
b c d e
[1,] -12.06324 0.06246085 11.33224 17.59872
[2,] -11.98567 0.07452748 11.32704 17.59960
[3,] -12.09357 0.06657089 11.32434 17.59852
[4,] -12.05177 0.06598188 11.32562 17.58103
[5,] -12.03872 0.06168509 11.31920 17.58839
[6,] -12.18751 0.05882145 11.32622 17.60424
[7,] -12.07366 0.06399193 11.32925 17.58170
[8,] -12.12737 0.06606412 11.32382 17.60008
[9,] -12.03098 0.06391563 11.32524 17.59114
[10,] -11.88679 0.06226664 11.32222 17.61069
[11,] -12.01773 0.07048660 11.31931 17.57317
[12,] -12.07935 0.06810776 11.32861 17.59939
[13,] -12.10917 0.08103771 11.32423 17.60329
[14,] -11.95692 0.07822810 11.32397 17.61463
[15,] -12.06905 0.05936599 11.32550 17.59635
[16,] -12.04772 0.06773819 11.33348 17.60168
[17,] -12.16097 0.06339438 11.33037 17.60427
[18,] -12.11225 0.07850313 11.32640 17.60266
[19,] -12.12372 0.07955945 11.31910 17.60072
[20,] -12.07232 0.06780612 11.32548 17.59855
$ITER$rmse
[1] 0.08954116 0.08407532 0.08676906 0.08893704 0.08965883 0.08623156
[7] 0.08881957 0.08837512 0.09154310 0.08735406 0.08686161 0.08496171
[13] 0.09157775 0.08687119 0.08759583 0.08956198 0.08693185 0.09145619
[19] 0.08859550 0.08911754
$ITER$rss
[1] 0.3207048 0.2827464 0.3011548 0.3163919 0.3215482 0.2974353 0.3155566
[8] 0.3124064 0.3352056 0.3052292 0.3017976 0.2887397 0.3354594 0.3018642
[15] 0.3069212 0.3208539 0.3022858 0.3345694 0.3139665 0.3176774
$ITER$gof
Rsq Rsq.ad AIC AICc BIC resVar RMSE
[1,] 0.9997042 0.9996820 -81.67606 -80.65042 -72.75511 0.008017620 0.08537415
[2,] 0.9997520 0.9997334 -87.21877 -86.19313 -78.29782 0.007068660 0.08016267
[3,] 0.9997212 0.9997003 -84.44352 -83.41787 -75.52257 0.007528869 0.08273105
[4,] 0.9997133 0.9996918 -82.27180 -81.24616 -73.35085 0.007909796 0.08479814
[5,] 0.9997106 0.9996889 -81.56050 -80.53485 -72.63955 0.008038705 0.08548634
[6,] 0.9997309 0.9997107 -84.99033 -83.96469 -76.06938 0.007435882 0.08221857
[7,] 0.9996992 0.9996767 -82.38811 -81.36247 -73.46716 0.007888915 0.08468613
[8,] 0.9997001 0.9996776 -82.82956 -81.80392 -73.90862 0.007810161 0.08426237
[9,] 0.9996984 0.9996758 -79.73025 -78.70461 -70.80930 0.008380139 0.08728292
[10,] 0.9997308 0.9997106 -83.85221 -82.82657 -74.93126 0.007630731 0.08328882
[11,] 0.9997307 0.9997105 -84.34970 -83.32406 -75.42875 0.007544939 0.08281930
[12,] 0.9997485 0.9997297 -86.29586 -85.27022 -77.37491 0.007218492 0.08100781
[13,] 0.9996604 0.9996349 -79.69695 -78.67130 -70.77600 0.008386485 0.08731596
[14,] 0.9997234 0.9997027 -84.33999 -83.31435 -75.41904 0.007546604 0.08282843
[15,] 0.9997269 0.9997065 -83.60899 -82.58334 -74.68804 0.007673029 0.08351934
[16,] 0.9997137 0.9996922 -81.65561 -80.62997 -72.73466 0.008021348 0.08539399
[17,] 0.9997237 0.9997030 -84.27857 -83.25293 -75.35762 0.007557146 0.08288626
[18,] 0.9996625 0.9996372 -79.81384 -78.78820 -70.89289 0.008364234 0.08720005
[19,] 0.9997178 0.9996966 -82.61039 -81.58475 -73.68944 0.007849163 0.08447250
[20,] 0.9997226 0.9997018 -82.09338 -81.06774 -73.17243 0.007941936 0.08497024
$ITER$eff
eff cpD1 cpD2 cpE cpR cpT Cy0 cpCQ cpMR fluo init1
[1,] 1.966718 17.36 15.44 NA NA NA NA NA NA 1.989446 0.06246085
[2,] 1.948983 17.36 15.42 NA NA NA NA NA NA 1.989025 0.07452748
[3,] 1.966562 17.36 15.44 NA NA NA NA NA NA 1.985388 0.06657089
[4,] 1.964052 17.34 15.42 NA NA NA NA NA NA 1.988037 0.06598188
[5,] 1.965259 17.35 15.43 NA NA NA NA NA NA 1.990521 0.06168509
[6,] 1.981176 17.37 15.47 NA NA NA NA NA NA 1.991111 0.05882145
[7,] 1.967051 17.34 15.43 NA NA NA NA NA NA 1.994187 0.06399193
[8,] 1.969693 17.36 15.45 NA NA NA NA NA NA 1.988635 0.06606412
[9,] 1.962378 17.35 15.43 NA NA NA NA NA NA 1.992025 0.06391563
[10,] 1.950549 17.36 15.41 NA NA NA NA NA NA 1.974662 0.06226664
[11,] 1.956599 17.33 15.41 NA NA NA NA NA NA 1.993958 0.07048660
[12,] 1.963378 17.36 15.44 NA NA NA NA NA NA 1.989404 0.06810776
[13,] 1.953401 17.36 15.45 NA NA NA NA NA NA 2.001379 0.08103771
[14,] 1.941331 17.37 15.43 NA NA NA NA NA NA 1.993716 0.07822810
[15,] 1.970229 17.36 15.44 NA NA NA NA NA NA 1.987103 0.05936599
[16,] 1.959936 17.36 15.44 NA NA NA NA NA NA 1.994036 0.06773819
[17,] 1.975137 17.37 15.46 NA NA NA NA NA NA 1.988493 0.06339438
[18,] 1.956135 17.36 15.45 NA NA NA NA NA NA 1.999693 0.07850313
[19,] 1.956375 17.36 15.45 NA NA NA NA NA NA 1.999068 0.07955945
[20,] 1.962702 17.36 15.44 NA NA NA NA NA NA 1.991007 0.06780612
init2 cf
[1,] 5.799019e-05 NA
[2,] 6.757716e-05 NA
[3,] 5.794269e-05 NA
[4,] 5.997978e-05 NA
[5,] 5.908811e-05 NA
[6,] 5.078040e-05 NA
[7,] 5.836999e-05 NA
[8,] 5.624677e-05 NA
[9,] 6.048627e-05 NA
[10,] 6.670758e-05 NA
[11,] 6.422042e-05 NA
[12,] 5.953100e-05 NA
[13,] 6.435793e-05 NA
[14,] 7.149665e-05 NA
[15,] 5.634831e-05 NA
[16,] 6.130810e-05 NA
[17,] 5.352932e-05 NA
[18,] 6.292915e-05 NA
[19,] 6.279034e-05 NA
[20,] 5.989673e-05 NA
$CONF
$CONF$coef
2.5% 97.5%
b -12.1749078 -11.92010052
c 0.0590801 0.08033553
d 11.3191458 11.33288991
e 17.5769019 17.61275712
$CONF$rmse
2.5% 97.5%
x 0.08449636 0.09156129
$CONF$rss
2.5% 97.5%
x 0.2855932 0.3353388
$CONF$gof
2.5% 97.5%
Rsq 0.99966140 0.999750370
Rsq.ad 0.99963600 0.999731648
AIC -86.78038894 -79.712764627
AICc -85.75474791 -78.687123601
BIC -77.85944077 -70.791816457
resVar 0.00713983 0.008383471
RMSE 0.08056411 0.087300268
$CONF$eff
2.5% 97.5%
eff 1.944966e+00 1.978307e+00
cpD1 1.733475e+01 1.737000e+01
cpD2 1.541000e+01 1.546525e+01
cpE NA NA
cpR NA NA
cpT NA NA
Cy0 NA NA
cpCQ NA NA
cpMR NA NA
fluo 1.979757e+00 2.000578e+00
init1 5.908010e-02 8.033553e-02
init2 5.208613e-05 6.963489e-05
cf NA NA
qpcR documentation built on May 2, 2019, 5:17 a.m.
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Description Usage Arguments Details Value Author(s) References Examples
Description
Confidence intervals for the estimated parameters and goodness-of-fit measures are calculated for a nonlinear qPCR data fit by either
a) boostrapping the residuals of the fit or
b) jackknifing and refitting the data.
Confidence intervals can also be calculated for all parameters obtained from the efficiency analysis.
Usage
1 2 |
Arguments
object |
an object of class 'pcrfit'. |
type |
either |
B |
numeric. The number of iterations. |
njack |
numeric. In case of |
plot |
should the fitting and final results be displayed as a plot? |
do.eff |
logical. If |
conf |
the confidence level. |
verbose |
logical. If |
... |
other parameters to be passed on to the plotting functions. |
Details
Non-parametric bootstrapping is applied using the centered residuals.
1) Obtain the residuals from the fit:
\hat{\varepsilon}_t = y_t - f(x_t, \hat{θ})
2) Draw bootstrap pseudodata:
y_{t}^{\ast} = f(x_t, \hat{θ}) + ε_{t}^{\ast}
where ε_{t}^{\ast} are i.i.d. from distribution \hat{F}, where the residuals from the original fit are centered at zero.
3) Fit \hatθ^\ast by nonlinear least-squares.
4) Repeat B times, yielding bootstrap replications
\hatθ^{\ast 1}, \hatθ^{\ast 2}, …, \hatθ^{\ast B}
One can then characterize the EDF and calculate confidence intervals for each parameter:
θ \in [EDF^{-1}(α/2), EDF^{-1}(1-α/2)]
The jackknife alternative is to perform the bootstrap on the data-predictor vector, i.e. eliminating a certain number of datapoints.
If the residuals are correlated or have non-constant variance the latter is recommended. This may be the case in qPCR data,
as the variance in the low fluorescence region (ground phase) is usually much higher than in the rest of the curve.
Value
A list containing the following items:
ITER |
a list containing each of the results from the iterations. |
CONF |
a list containing the confidence intervals for each item in |
Each item contains subitems for the coefficients (coef), root-mean-squared error (rmse), residual sum-of-squares (rss), goodness-of-fit measures (gof) and the efficiency analysis (eff). If plot = TRUE, all data is plotted as boxplots including confidence intervals.
Author(s)
Andrej-Nikolai Spiess
References
Nonlinear regression analysis and its applications.
Bates DM & Watts DG.
Wiley, Chichester, UK, 1988.
Nonlinear regression.
Seber GAF & Wild CJ.
Wiley, New York, 1989.
Boostrap accuracy for non-linear regression models.
Roy T.
J Chemometics (1994), 8: 37-44.
Examples
1 2 3 4 5 6 7 8 9 10 |
Example output
Loading required package: MASS
Loading required package: minpack.lm
Loading required package: rgl
Loading required package: robustbase
Loading required package: Matrix
Warning messages:
1: In rgl.init(initValue, onlyNULL) : RGL: unable to open X11 display
2: 'rgl_init' failed, running with rgl.useNULL = TRUE
3: .onUnload failed in unloadNamespace() for 'rgl', details:
call: fun(...)
error: object 'rgl_quit' not found
.........10.........20
fitting converged in 100% of iterations.
$ITER
$ITER$coef
b c d e
[1,] -12.21118 0.09686212 11.33265 17.55819
[2,] -12.07278 0.07016143 11.31772 17.61487
[3,] -11.81028 0.03597171 11.33150 17.53671
[4,] -11.97491 0.05733131 11.31543 17.61115
[5,] -11.83458 0.08998748 11.30267 17.57865
[6,] -11.76470 0.07215907 11.34185 17.63384
[7,] -12.02630 0.03820658 11.32024 17.56343
[8,] -12.16614 0.08235887 11.33595 17.57804
[9,] -12.01651 0.06370201 11.34809 17.62744
[10,] -11.90387 0.06401986 11.31160 17.59889
[11,] -12.01525 0.07762558 11.32354 17.57681
[12,] -12.05149 0.09601110 11.32681 17.63113
[13,] -12.09255 0.05652215 11.32326 17.60491
[14,] -12.33257 0.03743030 11.30060 17.53166
[15,] -12.02775 0.07860079 11.34630 17.61969
[16,] -12.34194 0.06200407 11.32437 17.58958
[17,] -12.33862 0.02339232 11.29593 17.57953
[18,] -12.41745 0.07225319 11.32995 17.62079
[19,] -12.12952 0.08079887 11.32357 17.61310
[20,] -12.43329 0.07113203 11.30092 17.54731
$ITER$rmse
[1] 0.07920127 0.08121134 0.07748896 0.08615544 0.08283411 0.08588817
[7] 0.08066167 0.08314796 0.07672933 0.07404001 0.08109171 0.08366045
[13] 0.09358520 0.07718795 0.09334495 0.08065552 0.08228887 0.08582896
[19] 0.08984434 0.08746631
$ITER$rss
[1] 0.2822778 0.2967877 0.2702042 0.3340242 0.3087671 0.3319550 0.2927838
[8] 0.3111112 0.2649325 0.2466865 0.2959140 0.3149582 0.3941185 0.2681091
[15] 0.3920976 0.2927391 0.3047156 0.3314974 0.3632402 0.3442660
$ITER$gof
Rsq Rsq.ad AIC AICc BIC resVar
[1,] 0.9997701 0.9997548 -103.62153 -102.71244 -94.16243 0.006272841
[2,] 0.9997587 0.9997426 -101.16540 -100.25631 -91.70630 0.006595281
[3,] 0.9997811 0.9997665 -105.76350 -104.85441 -96.30440 0.006004538
[4,] 0.9997286 0.9997105 -95.37376 -94.46467 -85.91466 0.007422761
[5,] 0.9997465 0.9997296 -99.22646 -98.31737 -89.76736 0.006861490
[6,] 0.9997303 0.9997123 -95.67825 -94.76916 -86.21915 0.007376778
[7,] 0.9997630 0.9997472 -101.83095 -100.92185 -92.37184 0.006506306
[8,] 0.9997474 0.9997306 -98.85585 -97.94676 -89.39675 0.006913583
[9,] 0.9997859 0.9997717 -106.72894 -105.81985 -97.26984 0.005887390
[10,] 0.9997990 0.9997856 -110.22542 -109.31633 -100.76632 0.005481923
[11,] 0.9997590 0.9997429 -101.30986 -100.40077 -91.85076 0.006575866
[12,] 0.9997432 0.9997261 -98.25368 -97.34459 -88.79458 0.006999070
[13,] 0.9996807 0.9996594 -87.26730 -86.35821 -77.80819 0.008758189
[14,] 0.9997829 0.9997684 -106.14492 -105.23583 -96.68582 0.005957980
[15,] 0.9996823 0.9996611 -87.51920 -86.61011 -78.06009 0.008713280
[16,] 0.9997632 0.9997475 -101.83842 -100.92933 -92.37932 0.006505313
[17,] 0.9997539 0.9997375 -99.87366 -98.96457 -90.41456 0.006771458
[18,] 0.9997321 0.9997142 -95.74584 -94.83675 -86.28674 0.007366610
[19,] 0.9997046 0.9996850 -91.26507 -90.35598 -81.80597 0.008072005
[20,] 0.9997200 0.9997013 -93.89391 -92.98482 -84.43481 0.007650355
RMSE
[1,] 0.07589975
[2,] 0.07782603
[3,] 0.07425882
[4,] 0.08256404
[5,] 0.07938116
[6,] 0.08230791
[7,] 0.07729928
[8,] 0.07968192
[9,] 0.07353085
[10,] 0.07095364
[11,] 0.07771139
[12,] 0.08017305
[13,] 0.08968408
[14,] 0.07397036
[15,] 0.08945386
[16,] 0.07729338
[17,] 0.07885864
[18,] 0.08225116
[19,] 0.08609916
[20,] 0.08382026
$ITER$eff
eff cpD1 cpD2 cpE cpR cpT Cy0 cpCQ cpMR fluo init1
[1,] 1.951465 17.32 15.43 NA NA NA NA NA NA 2.019437 0.09686212
[2,] 1.959912 17.37 15.45 NA NA NA NA NA NA 1.986170 0.07016143
[3,] 1.974724 17.29 15.33 NA NA NA NA NA NA 1.951952 0.03597171
[4,] 1.962987 17.37 15.43 NA NA NA NA NA NA 1.974902 0.05733131
[5,] 1.921363 17.33 15.38 NA NA NA NA NA NA 2.002992 0.08998748
[6,] 1.927840 17.38 15.41 NA NA NA NA NA NA 1.987541 0.07215907
[7,] 1.990264 17.32 15.40 NA NA NA NA NA NA 1.963729 0.03820658
[8,] 1.959224 17.34 15.44 NA NA NA NA NA NA 2.007911 0.08235887
[9,] 1.960054 17.38 15.45 NA NA NA NA NA NA 1.984079 0.06370201
[10,] 1.950148 17.35 15.41 NA NA NA NA NA NA 1.983360 0.06401986
[11,] 1.949860 17.33 15.41 NA NA NA NA NA NA 1.997155 0.07762558
[12,] 1.931297 17.39 15.47 NA NA NA NA NA NA 2.020715 0.09601110
[13,] 1.974865 17.37 15.45 NA NA NA NA NA NA 1.982575 0.05652215
[14,] 2.023581 17.30 15.43 NA NA NA NA NA NA 1.969434 0.03743030
[15,] 1.946897 17.38 15.45 NA NA NA NA NA NA 2.002206 0.07860079
[16,] 1.994929 17.36 15.48 NA NA NA NA NA NA 1.990702 0.06200407
[17,] 2.033439 17.35 15.48 NA NA NA NA NA NA 1.965828 0.02339232
[18,] 1.987763 17.39 15.53 NA NA NA NA NA NA 2.013588 0.07225319
[19,] 1.955118 17.37 15.46 NA NA NA NA NA NA 1.998582 0.08079887
[20,] 1.997717 17.32 15.46 NA NA NA NA NA NA 1.997721 0.07113203
init2 cf
[1,] 6.682891e-05 NA
[2,] 6.066808e-05 NA
[3,] 5.759138e-05 NA
[4,] 5.968018e-05 NA
[5,] 8.704935e-05 NA
[6,] 8.042139e-05 NA
[7,] 4.896194e-05 NA
[8,] 6.208216e-05 NA
[9,] 6.053679e-05 NA
[10,] 6.721389e-05 NA
[11,] 6.783592e-05 NA
[12,] 7.645722e-05 NA
[13,] 5.384865e-05 NA
[14,] 3.723064e-05 NA
[15,] 6.778884e-05 NA
[16,] 4.530312e-05 NA
[17,] 3.327559e-05 NA
[18,] 4.681311e-05 NA
[19,] 6.297804e-05 NA
[20,] 4.511079e-05 NA
$CONF
$CONF$coef
2.5% 97.5%
b -12.42576604 -11.78634898
c 0.02936753 0.09645788
d 11.29814443 11.34723989
e 17.53405721 17.63255581
$CONF$rmse
2.5% 97.5%
x 0.07531743 0.09347108
$CONF$rss
2.5% 97.5%
x 0.2553534 0.3931586
$CONF$gof
2.5% 97.5%
Rsq 0.99968145 0.999792775
Rsq.ad 0.99966021 0.999778960
AIC -108.56459595 -87.386948870
AICc -107.65550505 -86.477857961
BIC -99.10549446 -77.927847379
resVar 0.00567452 0.008736857
RMSE 0.07217782 0.089574725
$CONF$eff
2.5% 97.5%
eff 1.924440e+00 2.028757e+00
cpD1 1.729475e+01 1.739000e+01
cpD2 1.535375e+01 1.550625e+01
cpE NA NA
cpR NA NA
cpT NA NA
Cy0 NA NA
cpCQ NA NA
cpMR NA NA
fluo 1.957546e+00 2.020108e+00
init1 2.936753e-02 9.645788e-02
init2 3.515424e-05 8.390107e-05
cf NA NA
.........10.........20
fitting converged in 100% of iterations.
$ITER
$ITER$coef
b c d e
[1,] -12.06324 0.06246085 11.33224 17.59872
[2,] -11.98567 0.07452748 11.32704 17.59960
[3,] -12.09357 0.06657089 11.32434 17.59852
[4,] -12.05177 0.06598188 11.32562 17.58103
[5,] -12.03872 0.06168509 11.31920 17.58839
[6,] -12.18751 0.05882145 11.32622 17.60424
[7,] -12.07366 0.06399193 11.32925 17.58170
[8,] -12.12737 0.06606412 11.32382 17.60008
[9,] -12.03098 0.06391563 11.32524 17.59114
[10,] -11.88679 0.06226664 11.32222 17.61069
[11,] -12.01773 0.07048660 11.31931 17.57317
[12,] -12.07935 0.06810776 11.32861 17.59939
[13,] -12.10917 0.08103771 11.32423 17.60329
[14,] -11.95692 0.07822810 11.32397 17.61463
[15,] -12.06905 0.05936599 11.32550 17.59635
[16,] -12.04772 0.06773819 11.33348 17.60168
[17,] -12.16097 0.06339438 11.33037 17.60427
[18,] -12.11225 0.07850313 11.32640 17.60266
[19,] -12.12372 0.07955945 11.31910 17.60072
[20,] -12.07232 0.06780612 11.32548 17.59855
$ITER$rmse
[1] 0.08954116 0.08407532 0.08676906 0.08893704 0.08965883 0.08623156
[7] 0.08881957 0.08837512 0.09154310 0.08735406 0.08686161 0.08496171
[13] 0.09157775 0.08687119 0.08759583 0.08956198 0.08693185 0.09145619
[19] 0.08859550 0.08911754
$ITER$rss
[1] 0.3207048 0.2827464 0.3011548 0.3163919 0.3215482 0.2974353 0.3155566
[8] 0.3124064 0.3352056 0.3052292 0.3017976 0.2887397 0.3354594 0.3018642
[15] 0.3069212 0.3208539 0.3022858 0.3345694 0.3139665 0.3176774
$ITER$gof
Rsq Rsq.ad AIC AICc BIC resVar RMSE
[1,] 0.9997042 0.9996820 -81.67606 -80.65042 -72.75511 0.008017620 0.08537415
[2,] 0.9997520 0.9997334 -87.21877 -86.19313 -78.29782 0.007068660 0.08016267
[3,] 0.9997212 0.9997003 -84.44352 -83.41787 -75.52257 0.007528869 0.08273105
[4,] 0.9997133 0.9996918 -82.27180 -81.24616 -73.35085 0.007909796 0.08479814
[5,] 0.9997106 0.9996889 -81.56050 -80.53485 -72.63955 0.008038705 0.08548634
[6,] 0.9997309 0.9997107 -84.99033 -83.96469 -76.06938 0.007435882 0.08221857
[7,] 0.9996992 0.9996767 -82.38811 -81.36247 -73.46716 0.007888915 0.08468613
[8,] 0.9997001 0.9996776 -82.82956 -81.80392 -73.90862 0.007810161 0.08426237
[9,] 0.9996984 0.9996758 -79.73025 -78.70461 -70.80930 0.008380139 0.08728292
[10,] 0.9997308 0.9997106 -83.85221 -82.82657 -74.93126 0.007630731 0.08328882
[11,] 0.9997307 0.9997105 -84.34970 -83.32406 -75.42875 0.007544939 0.08281930
[12,] 0.9997485 0.9997297 -86.29586 -85.27022 -77.37491 0.007218492 0.08100781
[13,] 0.9996604 0.9996349 -79.69695 -78.67130 -70.77600 0.008386485 0.08731596
[14,] 0.9997234 0.9997027 -84.33999 -83.31435 -75.41904 0.007546604 0.08282843
[15,] 0.9997269 0.9997065 -83.60899 -82.58334 -74.68804 0.007673029 0.08351934
[16,] 0.9997137 0.9996922 -81.65561 -80.62997 -72.73466 0.008021348 0.08539399
[17,] 0.9997237 0.9997030 -84.27857 -83.25293 -75.35762 0.007557146 0.08288626
[18,] 0.9996625 0.9996372 -79.81384 -78.78820 -70.89289 0.008364234 0.08720005
[19,] 0.9997178 0.9996966 -82.61039 -81.58475 -73.68944 0.007849163 0.08447250
[20,] 0.9997226 0.9997018 -82.09338 -81.06774 -73.17243 0.007941936 0.08497024
$ITER$eff
eff cpD1 cpD2 cpE cpR cpT Cy0 cpCQ cpMR fluo init1
[1,] 1.966718 17.36 15.44 NA NA NA NA NA NA 1.989446 0.06246085
[2,] 1.948983 17.36 15.42 NA NA NA NA NA NA 1.989025 0.07452748
[3,] 1.966562 17.36 15.44 NA NA NA NA NA NA 1.985388 0.06657089
[4,] 1.964052 17.34 15.42 NA NA NA NA NA NA 1.988037 0.06598188
[5,] 1.965259 17.35 15.43 NA NA NA NA NA NA 1.990521 0.06168509
[6,] 1.981176 17.37 15.47 NA NA NA NA NA NA 1.991111 0.05882145
[7,] 1.967051 17.34 15.43 NA NA NA NA NA NA 1.994187 0.06399193
[8,] 1.969693 17.36 15.45 NA NA NA NA NA NA 1.988635 0.06606412
[9,] 1.962378 17.35 15.43 NA NA NA NA NA NA 1.992025 0.06391563
[10,] 1.950549 17.36 15.41 NA NA NA NA NA NA 1.974662 0.06226664
[11,] 1.956599 17.33 15.41 NA NA NA NA NA NA 1.993958 0.07048660
[12,] 1.963378 17.36 15.44 NA NA NA NA NA NA 1.989404 0.06810776
[13,] 1.953401 17.36 15.45 NA NA NA NA NA NA 2.001379 0.08103771
[14,] 1.941331 17.37 15.43 NA NA NA NA NA NA 1.993716 0.07822810
[15,] 1.970229 17.36 15.44 NA NA NA NA NA NA 1.987103 0.05936599
[16,] 1.959936 17.36 15.44 NA NA NA NA NA NA 1.994036 0.06773819
[17,] 1.975137 17.37 15.46 NA NA NA NA NA NA 1.988493 0.06339438
[18,] 1.956135 17.36 15.45 NA NA NA NA NA NA 1.999693 0.07850313
[19,] 1.956375 17.36 15.45 NA NA NA NA NA NA 1.999068 0.07955945
[20,] 1.962702 17.36 15.44 NA NA NA NA NA NA 1.991007 0.06780612
init2 cf
[1,] 5.799019e-05 NA
[2,] 6.757716e-05 NA
[3,] 5.794269e-05 NA
[4,] 5.997978e-05 NA
[5,] 5.908811e-05 NA
[6,] 5.078040e-05 NA
[7,] 5.836999e-05 NA
[8,] 5.624677e-05 NA
[9,] 6.048627e-05 NA
[10,] 6.670758e-05 NA
[11,] 6.422042e-05 NA
[12,] 5.953100e-05 NA
[13,] 6.435793e-05 NA
[14,] 7.149665e-05 NA
[15,] 5.634831e-05 NA
[16,] 6.130810e-05 NA
[17,] 5.352932e-05 NA
[18,] 6.292915e-05 NA
[19,] 6.279034e-05 NA
[20,] 5.989673e-05 NA
$CONF
$CONF$coef
2.5% 97.5%
b -12.1749078 -11.92010052
c 0.0590801 0.08033553
d 11.3191458 11.33288991
e 17.5769019 17.61275712
$CONF$rmse
2.5% 97.5%
x 0.08449636 0.09156129
$CONF$rss
2.5% 97.5%
x 0.2855932 0.3353388
$CONF$gof
2.5% 97.5%
Rsq 0.99966140 0.999750370
Rsq.ad 0.99963600 0.999731648
AIC -86.78038894 -79.712764627
AICc -85.75474791 -78.687123601
BIC -77.85944077 -70.791816457
resVar 0.00713983 0.008383471
RMSE 0.08056411 0.087300268
$CONF$eff
2.5% 97.5%
eff 1.944966e+00 1.978307e+00
cpD1 1.733475e+01 1.737000e+01
cpD2 1.541000e+01 1.546525e+01
cpE NA NA
cpR NA NA
cpT NA NA
Cy0 NA NA
cpCQ NA NA
cpMR NA NA
fluo 1.979757e+00 2.000578e+00
init1 5.908010e-02 8.033553e-02
init2 5.208613e-05 6.963489e-05
cf NA NA
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