+ - - - - - -

Example evaluation of FOCUS Laboratory Data L1 to L3

Laboratory Data L1
Laboratory Data L2
Laboratory Data L3
Laboratory Data L4

Laboratory Data L1

- -

The following code defines example dataset L1 from the FOCUS kinetics -report, p. 284:

- -

library("mkin")
-FOCUS_2006_L1 = data.frame(
+The following code defines example dataset L1 from the FOCUS kinetics report, p. 284:
+library("mkin")
+## Loading required package: minpack.lm
+## Loading required package: rootSolve
+## Loading required package: inline
+## Loading required package: methods
+FOCUS_2006_L1 = data.frame(
   t = rep(c(0, 1, 2, 3, 5, 7, 14, 21, 30), each = 2),
   parent = c(88.3, 91.4, 85.6, 84.5, 78.9, 77.6, 
              72.0, 71.9, 50.3, 59.4, 47.0, 45.1,
              27.7, 27.3, 10.0, 10.4, 2.9, 4.0))
-FOCUS_2006_L1_mkin <- mkin_wide_to_long(FOCUS_2006_L1)
-
-
-Here we use the assumptions of simple first order (SFO), the case of declining
-rate constant over time (FOMC) and the case of two different phases of the
-kinetics (DFOP). For a more detailed discussion of the models, please see the
-FOCUS kinetics report.
-
-Since mkin version 0.9-32 (July 2014), we can use shorthand notation like SFO
-for parent only degradation models. The following two lines fit the model and
-produce the summary report of the model fit. This covers the numerical analysis
-given in the FOCUS report. 
-
-m.L1.SFO <- mkinfit("SFO", FOCUS_2006_L1_mkin, quiet=TRUE)
-summary(m.L1.SFO)
-
-
-## mkin version:    0.9.36 
+FOCUS_2006_L1_mkin <- mkin_wide_to_long(FOCUS_2006_L1)
+Here we use the assumptions of simple first order (SFO), the case of declining rate constant over time (FOMC) and the case of two different phases of the kinetics (DFOP). For a more detailed discussion of the models, please see the FOCUS kinetics report.
+Since mkin version 0.9-32 (July 2014), we can use shorthand notation like SFO for parent only degradation models. The following two lines fit the model and produce the summary report of the model fit. This covers the numerical analysis given in the FOCUS report.
+m.L1.SFO <- mkinfit("SFO", FOCUS_2006_L1_mkin, quiet=TRUE)
+summary(m.L1.SFO)
+## mkin version:    0.9.37 
 ## R version:       3.2.1 
-## Date of fit:     Sun Jun 21 18:14:52 2015 
-## Date of summary: Sun Jun 21 18:14:52 2015 
+## Date of fit:     Mon Jun 22 18:38:53 2015 
+## Date of summary: Mon Jun 22 18:38:53 2015 
 ## 
 ## Equations:
 ## d_parent = - k_parent_sink * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted with method Port using 37 model solutions performed in 0.096 s
+## Fitted with method Port using 37 model solutions performed in 0.089 s
 ## 
 ## Weighting: none
 ## 
@@ -315,39 +174,21 @@ summary(m.L1.SFO)
 ##    21   parent     10.0    12.416  -2.4163
 ##    21   parent     10.4    12.416  -2.0163
 ##    30   parent      2.9     5.251  -2.3513
-##    30   parent      4.0     5.251  -1.2513
-
-
+##    30   parent      4.0     5.251  -1.2513

A plot of the fit is obtained with the plot function for mkinfit objects.

- -

plot(m.L1.SFO)
-

- -

plot of chunk unnamed-chunk-4 -The residual plot can be easily obtained by

- -

mkinresplot(m.L1.SFO, ylab = "Observed", xlab = "Time")
-

- -

plot of chunk unnamed-chunk-5

- -

For comparison, the FOMC model is fitted as well, and the chi² error level -is checked.

- -

m.L1.FOMC <- mkinfit("FOMC", FOCUS_2006_L1_mkin, quiet=TRUE)
-

- +

plot(m.L1.SFO)

The residual plot can be easily obtained by

mkinresplot(m.L1.SFO, ylab = "Observed", xlab = "Time")

For comparison, the FOMC model is fitted as well, and the chi^2 error level is checked.

m.L1.FOMC <- mkinfit("FOMC", FOCUS_2006_L1_mkin, quiet=TRUE)

## Warning in mkinfit("FOMC", FOCUS_2006_L1_mkin, quiet = TRUE): Optimisation by method Port did not converge.
-## Convergence code is 1
-

- -

summary(m.L1.FOMC, data = FALSE)
-

- -

## mkin version:    0.9.36 
+## Convergence code is 1

summary(m.L1.FOMC, data = FALSE)

## mkin version:    0.9.37 
 ## R version:       3.2.1 
-## Date of fit:     Sun Jun 21 18:14:53 2015 
-## Date of summary: Sun Jun 21 18:14:53 2015 
+## Date of fit:     Mon Jun 22 18:38:54 2015 
+## Date of summary: Mon Jun 22 18:38:54 2015 
 ## 
 ## 
 ## Warning: Optimisation by method Port did not converge.
@@ -359,7 +200,7 @@ is checked.
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted with method Port using 188 model solutions performed in 0.486 s
+## Fitted with method Port using 188 model solutions performed in 0.397 s
 ## 
 ## Weighting: none
 ## 
@@ -408,55 +249,33 @@ is checked.
 ## 
 ## Estimated disappearance times:
 ##        DT50  DT90 DT50back
-## parent 7.25 24.08     7.25
-

- -

Due to the higher number of parameters, and the lower number of degrees of -freedom of the fit, the chi² error level is actually higher for the FOMC -model (3.6%) than for the SFO model (3.4%). Additionally, the parameters -log_alpha and log_beta internally fitted in the model have p-values for the two -sided t-test of 0.18 and 0.125, and their correlation is 1.000, indicating that -the model is overparameterised.

- -

The chi² error levels reported in Appendix 3 and Appendix 7 to the FOCUS -kinetics report are rounded to integer percentages and partly deviate by one -percentage point from the results calculated by mkin. The reason for -this is not known. However, mkin gives the same chi² error levels -as the kinfit package. Furthermore, the calculation routines of the kinfit -package have been extensively compared to the results obtained by the KinGUI -software, as documented in the kinfit package vignette. KinGUI is a widely used -standard package in this field.

- +## parent 7.25 24.08 7.25 +

Due to the higher number of parameters, and the lower number of degrees of freedom of the fit, the chi^2 error level is actually higher for the FOMC model (3.6%) than for the SFO model (3.4%). Additionally, the parameters log_alpha and log_beta internally fitted in the model have p-values for the two sided t-test of 0.18 and 0.125, and their correlation is 1.000, indicating that the model is overparameterised.

The chi^2 error levels reported in Appendix 3 and Appendix 7 to the FOCUS kinetics report are rounded to integer percentages and partly deviate by one percentage point from the results calculated by mkin. The reason for this is not known. However, mkin gives the same chi^2 error levels as the kinfit package. Furthermore, the calculation routines of the kinfit package have been extensively compared to the results obtained by the KinGUI software, as documented in the kinfit package vignette. KinGUI is a widely used standard package in this field.

Laboratory Data L2

- -

The following code defines example dataset L2 from the FOCUS kinetics -report, p. 287:

- -

FOCUS_2006_L2 = data.frame(
+The following code defines example dataset L2 from the FOCUS kinetics report, p. 287:
+FOCUS_2006_L2 = data.frame(
   t = rep(c(0, 1, 3, 7, 14, 28), each = 2),
   parent = c(96.1, 91.8, 41.4, 38.7,
              19.3, 22.3, 4.6, 4.6,
              2.6, 1.2, 0.3, 0.6))
-FOCUS_2006_L2_mkin <- mkin_wide_to_long(FOCUS_2006_L2)
-
-
+FOCUS_2006_L2_mkin <- mkin_wide_to_long(FOCUS_2006_L2)

Again, the SFO model is fitted and a summary is obtained:

- -

m.L2.SFO <- mkinfit("SFO", FOCUS_2006_L2_mkin, quiet=TRUE)
-summary(m.L2.SFO)
-

- -

## mkin version:    0.9.36 
+m.L2.SFO <- mkinfit("SFO", FOCUS_2006_L2_mkin, quiet=TRUE)
+summary(m.L2.SFO)
+## mkin version:    0.9.37 
 ## R version:       3.2.1 
-## Date of fit:     Sun Jun 21 18:14:53 2015 
-## Date of summary: Sun Jun 21 18:14:53 2015 
+## Date of fit:     Mon Jun 22 18:38:54 2015 
+## Date of summary: Mon Jun 22 18:38:54 2015 
 ## 
 ## Equations:
 ## d_parent = - k_parent_sink * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted with method Port using 41 model solutions performed in 0.101 s
+## Fitted with method Port using 41 model solutions performed in 0.086 s
 ## 
 ## Weighting: none
 ## 
@@ -519,54 +338,32 @@ summary(m.L2.SFO)
 ##    14   parent      2.6 8.532e-03   2.5915
 ##    14   parent      1.2 8.532e-03   1.1915
 ##    28   parent      0.3 7.958e-07   0.3000
-##    28   parent      0.6 7.958e-07   0.6000
-
-
-The chi² error level of 14% suggests that the model does not fit very well.
-This is also obvious from the plots of the fit and the residuals.
-
-par(mfrow = c(2, 1))
+##    28   parent      0.6 7.958e-07   0.6000
+The chi^2 error level of 14% suggests that the model does not fit very well. This is also obvious from the plots of the fit and the residuals.
+par(mfrow = c(2, 1))
 plot(m.L2.SFO)
-mkinresplot(m.L2.SFO)
-
-
- 
-
-In the FOCUS kinetics report, it is stated that there is no apparent systematic
-error observed from the residual plot up to the measured DT90 (approximately at
-day 5), and there is an underestimation beyond that point.
-
-We may add that it is difficult to judge the random nature of the residuals just 
-from the three samplings at days 0, 1 and 3. Also, it is not clear a
-priori why a consistent underestimation after the approximate DT90 should be
-irrelevant. However, this can be rationalised by the fact that the FOCUS fate
-models generally only implement SFO kinetics.
-
-For comparison, the FOMC model is fitted as well, and the chi² error level
-is checked.
-
-m.L2.FOMC <- mkinfit("FOMC", FOCUS_2006_L2_mkin, quiet = TRUE)
+mkinresplot(m.L2.SFO)
+
+In the FOCUS kinetics report, it is stated that there is no apparent systematic error observed from the residual plot up to the measured DT90 (approximately at day 5), and there is an underestimation beyond that point.
+We may add that it is difficult to judge the random nature of the residuals just from the three samplings at days 0, 1 and 3. Also, it is not clear a priori why a consistent underestimation after the approximate DT90 should be irrelevant. However, this can be rationalised by the fact that the FOCUS fate models generally only implement SFO kinetics.
+For comparison, the FOMC model is fitted as well, and the chi^2 error level is checked.
+m.L2.FOMC <- mkinfit("FOMC", FOCUS_2006_L2_mkin, quiet = TRUE)
 par(mfrow = c(2, 1))
 plot(m.L2.FOMC)
-mkinresplot(m.L2.FOMC)
-
-
- 
-
-summary(m.L2.FOMC, data = FALSE)
-
-
-## mkin version:    0.9.36 
+mkinresplot(m.L2.FOMC)
+
+summary(m.L2.FOMC, data = FALSE)
+## mkin version:    0.9.37 
 ## R version:       3.2.1 
-## Date of fit:     Sun Jun 21 18:14:54 2015 
-## Date of summary: Sun Jun 21 18:14:54 2015 
+## Date of fit:     Mon Jun 22 18:38:54 2015 
+## Date of summary: Mon Jun 22 18:38:54 2015 
 ## 
 ## Equations:
 ## d_parent = - (alpha/beta) * 1/((time/beta) + 1) * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted with method Port using 81 model solutions performed in 0.213 s
+## Fitted with method Port using 81 model solutions performed in 0.175 s
 ## 
 ## Weighting: none
 ## 
@@ -615,40 +412,23 @@ mkinresplot(m.L2.FOMC)
 ## 
 ## Estimated disappearance times:
 ##          DT50  DT90 DT50back
-## parent 0.8092 5.356    1.612
-
-
-The error level at which the chi² test passes is much lower in this case.
-Therefore, the FOMC model provides a better description of the data, as less
-experimental error has to be assumed in order to explain the data.
-
-Fitting the four parameter DFOP model further reduces the chi² error level. 
-
-m.L2.DFOP <- mkinfit("DFOP", FOCUS_2006_L2_mkin, quiet = TRUE)
-plot(m.L2.DFOP)
-
-
- 
-
-Here, the default starting parameters for the DFOP model obviously do not lead
-to a reasonable solution. Therefore the fit is repeated with different starting
-parameters.
-
-m.L2.DFOP <- mkinfit("DFOP", FOCUS_2006_L2_mkin, 
+## parent 0.8092 5.356    1.612
+The error level at which the chi^2 test passes is much lower in this case. Therefore, the FOMC model provides a better description of the data, as less experimental error has to be assumed in order to explain the data.
+Fitting the four parameter DFOP model further reduces the chi^2 error level.
+m.L2.DFOP <- mkinfit("DFOP", FOCUS_2006_L2_mkin, quiet = TRUE)
+plot(m.L2.DFOP)
+
+Here, the default starting parameters for the DFOP model obviously do not lead to a reasonable solution. Therefore the fit is repeated with different starting parameters.
+m.L2.DFOP <- mkinfit("DFOP", FOCUS_2006_L2_mkin, 
   parms.ini = c(k1 = 1, k2 = 0.01, g = 0.8),
   quiet=TRUE)
-plot(m.L2.DFOP)
-
-
- 
-
-summary(m.L2.DFOP, data = FALSE)
-
-
-## mkin version:    0.9.36 
+plot(m.L2.DFOP)
+
+summary(m.L2.DFOP, data = FALSE)
+## mkin version:    0.9.37 
 ## R version:       3.2.1 
-## Date of fit:     Sun Jun 21 18:14:56 2015 
-## Date of summary: Sun Jun 21 18:14:56 2015 
+## Date of fit:     Mon Jun 22 18:38:56 2015 
+## Date of summary: Mon Jun 22 18:38:56 2015 
 ## 
 ## Equations:
 ## d_parent = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -657,7 +437,7 @@ plot(m.L2.DFOP)
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted with method Port using 336 model solutions performed in 0.851 s
+## Fitted with method Port using 336 model solutions performed in 0.751 s
 ## 
 ## Weighting: none
 ## 
@@ -707,47 +487,32 @@ plot(m.L2.DFOP)
 ## 
 ## Estimated disappearance times:
 ##        DT50 DT90 DT50_k1 DT50_k2
-## parent   NA   NA 0.03058   2.058
-
-
-Here, the DFOP model is clearly the best-fit model for dataset L2 based on the 
-chi² error level criterion. However, the failure to calculate the covariance
-matrix indicates that the parameter estimates correlate excessively. Therefore,
-the FOMC model may be preferred for this dataset.
-
+## parent   NA   NA 0.03058   2.058

Here, the DFOP model is clearly the best-fit model for dataset L2 based on the chi^2 error level criterion. However, the failure to calculate the covariance matrix indicates that the parameter estimates correlate excessively. Therefore, the FOMC model may be preferred for this dataset.

Laboratory Data L3

- -

The following code defines example dataset L3 from the FOCUS kinetics report, -p. 290.

- -

FOCUS_2006_L3 = data.frame(
+The following code defines example dataset L3 from the FOCUS kinetics report, p. 290.
+FOCUS_2006_L3 = data.frame(
   t = c(0, 3, 7, 14, 30, 60, 91, 120),
   parent = c(97.8, 60, 51, 43, 35, 22, 15, 12))
-FOCUS_2006_L3_mkin <- mkin_wide_to_long(FOCUS_2006_L3)
-
-
+FOCUS_2006_L3_mkin <- mkin_wide_to_long(FOCUS_2006_L3)

SFO model, summary and plot:

- -

m.L3.SFO <- mkinfit("SFO", FOCUS_2006_L3_mkin, quiet = TRUE)
-plot(m.L3.SFO)
-

- -

plot of chunk unnamed-chunk-14

- -

summary(m.L3.SFO)
-

- -

## mkin version:    0.9.36 
+m.L3.SFO <- mkinfit("SFO", FOCUS_2006_L3_mkin, quiet = TRUE)
+plot(m.L3.SFO)
+
+summary(m.L3.SFO)
+## mkin version:    0.9.37 
 ## R version:       3.2.1 
-## Date of fit:     Sun Jun 21 18:14:56 2015 
-## Date of summary: Sun Jun 21 18:14:56 2015 
+## Date of fit:     Mon Jun 22 18:38:56 2015 
+## Date of summary: Mon Jun 22 18:38:56 2015 
 ## 
 ## Equations:
 ## d_parent = - k_parent_sink * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted with method Port using 43 model solutions performed in 0.103 s
+## Fitted with method Port using 43 model solutions performed in 0.088 s
 ## 
 ## Weighting: none
 ## 
@@ -806,34 +571,24 @@ plot(m.L3.SFO)
 ##    30   parent     35.0    35.084  -0.0839
 ##    60   parent     22.0    16.440   5.5602
 ##    91   parent     15.0     7.511   7.4887
-##   120   parent     12.0     3.610   8.3903
-
-
-The chi² error level of 21% as well as the plot suggest that the model
-does not fit very well. 
-
+##   120   parent     12.0     3.610   8.3903

The chi^2 error level of 21% as well as the plot suggest that the model does not fit very well.

The FOMC model performs better:

- -

m.L3.FOMC <- mkinfit("FOMC", FOCUS_2006_L3_mkin, quiet = TRUE)
-plot(m.L3.FOMC)
-

- -

plot of chunk unnamed-chunk-15

- -

summary(m.L3.FOMC, data = FALSE)
-

- -

## mkin version:    0.9.36 
+m.L3.FOMC <- mkinfit("FOMC", FOCUS_2006_L3_mkin, quiet = TRUE)
+plot(m.L3.FOMC)
+
+summary(m.L3.FOMC, data = FALSE)
+## mkin version:    0.9.37 
 ## R version:       3.2.1 
-## Date of fit:     Sun Jun 21 18:14:56 2015 
-## Date of summary: Sun Jun 21 18:14:56 2015 
+## Date of fit:     Mon Jun 22 18:38:57 2015 
+## Date of summary: Mon Jun 22 18:38:57 2015 
 ## 
 ## Equations:
 ## d_parent = - (alpha/beta) * 1/((time/beta) + 1) * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted with method Port using 83 model solutions performed in 0.197 s
+## Fitted with method Port using 83 model solutions performed in 0.178 s
 ## 
 ## Weighting: none
 ## 
@@ -882,27 +637,17 @@ plot(m.L3.FOMC)
 ## 
 ## Estimated disappearance times:
 ##         DT50  DT90 DT50back
-## parent 7.729 431.2    129.8
-
-
-The error level at which the chi² test passes is 7% in this case.
-
-Fitting the four parameter DFOP model further reduces the chi² error level
-considerably:
-
-m.L3.DFOP <- mkinfit("DFOP", FOCUS_2006_L3_mkin, quiet = TRUE)
-plot(m.L3.DFOP)
-
-
- 
-
-summary(m.L3.DFOP, data = FALSE)
-
-
-## mkin version:    0.9.36 
+## parent 7.729 431.2    129.8
+The error level at which the chi^2 test passes is 7% in this case.
+Fitting the four parameter DFOP model further reduces the chi^2 error level considerably:
+m.L3.DFOP <- mkinfit("DFOP", FOCUS_2006_L3_mkin, quiet = TRUE)
+plot(m.L3.DFOP)
+
+summary(m.L3.DFOP, data = FALSE)
+## mkin version:    0.9.37 
 ## R version:       3.2.1 
-## Date of fit:     Sun Jun 21 18:14:57 2015 
-## Date of summary: Sun Jun 21 18:14:57 2015 
+## Date of fit:     Mon Jun 22 18:38:57 2015 
+## Date of summary: Mon Jun 22 18:38:57 2015 
 ## 
 ## Equations:
 ## d_parent = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -911,7 +656,7 @@ plot(m.L3.DFOP)
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted with method Port using 137 model solutions performed in 0.341 s
+## Fitted with method Port using 137 model solutions performed in 0.292 s
 ## 
 ## Weighting: none
 ## 
@@ -965,52 +710,33 @@ plot(m.L3.DFOP)
 ## 
 ## Estimated disappearance times:
 ##         DT50 DT90 DT50_k1 DT50_k2
-## parent 7.464  123   1.343   50.37
-
-
-Here, a look to the model plot, the confidence intervals of the parameters 
-and the correlation matrix suggest that the parameter estimates are reliable, and
-the DFOP model can be used as the best-fit model based on the chi² error
-level criterion for laboratory data L3.
-
-This is also an example where the standard t-test for the parameter g_ilr is
-misleading, as it tests for a significant difference from zero. In this case, 
-zero appears to be the correct value for this parameter, and the confidence 
-interval for the backtransformed parameter g is quite narrow.
-
+## parent 7.464  123   1.343   50.37

Here, a look to the model plot, the confidence intervals of the parameters and the correlation matrix suggest that the parameter estimates are reliable, and the DFOP model can be used as the best-fit model based on the chi^2 error level criterion for laboratory data L3.

This is also an example where the standard t-test for the parameter g_ilr is misleading, as it tests for a significant difference from zero. In this case, zero appears to be the correct value for this parameter, and the confidence interval for the backtransformed parameter g is quite narrow.

Laboratory Data L4

- -

The following code defines example dataset L4 from the FOCUS kinetics -report, p. 293:

- -

FOCUS_2006_L4 = data.frame(
+The following code defines example dataset L4 from the FOCUS kinetics report, p. 293:
+FOCUS_2006_L4 = data.frame(
   t = c(0, 3, 7, 14, 30, 60, 91, 120),
   parent = c(96.6, 96.3, 94.3, 88.8, 74.9, 59.9, 53.5, 49.0))
-FOCUS_2006_L4_mkin <- mkin_wide_to_long(FOCUS_2006_L4)
-
-
+FOCUS_2006_L4_mkin <- mkin_wide_to_long(FOCUS_2006_L4)

SFO model, summary and plot:

- -

m.L4.SFO <- mkinfit("SFO", FOCUS_2006_L4_mkin, quiet = TRUE)
-plot(m.L4.SFO)
-

- -

plot of chunk unnamed-chunk-18

- -

summary(m.L4.SFO, data = FALSE)
-

- -

## mkin version:    0.9.36 
+m.L4.SFO <- mkinfit("SFO", FOCUS_2006_L4_mkin, quiet = TRUE)
+plot(m.L4.SFO)
+
+summary(m.L4.SFO, data = FALSE)
+## mkin version:    0.9.37 
 ## R version:       3.2.1 
-## Date of fit:     Sun Jun 21 18:14:57 2015 
-## Date of summary: Sun Jun 21 18:14:57 2015 
+## Date of fit:     Mon Jun 22 18:38:57 2015 
+## Date of summary: Mon Jun 22 18:38:57 2015 
 ## 
 ## Equations:
 ## d_parent = - k_parent_sink * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted with method Port using 46 model solutions performed in 0.111 s
+## Fitted with method Port using 46 model solutions performed in 0.102 s
 ## 
 ## Weighting: none
 ## 
@@ -1058,34 +784,24 @@ plot(m.L4.SFO)
 ## 
 ## Estimated disappearance times:
 ##        DT50 DT90
-## parent  106  352
-
-
-The chi² error level of 3.3% as well as the plot suggest that the model
-fits very well. 
-
+## parent  106  352

The chi^2 error level of 3.3% as well as the plot suggest that the model fits very well.

The FOMC model for comparison:

- -

m.L4.FOMC <- mkinfit("FOMC", FOCUS_2006_L4_mkin, quiet = TRUE)
-plot(m.L4.FOMC)
-

- -

plot of chunk unnamed-chunk-19

- -

summary(m.L4.FOMC, data = FALSE)
-

- -

## mkin version:    0.9.36 
+m.L4.FOMC <- mkinfit("FOMC", FOCUS_2006_L4_mkin, quiet = TRUE)
+plot(m.L4.FOMC)
+
+summary(m.L4.FOMC, data = FALSE)
+## mkin version:    0.9.37 
 ## R version:       3.2.1 
-## Date of fit:     Sun Jun 21 18:14:57 2015 
-## Date of summary: Sun Jun 21 18:14:57 2015 
+## Date of fit:     Mon Jun 22 18:38:58 2015 
+## Date of summary: Mon Jun 22 18:38:58 2015 
 ## 
 ## Equations:
 ## d_parent = - (alpha/beta) * 1/((time/beta) + 1) * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted with method Port using 66 model solutions performed in 0.162 s
+## Fitted with method Port using 66 model solutions performed in 0.137 s
 ## 
 ## Weighting: none
 ## 
@@ -1134,12 +850,22 @@ plot(m.L4.FOMC)
 ## 
 ## Estimated disappearance times:
 ##         DT50 DT90 DT50back
-## parent 108.9 1644    494.9
-
+## parent 108.9 1644    494.9

The error level at which the chi^2 test passes is slightly lower for the FOMC model. However, the difference appears negligible.

The error level at which the chi² test passes is slightly lower for the FOMC -model. However, the difference appears negligible.

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Example evaluation of FOCUS Laboratory Data L1 to L3

Johannes Ranke

2015-06-22

Example evaluation of FOCUS Laboratory Data L1 to L3

Laboratory Data L1

Laboratory Data L2

Laboratory Data L3

Laboratory Data L4