diff options
Diffstat (limited to 'vignettes')
| -rw-r--r-- | vignettes/FOCUS_L.Rmd | 81 | ||||
| -rw-r--r-- | vignettes/FOCUS_L.html | 328 | ||||
| -rw-r--r-- | vignettes/mkin.pdf | bin | 160326 -> 160326 bytes |
3 files changed, 200 insertions, 209 deletions
diff --git a/vignettes/FOCUS_L.Rmd b/vignettes/FOCUS_L.Rmd index 04d5f831..cd7711f6 100644 --- a/vignettes/FOCUS_L.Rmd +++ b/vignettes/FOCUS_L.Rmd @@ -13,7 +13,7 @@ opts_chunk$set(tidy = FALSE, cache = TRUE) ## Laboratory Data L1
The following code defines example dataset L1 from the FOCUS kinetics
-report, p. 284
+report, p. 284:
```{r}
library("mkin")
@@ -25,27 +25,18 @@ FOCUS_2006_L1 = data.frame( FOCUS_2006_L1_mkin <- mkin_wide_to_long(FOCUS_2006_L1)
```
-The next step is to set up the models used for the kinetic analysis. Note that
-the model definitions contain the names of the observed variables in the data.
-In this case, there is only one variable called `parent`.
+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.
-```{r}
-SFO <- mkinmod(parent = list(type = "SFO"))
-FOMC <- mkinmod(parent = list(type = "FOMC"))
-DFOP <- mkinmod(parent = list(type = "DFOP"))
-```
-
-The three models cover the first assumption 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.
-
-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.
+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.
```{r}
-m.L1.SFO <- mkinfit(SFO, FOCUS_2006_L1_mkin, quiet=TRUE)
+m.L1.SFO <- mkinfit("SFO", FOCUS_2006_L1_mkin, quiet=TRUE)
summary(m.L1.SFO)
```
@@ -64,32 +55,30 @@ For comparison, the FOMC model is fitted as well, and the chi^2 error level is checked.
```{r}
-m.L1.FOMC <- mkinfit(FOMC, FOCUS_2006_L1_mkin, quiet=TRUE)
+m.L1.FOMC <- mkinfit("FOMC", FOCUS_2006_L1_mkin, quiet=TRUE)
summary(m.L1.FOMC, data = FALSE)
```
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 covariance
-matrix can not be obtained, indicating overparameterisation of the model.
-As a consequence, no standard errors for transformed parameters nor
-confidence intervals for backtransformed parameters are available.
+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.
-Therefore, the reason for the difference was not investigated further.
+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
+report, p. 287:
```{r}
FOCUS_2006_L2 = data.frame(
@@ -100,10 +89,10 @@ FOCUS_2006_L2 = data.frame( FOCUS_2006_L2_mkin <- mkin_wide_to_long(FOCUS_2006_L2)
```
-Again, the SFO model is fitted and a summary is obtained.
+Again, the SFO model is fitted and a summary is obtained:
```{r}
-m.L2.SFO <- mkinfit(SFO, FOCUS_2006_L2_mkin, quiet=TRUE)
+m.L2.SFO <- mkinfit("SFO", FOCUS_2006_L2_mkin, quiet=TRUE)
summary(m.L2.SFO)
```
@@ -130,7 +119,7 @@ For comparison, the FOMC model is fitted as well, and the chi^2 error level is checked.
```{r fig.height = 8}
-m.L2.FOMC <- mkinfit(FOMC, FOCUS_2006_L2_mkin, quiet = TRUE)
+m.L2.FOMC <- mkinfit("FOMC", FOCUS_2006_L2_mkin, quiet = TRUE)
par(mfrow = c(2, 1))
plot(m.L2.FOMC)
mkinresplot(m.L2.FOMC)
@@ -144,7 +133,7 @@ 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.
```{r fig.height = 5}
-m.L2.DFOP <- mkinfit(DFOP, FOCUS_2006_L2_mkin, quiet = TRUE)
+m.L2.DFOP <- mkinfit("DFOP", FOCUS_2006_L2_mkin, quiet = TRUE)
plot(m.L2.DFOP)
```
@@ -153,7 +142,7 @@ to a reasonable solution. Therefore the fit is repeated with different starting parameters.
```{r fig.height = 5}
-m.L2.DFOP <- mkinfit(DFOP, FOCUS_2006_L2_mkin,
+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)
@@ -180,7 +169,7 @@ FOCUS_2006_L3_mkin <- mkin_wide_to_long(FOCUS_2006_L3) SFO model, summary and plot:
```{r fig.height = 5}
-m.L3.SFO <- mkinfit(SFO, FOCUS_2006_L3_mkin, quiet = TRUE)
+m.L3.SFO <- mkinfit("SFO", FOCUS_2006_L3_mkin, quiet = TRUE)
plot(m.L3.SFO)
summary(m.L3.SFO)
```
@@ -191,7 +180,7 @@ does not fit very well. The FOMC model performs better:
```{r fig.height = 5}
-m.L3.FOMC <- mkinfit(FOMC, FOCUS_2006_L3_mkin, quiet = TRUE)
+m.L3.FOMC <- mkinfit("FOMC", FOCUS_2006_L3_mkin, quiet = TRUE)
plot(m.L3.FOMC)
summary(m.L3.FOMC, data = FALSE)
```
@@ -202,7 +191,7 @@ Fitting the four parameter DFOP model further reduces the chi^2 error level considerably:
```{r fig.height = 5}
-m.L3.DFOP <- mkinfit(DFOP, FOCUS_2006_L3_mkin, quiet = TRUE)
+m.L3.DFOP <- mkinfit("DFOP", FOCUS_2006_L3_mkin, quiet = TRUE)
plot(m.L3.DFOP)
summary(m.L3.DFOP, data = FALSE)
```
@@ -212,10 +201,15 @@ and the correlation matrix suggest that the parameter estimates are reliable, an 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
+report, p. 293:
```{r}
FOCUS_2006_L4 = data.frame(
@@ -227,7 +221,7 @@ FOCUS_2006_L4_mkin <- mkin_wide_to_long(FOCUS_2006_L4) SFO model, summary and plot:
```{r fig.height = 5}
-m.L4.SFO <- mkinfit(SFO, FOCUS_2006_L4_mkin, quiet = TRUE)
+m.L4.SFO <- mkinfit("SFO", FOCUS_2006_L4_mkin, quiet = TRUE)
plot(m.L4.SFO)
summary(m.L4.SFO, data = FALSE)
```
@@ -235,14 +229,13 @@ summary(m.L4.SFO, data = FALSE) 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
+The FOMC model for comparison:
```{r fig.height = 5}
-m.L4.FOMC <- mkinfit(FOMC, FOCUS_2006_L4_mkin, quiet = TRUE)
+m.L4.FOMC <- mkinfit("FOMC", FOCUS_2006_L4_mkin, quiet = TRUE)
plot(m.L4.FOMC)
summary(m.L4.FOMC, data = FALSE)
```
The error level at which the chi^2 test passes is slightly lower for the FOMC
model. However, the difference appears negligible.
-
diff --git a/vignettes/FOCUS_L.html b/vignettes/FOCUS_L.html index 85fadbfe..614fcf32 100644 --- a/vignettes/FOCUS_L.html +++ b/vignettes/FOCUS_L.html @@ -190,7 +190,7 @@ hr { <h2>Laboratory Data L1</h2> <p>The following code defines example dataset L1 from the FOCUS kinetics -report, p. 284</p> +report, p. 284:</p> <pre><code class="r">library("mkin") </code></pre> @@ -207,51 +207,43 @@ report, p. 284</p> FOCUS_2006_L1_mkin <- mkin_wide_to_long(FOCUS_2006_L1) </code></pre> -<p>The next step is to set up the models used for the kinetic analysis. Note that -the model definitions contain the names of the observed variables in the data. -In this case, there is only one variable called <code>parent</code>.</p> +<p>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.</p> -<pre><code class="r">SFO <- mkinmod(parent = list(type = "SFO")) -FOMC <- mkinmod(parent = list(type = "FOMC")) -DFOP <- mkinmod(parent = list(type = "DFOP")) -</code></pre> - -<p>The three models cover the first assumption 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.</p> +<p>Since mkin version 0.9-32 (July 2014), we can use shorthand notation like <code>SFO</code> +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. </p> -<p>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.</p> - -<pre><code class="r">m.L1.SFO <- mkinfit(SFO, FOCUS_2006_L1_mkin, quiet=TRUE) +<pre><code class="r">m.L1.SFO <- mkinfit("SFO", FOCUS_2006_L1_mkin, quiet=TRUE) summary(m.L1.SFO) </code></pre> <pre><code>## mkin version: 0.9.32 ## R version: 3.1.1 -## Date of fit: Thu Jul 17 12:37:41 2014 -## Date of summary: Thu Jul 17 12:37:41 2014 +## Date of fit: Mon Jul 21 09:14:29 2014 +## Date of summary: Mon Jul 21 09:14:29 2014 ## ## Equations: ## [1] d_parent = - k_parent_sink * parent ## ## Model predictions using solution type analytical ## -## Fitted with method Marq using 14 model solutions performed in 0.087 s +## Fitted with method Marq using 14 model solutions performed in 0.081 s ## ## Weighting: none ## ## Starting values for parameters to be optimised: ## value type -## parent_0 100.0 state -## k_parent_sink 0.1 deparm +## parent_0 89.85 state +## k_parent_sink 0.10 deparm ## ## Starting values for the transformed parameters actually optimised: -## value lower upper -## parent_0 100.000 -Inf Inf -## log_k_parent_sink -2.303 -Inf Inf +## value lower upper +## parent_0 89.850 -Inf Inf +## log_k_parent_sink -2.303 -Inf Inf ## ## Fixed parameter values: ## None @@ -259,7 +251,7 @@ summary(m.L1.SFO) ## Optimised, transformed parameters: ## Estimate Std. Error Lower Upper t value Pr(>|t|) ## parent_0 92.50 1.3700 89.60 95.40 67.6 4.34e-21 -## log_k_parent_sink -2.35 0.0406 -2.43 -2.26 -57.9 5.15e-20 +## log_k_parent_sink -2.35 0.0406 -2.43 -2.26 -57.9 5.16e-20 ## Pr(>t) ## parent_0 2.17e-21 ## log_k_parent_sink 2.58e-20 @@ -316,67 +308,70 @@ summary(m.L1.SFO) <pre><code class="r">plot(m.L1.SFO) </code></pre> -<p><img 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alt="plot of chunk unnamed-chunk-4"/> </p> <p>The residual plot can be easily obtained by</p> <pre><code class="r">mkinresplot(m.L1.SFO, ylab = "Observed", xlab = "Time") </code></pre> -<p><img src="data:image/png;base64,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alt="plot of chunk unnamed-chunk-5"/> </p> <p>For comparison, the FOMC model is fitted as well, and the chi<sup>2</sup> error level is checked.</p> -<pre><code class="r">m.L1.FOMC <- mkinfit(FOMC, FOCUS_2006_L1_mkin, quiet=TRUE) +<pre><code class="r">m.L1.FOMC <- mkinfit("FOMC", FOCUS_2006_L1_mkin, quiet=TRUE) summary(m.L1.FOMC, data = FALSE) </code></pre> <pre><code>## mkin version: 0.9.32 ## R version: 3.1.1 -## Date of fit: Thu Jul 17 12:37:42 2014 -## Date of summary: Thu Jul 17 12:37:42 2014 +## Date of fit: Mon Jul 21 09:14:30 2014 +## Date of summary: Mon Jul 21 09:14:30 2014 ## ## Equations: ## [1] d_parent = - (alpha/beta) * ((time/beta) + 1)^-1 * parent ## ## Model predictions using solution type analytical ## -## Fitted with method Marq using 45 model solutions performed in 0.266 s +## Fitted with method Marq using 53 model solutions performed in 0.32 s ## ## Weighting: none ## ## Starting values for parameters to be optimised: ## value type -## parent_0 100 state -## alpha 1 deparm -## beta 10 deparm +## parent_0 89.85 state +## alpha 1.00 deparm +## beta 10.00 deparm ## ## Starting values for the transformed parameters actually optimised: -## value lower upper -## parent_0 100.000 -Inf Inf -## log_alpha 0.000 -Inf Inf -## log_beta 2.303 -Inf Inf +## value lower upper +## parent_0 89.850 -Inf Inf +## log_alpha 0.000 -Inf Inf +## log_beta 2.303 -Inf Inf ## ## Fixed parameter values: ## None ## ## Optimised, transformed parameters: -## Estimate Std. Error Lower Upper t value Pr(>|t|) Pr(>t) -## parent_0 92.5 NA NA NA NA NA NA -## log_alpha 25.6 NA NA NA NA NA NA -## log_beta 28.0 NA NA NA NA NA NA +## Estimate Std. Error Lower Upper t value Pr(>|t|) Pr(>t) +## parent_0 92.5 1.45 89.40 95.6 63.60 1.17e-19 5.85e-20 +## log_alpha 14.9 10.60 -7.75 37.5 1.40 1.82e-01 9.08e-02 +## log_beta 17.2 10.60 -5.38 39.8 1.62 1.25e-01 6.26e-02 ## ## Parameter correlation: -## Could not estimate covariance matrix; singular system: +## parent_0 log_alpha log_beta +## parent_0 1.000 0.24 0.238 +## log_alpha 0.240 1.00 1.000 +## log_beta 0.238 1.00 1.000 ## ## Residual standard error: 3.05 on 15 degrees of freedom ## ## Backtransformed parameters: -## Estimate Lower Upper -## parent_0 9.25e+01 NA NA -## alpha 1.35e+11 NA NA -## beta 1.41e+12 NA NA +## Estimate Lower Upper +## parent_0 9.25e+01 8.94e+01 9.56e+01 +## alpha 2.85e+06 4.32e-04 1.88e+16 +## beta 2.98e+07 4.59e-03 1.93e+17 ## ## Chi2 error levels in percent: ## err.min n.optim df @@ -390,26 +385,24 @@ summary(m.L1.FOMC, data = FALSE) <p>Due to the higher number of parameters, and the lower number of degrees of freedom of the fit, the chi<sup>2</sup> error level is actually higher for the FOMC -model (3.6%) than for the SFO model (3.4%). Additionally, the covariance -matrix can not be obtained, indicating overparameterisation of the model. -As a consequence, no standard errors for transformed parameters nor -confidence intervals for backtransformed parameters are available.</p> +model (3.6%) than for the SFO model (3.4%). Additionally, the parameters +<code>log_alpha</code> and <code>log_beta</code> 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. </p> <p>The chi<sup>2</sup> 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<sup>2</sup> error levels -as the kinfit package.</p> - -<p>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. -Therefore, the reason for the difference was not investigated further.</p> +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. </p> <h2>Laboratory Data L2</h2> <p>The following code defines example dataset L2 from the FOCUS kinetics -report, p. 287</p> +report, p. 287:</p> <pre><code class="r">FOCUS_2006_L2 = data.frame( t = rep(c(0, 1, 3, 7, 14, 28), each = 2), @@ -419,35 +412,35 @@ report, p. 287</p> FOCUS_2006_L2_mkin <- mkin_wide_to_long(FOCUS_2006_L2) </code></pre> -<p>Again, the SFO model is fitted and a summary is obtained.</p> +<p>Again, the SFO model is fitted and a summary is obtained:</p> -<pre><code class="r">m.L2.SFO <- mkinfit(SFO, FOCUS_2006_L2_mkin, quiet=TRUE) +<pre><code class="r">m.L2.SFO <- mkinfit("SFO", FOCUS_2006_L2_mkin, quiet=TRUE) summary(m.L2.SFO) </code></pre> <pre><code>## mkin version: 0.9.32 ## R version: 3.1.1 -## Date of fit: Thu Jul 17 12:37:42 2014 -## Date of summary: Thu Jul 17 12:37:42 2014 +## Date of fit: Mon Jul 21 09:14:30 2014 +## Date of summary: Mon Jul 21 09:14:30 2014 ## ## Equations: ## [1] d_parent = - k_parent_sink * parent ## ## Model predictions using solution type analytical ## -## Fitted with method Marq using 32 model solutions performed in 0.357 s +## Fitted with method Marq using 29 model solutions performed in 0.155 s ## ## Weighting: none ## ## Starting values for parameters to be optimised: ## value type -## parent_0 100.0 state -## k_parent_sink 0.1 deparm +## parent_0 93.95 state +## k_parent_sink 0.10 deparm ## ## Starting values for the transformed parameters actually optimised: -## value lower upper -## parent_0 100.000 -Inf Inf -## log_k_parent_sink -2.303 -Inf Inf +## value lower upper +## parent_0 93.950 -Inf Inf +## log_k_parent_sink -2.303 -Inf Inf ## ## Fixed parameter values: ## None @@ -487,8 +480,8 @@ summary(m.L2.SFO) ## ## Data: ## time variable observed predicted residual -## 0 parent 96.1 9.15e+01 4.634 -## 0 parent 91.8 9.15e+01 0.334 +## 0 parent 96.1 9.15e+01 4.635 +## 0 parent 91.8 9.15e+01 0.335 ## 1 parent 41.4 4.71e+01 -5.740 ## 1 parent 38.7 4.71e+01 -8.440 ## 3 parent 19.3 1.25e+01 6.779 @@ -509,7 +502,7 @@ plot(m.L2.SFO) mkinresplot(m.L2.SFO) </code></pre> -<p><img 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alt="plot of chunk unnamed-chunk-9"/> </p> <p>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 @@ -524,42 +517,42 @@ models generally only implement SFO kinetics.</p> <p>For comparison, the FOMC model is fitted as well, and the chi<sup>2</sup> error level is checked.</p> -<pre><code class="r">m.L2.FOMC <- mkinfit(FOMC, FOCUS_2006_L2_mkin, quiet = TRUE) +<pre><code class="r">m.L2.FOMC <- mkinfit("FOMC", FOCUS_2006_L2_mkin, quiet = TRUE) par(mfrow = c(2, 1)) plot(m.L2.FOMC) mkinresplot(m.L2.FOMC) </code></pre> -<p><img 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alt="plot of chunk unnamed-chunk-10"/> </p> <pre><code class="r">summary(m.L2.FOMC, data = FALSE) </code></pre> <pre><code>## mkin version: 0.9.32 ## R version: 3.1.1 -## Date of fit: Thu Jul 17 12:37:43 2014 -## Date of summary: Thu Jul 17 12:37:43 2014 +## Date of fit: Mon Jul 21 09:14:31 2014 +## Date of summary: Mon Jul 21 09:14:31 2014 ## ## Equations: ## [1] d_parent = - (alpha/beta) * ((time/beta) + 1)^-1 * parent ## ## Model predictions using solution type analytical ## -## Fitted with method Marq using 39 model solutions performed in 0.235 s +## Fitted with method Marq using 35 model solutions performed in 0.199 s ## ## Weighting: none ## ## Starting values for parameters to be optimised: ## value type -## parent_0 100 state -## alpha 1 deparm -## beta 10 deparm +## parent_0 93.95 state +## alpha 1.00 deparm +## beta 10.00 deparm ## ## Starting values for the transformed parameters actually optimised: -## value lower upper -## parent_0 100.000 -Inf Inf -## log_alpha 0.000 -Inf Inf -## log_beta 2.303 -Inf Inf +## value lower upper +## parent_0 93.950 -Inf Inf +## log_alpha 0.000 -Inf Inf +## log_beta 2.303 -Inf Inf ## ## Fixed parameter values: ## None @@ -600,62 +593,62 @@ experimental error has to be assumed in order to explain the data.</p> <p>Fitting the four parameter DFOP model further reduces the chi<sup>2</sup> error level. </p> -<pre><code class="r">m.L2.DFOP <- mkinfit(DFOP, FOCUS_2006_L2_mkin, quiet = TRUE) +<pre><code class="r">m.L2.DFOP <- mkinfit("DFOP", FOCUS_2006_L2_mkin, quiet = TRUE) plot(m.L2.DFOP) </code></pre> -<p><img 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alt="plot of chunk unnamed-chunk-12"/> </p> +<p><img 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alt="plot of chunk unnamed-chunk-11"/> </p> <p>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.</p> -<pre><code class="r">m.L2.DFOP <- mkinfit(DFOP, FOCUS_2006_L2_mkin, +<pre><code class="r">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) </code></pre> -<p><img 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alt="plot of chunk unnamed-chunk-13"/> </p> +<p><img 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alt="plot of chunk unnamed-chunk-12"/> </p> <pre><code class="r">summary(m.L2.DFOP, data = FALSE) </code></pre> <pre><code>## mkin version: 0.9.32 ## R version: 3.1.1 -## Date of fit: Thu Jul 17 12:37:44 2014 -## Date of summary: Thu Jul 17 12:37:44 2014 +## Date of fit: Mon Jul 21 09:14:31 2014 +## Date of summary: Mon Jul 21 09:14:31 2014 ## ## Equations: ## [1] d_parent = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) * parent ## ## Model predictions using solution type analytical ## -## Fitted with method Marq using 54 model solutions performed in 0.423 s +## Fitted with method Marq using 43 model solutions performed in 0.241 s ## ## Weighting: none ## ## Starting values for parameters to be optimised: ## value type -## parent_0 1e+02 state -## k1 1e+00 deparm -## k2 1e-02 deparm -## g 8e-01 deparm +## parent_0 93.95 state +## k1 1.00 deparm +## k2 0.01 deparm +## g 0.80 deparm ## ## Starting values for the transformed parameters actually optimised: -## value lower upper -## parent_0 100.0000 -Inf Inf -## log_k1 0.0000 -Inf Inf -## log_k2 -4.6052 -Inf Inf -## g_ilr 0.9803 -Inf Inf +## value lower upper +## parent_0 93.9500 -Inf Inf +## log_k1 0.0000 -Inf Inf +## log_k2 -4.6052 -Inf Inf +## g_ilr 0.9803 -Inf Inf ## ## Fixed parameter values: ## None ## ## Optimised, transformed parameters: ## Estimate Std. Error Lower Upper t value Pr(>|t|) Pr(>t) -## parent_0 93.900 NA NA NA NA NA NA -## log_k1 4.960 NA NA NA NA NA NA +## parent_0 94.000 NA NA NA NA NA NA +## log_k1 6.160 NA NA NA NA NA NA ## log_k2 -1.090 NA NA NA NA NA NA ## g_ilr -0.282 NA NA NA NA NA NA ## @@ -666,8 +659,8 @@ plot(m.L2.DFOP) ## ## Backtransformed parameters: ## Estimate Lower Upper -## parent_0 93.900 NA NA -## k1 142.000 NA NA +## parent_0 94.000 NA NA +## k1 476.000 NA NA ## k2 0.337 NA NA ## g 0.402 NA NA ## @@ -678,7 +671,7 @@ plot(m.L2.DFOP) ## ## Estimated disappearance times: ## DT50 DT90 DT50_k1 DT50_k2 -## parent NA NA 0.00487 2.06 +## parent NA NA 0.00146 2.06 </code></pre> <p>Here, the DFOP model is clearly the best-fit model for dataset L2 based on the @@ -699,38 +692,38 @@ FOCUS_2006_L3_mkin <- mkin_wide_to_long(FOCUS_2006_L3) <p>SFO model, summary and plot:</p> -<pre><code class="r">m.L3.SFO <- mkinfit(SFO, FOCUS_2006_L3_mkin, quiet = TRUE) +<pre><code class="r">m.L3.SFO <- mkinfit("SFO", FOCUS_2006_L3_mkin, quiet = TRUE) plot(m.L3.SFO) </code></pre> -<p><img 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alt="plot of chunk unnamed-chunk-14"/> </p> <pre><code class="r">summary(m.L3.SFO) </code></pre> <pre><code>## mkin version: 0.9.32 ## R version: 3.1.1 -## Date of fit: Thu Jul 17 12:37:45 2014 -## Date of summary: Thu Jul 17 12:37:45 2014 +## Date of fit: Mon Jul 21 09:14:32 2014 +## Date of summary: Mon Jul 21 09:14:32 2014 ## ## Equations: ## [1] d_parent = - k_parent_sink * parent ## ## Model predictions using solution type analytical ## -## Fitted with method Marq using 44 model solutions performed in 0.241 s +## Fitted with method Marq using 44 model solutions performed in 0.242 s ## ## Weighting: none ## ## Starting values for parameters to be optimised: ## value type -## parent_0 100.0 state +## parent_0 97.8 state ## k_parent_sink 0.1 deparm ## ## Starting values for the transformed parameters actually optimised: -## value lower upper -## parent_0 100.000 -Inf Inf -## log_k_parent_sink -2.303 -Inf Inf +## value lower upper +## parent_0 97.800 -Inf Inf +## log_k_parent_sink -2.303 -Inf Inf ## ## Fixed parameter values: ## None @@ -770,7 +763,7 @@ plot(m.L3.SFO) ## ## Data: ## time variable observed predicted residual -## 0 parent 97.8 74.87 22.9273 +## 0 parent 97.8 74.87 22.9274 ## 3 parent 60.0 69.41 -9.4065 ## 7 parent 51.0 62.73 -11.7340 ## 14 parent 43.0 52.56 -9.5634 @@ -785,40 +778,40 @@ does not fit very well. </p> <p>The FOMC model performs better:</p> -<pre><code class="r">m.L3.FOMC <- mkinfit(FOMC, FOCUS_2006_L3_mkin, quiet = TRUE) +<pre><code class="r">m.L3.FOMC <- mkinfit("FOMC", FOCUS_2006_L3_mkin, quiet = TRUE) plot(m.L3.FOMC) </code></pre> -<p><img 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alt="plot of chunk unnamed-chunk-15"/> </p> <pre><code class="r">summary(m.L3.FOMC, data = FALSE) </code></pre> <pre><code>## mkin version: 0.9.32 ## R version: 3.1.1 -## Date of fit: Thu Jul 17 12:37:45 2014 -## Date of summary: Thu Jul 17 12:37:45 2014 +## Date of fit: Mon Jul 21 09:14:32 2014 +## Date of summary: Mon Jul 21 09:14:32 2014 ## ## Equations: ## [1] d_parent = - (alpha/beta) * ((time/beta) + 1)^-1 * parent ## ## Model predictions using solution type analytical ## -## Fitted with method Marq using 26 model solutions performed in 0.208 s +## Fitted with method Marq using 26 model solutions performed in 0.143 s ## ## Weighting: none ## ## Starting values for parameters to be optimised: ## value type -## parent_0 100 state -## alpha 1 deparm -## beta 10 deparm +## parent_0 97.8 state +## alpha 1.0 deparm +## beta 10.0 deparm ## ## Starting values for the transformed parameters actually optimised: -## value lower upper -## parent_0 100.000 -Inf Inf -## log_alpha 0.000 -Inf Inf -## log_beta 2.303 -Inf Inf +## value lower upper +## parent_0 97.800 -Inf Inf +## log_alpha 0.000 -Inf Inf +## log_beta 2.303 -Inf Inf ## ## Fixed parameter values: ## None @@ -858,42 +851,42 @@ plot(m.L3.FOMC) <p>Fitting the four parameter DFOP model further reduces the chi<sup>2</sup> error level considerably:</p> -<pre><code class="r">m.L3.DFOP <- mkinfit(DFOP, FOCUS_2006_L3_mkin, quiet = TRUE) +<pre><code class="r">m.L3.DFOP <- mkinfit("DFOP", FOCUS_2006_L3_mkin, quiet = TRUE) plot(m.L3.DFOP) </code></pre> -<p><img 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alt="plot of chunk unnamed-chunk-16"/> </p> <pre><code class="r">summary(m.L3.DFOP, data = FALSE) </code></pre> <pre><code>## mkin version: 0.9.32 ## R version: 3.1.1 -## Date of fit: Thu Jul 17 12:37:46 2014 -## Date of summary: Thu Jul 17 12:37:46 2014 +## Date of fit: Mon Jul 21 09:14:32 2014 +## Date of summary: Mon Jul 21 09:14:32 2014 ## ## Equations: ## [1] d_parent = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) * parent ## ## Model predictions using solution type analytical ## -## Fitted with method Marq using 37 model solutions performed in 0.338 s +## Fitted with method Marq using 37 model solutions performed in 0.21 s ## ## Weighting: none ## ## Starting values for parameters to be optimised: ## value type -## parent_0 1e+02 state -## k1 1e-01 deparm -## k2 1e-02 deparm -## g 5e-01 deparm +## parent_0 97.80 state +## k1 0.10 deparm +## k2 0.01 deparm +## g 0.50 deparm ## ## Starting values for the transformed parameters actually optimised: -## value lower upper -## parent_0 100.000 -Inf Inf -## log_k1 -2.303 -Inf Inf -## log_k2 -4.605 -Inf Inf -## g_ilr 0.000 -Inf Inf +## value lower upper +## parent_0 97.800 -Inf Inf +## log_k1 -2.303 -Inf Inf +## log_k2 -4.605 -Inf Inf +## g_ilr 0.000 -Inf Inf ## ## Fixed parameter values: ## None @@ -936,10 +929,15 @@ and the correlation matrix suggest that the parameter estimates are reliable, an the DFOP model can be used as the best-fit model based on the chi<sup>2</sup> error level criterion for laboratory data L3.</p> +<p>This is also an example where the standard t-test for the parameter <code>g_ilr</code> 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 <code>g</code> is quite narrow.</p> + <h2>Laboratory Data L4</h2> <p>The following code defines example dataset L4 from the FOCUS kinetics -report, p. 293</p> +report, p. 293:</p> <pre><code class="r">FOCUS_2006_L4 = data.frame( t = c(0, 3, 7, 14, 30, 60, 91, 120), @@ -949,38 +947,38 @@ FOCUS_2006_L4_mkin <- mkin_wide_to_long(FOCUS_2006_L4) <p>SFO model, summary and plot:</p> -<pre><code class="r">m.L4.SFO <- mkinfit(SFO, FOCUS_2006_L4_mkin, quiet = TRUE) +<pre><code class="r">m.L4.SFO <- mkinfit("SFO", FOCUS_2006_L4_mkin, quiet = TRUE) plot(m.L4.SFO) </code></pre> -<p><img 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alt="plot of chunk unnamed-chunk-18"/> </p> <pre><code class="r">summary(m.L4.SFO, data = FALSE) </code></pre> <pre><code>## mkin version: 0.9.32 ## R version: 3.1.1 -## Date of fit: Thu Jul 17 12:37:46 2014 -## Date of summary: Thu Jul 17 12:37:46 2014 +## Date of fit: Mon Jul 21 09:14:33 2014 +## Date of summary: Mon Jul 21 09:14:33 2014 ## ## Equations: ## [1] d_parent = - k_parent_sink * parent ## ## Model predictions using solution type analytical ## -## Fitted with method Marq using 20 model solutions performed in 0.127 s +## Fitted with method Marq using 20 model solutions performed in 0.109 s ## ## Weighting: none ## ## Starting values for parameters to be optimised: ## value type -## parent_0 100.0 state +## parent_0 96.6 state ## k_parent_sink 0.1 deparm ## ## Starting values for the transformed parameters actually optimised: -## value lower upper -## parent_0 100.000 -Inf Inf -## log_k_parent_sink -2.303 -Inf Inf +## value lower upper +## parent_0 96.600 -Inf Inf +## log_k_parent_sink -2.303 -Inf Inf ## ## Fixed parameter values: ## None @@ -1022,42 +1020,42 @@ plot(m.L4.SFO) <p>The chi<sup>2</sup> error level of 3.3% as well as the plot suggest that the model fits very well. </p> -<p>The FOMC model for comparison</p> +<p>The FOMC model for comparison:</p> -<pre><code class="r">m.L4.FOMC <- mkinfit(FOMC, FOCUS_2006_L4_mkin, quiet = TRUE) +<pre><code class="r">m.L4.FOMC <- mkinfit("FOMC", FOCUS_2006_L4_mkin, quiet = TRUE) plot(m.L4.FOMC) </code></pre> -<p><img 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alt="plot of chunk unnamed-chunk-19"/> </p> <pre><code class="r">summary(m.L4.FOMC, data = FALSE) </code></pre> <pre><code>## mkin version: 0.9.32 ## R version: 3.1.1 -## Date of fit: Thu Jul 17 12:37:46 2014 -## Date of summary: Thu Jul 17 12:37:46 2014 +## Date of fit: Mon Jul 21 09:14:33 2014 +## Date of summary: Mon Jul 21 09:14:33 2014 ## ## Equations: ## [1] d_parent = - (alpha/beta) * ((time/beta) + 1)^-1 * parent ## ## Model predictions using solution type analytical ## -## Fitted with method Marq using 53 model solutions performed in 0.355 s +## Fitted with method Marq using 48 model solutions performed in 0.26 s ## ## Weighting: none ## ## Starting values for parameters to be optimised: ## value type -## parent_0 100 state -## alpha 1 deparm -## beta 10 deparm +## parent_0 96.6 state +## alpha 1.0 deparm +## beta 10.0 deparm ## ## Starting values for the transformed parameters actually optimised: -## value lower upper -## parent_0 100.000 -Inf Inf -## log_alpha 0.000 -Inf Inf -## log_beta 2.303 -Inf Inf +## value lower upper +## parent_0 96.600 -Inf Inf +## log_alpha 0.000 -Inf Inf +## log_beta 2.303 -Inf Inf ## ## Fixed parameter values: ## None diff --git a/vignettes/mkin.pdf b/vignettes/mkin.pdf Binary files differindex 9cf1b3e5..b69ddddc 100644 --- a/vignettes/mkin.pdf +++ b/vignettes/mkin.pdf |