From 6733555d7a9315c55001770bacc4c61c4d4f39d5 Mon Sep 17 00:00:00 2001 From: Johannes Ranke Date: Sun, 21 Jun 2015 01:46:51 +0200 Subject: Do the t-test for untransformed parameters --- vignettes/FOCUS_D.html | 50 +++--- vignettes/FOCUS_L.html | 357 ++++++++++++++++++++++------------------- vignettes/FOCUS_Z.Rnw | 2 + vignettes/FOCUS_Z.pdf | Bin 215014 -> 224256 bytes vignettes/compiled_models.html | 42 ++--- vignettes/mkin.pdf | Bin 160260 -> 160260 bytes 6 files changed, 232 insertions(+), 219 deletions(-) (limited to 'vignettes') diff --git a/vignettes/FOCUS_D.html b/vignettes/FOCUS_D.html index 6573cc7a..b1ea64ea 100644 --- a/vignettes/FOCUS_D.html +++ b/vignettes/FOCUS_D.html @@ -215,13 +215,7 @@ library we look a the data. We have observed concentrations in the column named named parent and m1.

library("mkin")
-
- -
## Loading required package: minpack.lm
-## Loading required package: rootSolve
-
- -
print(FOCUS_2006_D)
+print(FOCUS_2006_D)
 
##      name time  value
@@ -276,7 +270,7 @@ kinetics (SFO) to one metabolite named m1, which also degrades with SFO kinetics
 
 
The call to mkinmod returns a degradation model. The differential equations represented in 
 R code can be found in the character vector $diffs of the mkinmod object. If
-the ccSolve package is installed and functional, the differential equation model
+the gcc compiler is installed and functional, the differential equation model
 will be compiled from auto-generated C code.

 
 
SFO_SFO <- mkinmod(parent = mkinsub("SFO", "m1"), m1 = mkinsub("SFO"))
@@ -312,7 +306,7 @@ using the plot method for mkinfit objects.

 
mkinparplot(fit)
 

 
-
plot of chunk unnamed-chunk-6 

+
plot of chunk unnamed-chunk-6 

 
 
A comprehensive report of the results is obtained using the summary method for mkinfit
 objects.

@@ -321,9 +315,9 @@ objects.

 

 
 
## mkin version:    0.9.36 
-## R version:       3.2.0 
-## Date of fit:     Fri Jun  5 14:20:31 2015 
-## Date of summary: Fri Jun  5 14:20:31 2015 
+## R version:       3.2.1 
+## Date of fit:     Sun Jun 21 01:47:59 2015 
+## Date of summary: Sun Jun 21 01:47:59 2015 
 ## 
 ## Equations:
 ## d_parent = - k_parent_sink * parent - k_parent_m1 * parent
@@ -331,7 +325,7 @@ objects.

 ## 
 ## Model predictions using solution type deSolve 
 ## 
-## Fitted with method Port using 153 model solutions performed in 0.621 s
+## Fitted with method Port using 153 model solutions performed in 0.698 s
 ## 
 ## Weighting: none
 ## 
@@ -353,17 +347,12 @@ objects.

 ##      value  type
 ## m1_0     0 state
 ## 
-## Optimised, transformed parameters:
-##                   Estimate Std. Error  Lower   Upper t value  Pr(>|t|)
-## parent_0            99.600    1.61400 96.330 102.900   61.72 4.048e-38
-## log_k_parent_sink   -3.038    0.07826 -3.197  -2.879  -38.82 5.601e-31
-## log_k_parent_m1     -2.980    0.04124 -3.064  -2.897  -72.27 1.446e-40
-## log_k_m1_sink       -5.248    0.13610 -5.523  -4.972  -38.56 7.087e-31
-##                      Pr(>t)
-## parent_0          2.024e-38
-## log_k_parent_sink 2.800e-31
-## log_k_parent_m1   7.228e-41
-## log_k_m1_sink     3.543e-31
+## Optimised, transformed parameters with symmetric confidence intervals:
+##                   Estimate Std. Error  Lower   Upper
+## parent_0            99.600    1.61400 96.330 102.900
+## log_k_parent_sink   -3.038    0.07826 -3.197  -2.879
+## log_k_parent_m1     -2.980    0.04124 -3.064  -2.897
+## log_k_m1_sink       -5.248    0.13610 -5.523  -4.972
 ## 
 ## Parameter correlation:
 ##                   parent_0 log_k_parent_sink log_k_parent_m1 log_k_m1_sink
@@ -375,11 +364,14 @@ objects.

 ## Residual standard error: 3.211 on 36 degrees of freedom
 ## 
 ## Backtransformed parameters:
-##                Estimate     Lower     Upper
-## parent_0      99.600000 96.330000 1.029e+02
-## k_parent_sink  0.047920  0.040890 5.616e-02
-## k_parent_m1    0.050780  0.046700 5.521e-02
-## k_m1_sink      0.005261  0.003992 6.933e-03
+##   Confidence intervals for internally transformed parameters are asymmetric.
+##   t-test (unrealistically) based on the assumption of normal distribution
+##   for estimators of untransformed parameters.
+##                Estimate t value    Pr(>t)     Lower     Upper
+## parent_0      99.600000  61.720 2.024e-38 96.330000 1.029e+02
+## k_parent_sink  0.047920  12.780 3.050e-15  0.040890 5.616e-02
+## k_parent_m1    0.050780  24.250 3.407e-24  0.046700 5.521e-02
+## k_m1_sink      0.005261   7.349 5.758e-09  0.003992 6.933e-03
 ## 
 ## Chi2 error levels in percent:
 ##          err.min n.optim df
diff --git a/vignettes/FOCUS_L.html b/vignettes/FOCUS_L.html
index 96ea70ce..692caf93 100644
--- a/vignettes/FOCUS_L.html
+++ b/vignettes/FOCUS_L.html
@@ -214,13 +214,7 @@ hr {
 report, p. 284:

 
 
library("mkin")
-

-
-
## Loading required package: minpack.lm
-## Loading required package: rootSolve
-

-
-
FOCUS_2006_L1 = data.frame(
+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,
@@ -242,17 +236,17 @@ given in the FOCUS report. 

 summary(m.L1.SFO)
 

 
-
## mkin version:    0.9.35 
-## R version:       3.1.2 
-## Date of fit:     Sat Feb 21 14:44:53 2015 
-## Date of summary: Sat Feb 21 14:44:53 2015 
+
## mkin version:    0.9.36 
+## R version:       3.2.1 
+## Date of fit:     Sun Jun 21 01:47:59 2015 
+## Date of summary: Sun Jun 21 01:47:59 2015 
 ## 
 ## Equations:
 ## d_parent = - k_parent_sink * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted with method Port using 37 model solutions performed in 0.098 s
+## Fitted with method Port using 37 model solutions performed in 0.093 s
 ## 
 ## Weighting: none
 ## 
@@ -269,13 +263,10 @@ summary(m.L1.SFO)
 ## Fixed parameter values:
 ## None
 ## 
-## Optimised, transformed parameters:
-##                   Estimate Std. Error  Lower  Upper t value  Pr(>|t|)
-## parent_0            92.470    1.36800 89.570 95.370   67.58 4.339e-21
-## log_k_parent_sink   -2.347    0.04057 -2.433 -2.261  -57.86 5.155e-20
-##                      Pr(>t)
-## parent_0          2.170e-21
-## log_k_parent_sink 2.577e-20
+## Optimised, transformed parameters with symmetric confidence intervals:
+##                   Estimate Std. Error  Lower  Upper
+## parent_0            92.470    1.36800 89.570 95.370
+## log_k_parent_sink   -2.347    0.04057 -2.433 -2.261
 ## 
 ## Parameter correlation:
 ##                   parent_0 log_k_parent_sink
@@ -285,9 +276,12 @@ summary(m.L1.SFO)
 ## Residual standard error: 2.948 on 16 degrees of freedom
 ## 
 ## Backtransformed parameters:
-##               Estimate    Lower   Upper
-## parent_0      92.47000 89.57000 95.3700
-## k_parent_sink  0.09561  0.08773  0.1042
+##   Confidence intervals for internally transformed parameters are asymmetric.
+##   t-test (unrealistically) based on the assumption of normal distribution
+##   for estimators of untransformed parameters.
+##               Estimate t value    Pr(>t)    Lower   Upper
+## parent_0      92.47000   67.58 2.170e-21 89.57000 95.3700
+## k_parent_sink  0.09561   24.65 1.867e-14  0.08773  0.1042
 ## 
 ## Chi2 error levels in percent:
 ##          err.min n.optim df
@@ -341,20 +335,31 @@ The residual plot can be easily obtained by

 is checked.

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

 
-
## mkin version:    0.9.35 
-## R version:       3.1.2 
-## Date of fit:     Sat Feb 21 14:44:55 2015 
-## Date of summary: Sat Feb 21 14:44:55 2015 
+
## 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 
+## R version:       3.2.1 
+## Date of fit:     Sun Jun 21 01:48:00 2015 
+## Date of summary: Sun Jun 21 01:48:00 2015 
+## 
+## 
+## Warning: Optimisation by method Port did not converge.
+## Convergence code is 1 
+## 
 ## 
 ## Equations:
-## d_parent = - (alpha/beta) * ((time/beta) + 1)^-1 * parent
+## d_parent = - (alpha/beta) * 1/((time/beta) + 1) * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted with method Port using 611 model solutions performed in 1.509 s
+## Fitted with method Port using 188 model solutions performed in 0.463 s
 ## 
 ## Weighting: none
 ## 
@@ -373,29 +378,28 @@ summary(m.L1.FOMC, data = FALSE)
 ## Fixed parameter values:
 ## None
 ## 
-## Optimised, transformed parameters:
-##           Estimate Std. Error    Lower   Upper  t value  Pr(>|t|)
-## parent_0     92.47      1.482    89.31   95.63 62.39000 1.546e-19
-## log_alpha    11.25    598.200 -1264.00 1286.00  0.01880 9.852e-01
-## log_beta     13.60    598.200 -1261.00 1289.00  0.02273 9.822e-01
-##              Pr(>t)
-## parent_0  7.730e-20
-## log_alpha 4.926e-01
-## log_beta  4.911e-01
+## Optimised, transformed parameters with symmetric confidence intervals:
+##           Estimate Std. Error  Lower Upper
+## parent_0     92.47      1.422  89.44 95.50
+## log_alpha    15.43     15.080 -16.71 47.58
+## log_beta     17.78     15.090 -14.37 49.93
 ## 
 ## Parameter correlation:
 ##           parent_0 log_alpha log_beta
-## parent_0    1.0000   -0.3016  -0.3016
-## log_alpha  -0.3016    1.0000   1.0000
-## log_beta   -0.3016    1.0000   1.0000
+## parent_0    1.0000    0.1129   0.1112
+## log_alpha   0.1129    1.0000   1.0000
+## log_beta    0.1112    1.0000   1.0000
 ## 
 ## Residual standard error: 3.045 on 15 degrees of freedom
 ## 
 ## Backtransformed parameters:
-##           Estimate Lower Upper
-## parent_0     92.47 89.31 95.63
-## alpha     76830.00  0.00   Inf
-## beta     803500.00  0.00   Inf
+##   Confidence intervals for internally transformed parameters are asymmetric.
+##   t-test (unrealistically) based on the assumption of normal distribution
+##   for estimators of untransformed parameters.
+##           Estimate t value    Pr(>t)     Lower     Upper
+## parent_0 9.247e+01  65.150 4.044e-20 8.944e+01 9.550e+01
+## alpha    5.044e+06   1.271 1.115e-01 5.510e-08 4.618e+20
+## beta     5.276e+07   1.259 1.137e-01 5.732e-07 4.857e+21
 ## 
 ## Chi2 error levels in percent:
 ##          err.min n.optim df
@@ -403,8 +407,8 @@ summary(m.L1.FOMC, data = FALSE)
 ## parent     3.619       3  6
 ## 
 ## Estimated disappearance times:
-##         DT50  DT90 DT50back
-## parent 7.249 24.08    7.249
+##        DT50  DT90 DT50back
+## parent 7.25 24.08     7.25
 

 
 
Due to the higher number of parameters, and the lower number of degrees of
@@ -442,17 +446,17 @@ FOCUS_2006_L2_mkin <- mkin_wide_to_long(FOCUS_2006_L2)
 summary(m.L2.SFO)
 

 
-
## mkin version:    0.9.35 
-## R version:       3.1.2 
-## Date of fit:     Sat Feb 21 14:44:55 2015 
-## Date of summary: Sat Feb 21 14:44:55 2015 
+
## mkin version:    0.9.36 
+## R version:       3.2.1 
+## Date of fit:     Sun Jun 21 01:48:00 2015 
+## Date of summary: Sun Jun 21 01:48:00 2015 
 ## 
 ## Equations:
 ## d_parent = - k_parent_sink * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted with method Port using 41 model solutions performed in 0.1 s
+## Fitted with method Port using 41 model solutions performed in 0.097 s
 ## 
 ## Weighting: none
 ## 
@@ -469,13 +473,10 @@ summary(m.L2.SFO)
 ## Fixed parameter values:
 ## None
 ## 
-## Optimised, transformed parameters:
-##                   Estimate Std. Error   Lower   Upper t value  Pr(>|t|)
-## parent_0           91.4700     3.8070 82.9800 99.9500  24.030 3.545e-10
-## log_k_parent_sink  -0.4112     0.1074 -0.6505 -0.1719  -3.828 3.329e-03
-##                      Pr(>t)
-## parent_0          1.773e-10
-## log_k_parent_sink 1.664e-03
+## Optimised, transformed parameters with symmetric confidence intervals:
+##                   Estimate Std. Error   Lower   Upper
+## parent_0           91.4700     3.8070 82.9800 99.9500
+## log_k_parent_sink  -0.4112     0.1074 -0.6505 -0.1719
 ## 
 ## Parameter correlation:
 ##                   parent_0 log_k_parent_sink
@@ -485,9 +486,12 @@ summary(m.L2.SFO)
 ## Residual standard error: 5.51 on 10 degrees of freedom
 ## 
 ## Backtransformed parameters:
-##               Estimate   Lower   Upper
-## parent_0       91.4700 82.9800 99.9500
-## k_parent_sink   0.6629  0.5218  0.8421
+##   Confidence intervals for internally transformed parameters are asymmetric.
+##   t-test (unrealistically) based on the assumption of normal distribution
+##   for estimators of untransformed parameters.
+##               Estimate t value    Pr(>t)   Lower   Upper
+## parent_0       91.4700   24.03 1.773e-10 82.9800 99.9500
+## k_parent_sink   0.6629    9.31 1.525e-06  0.5218  0.8421
 ## 
 ## Chi2 error levels in percent:
 ##          err.min n.optim df
@@ -552,17 +556,17 @@ mkinresplot(m.L2.FOMC)
 
summary(m.L2.FOMC, data = FALSE)
 

 
-
## mkin version:    0.9.35 
-## R version:       3.1.2 
-## Date of fit:     Sat Feb 21 14:44:55 2015 
-## Date of summary: Sat Feb 21 14:44:55 2015 
+
## mkin version:    0.9.36 
+## R version:       3.2.1 
+## Date of fit:     Sun Jun 21 01:48:00 2015 
+## Date of summary: Sun Jun 21 01:48:00 2015 
 ## 
 ## Equations:
-## d_parent = - (alpha/beta) * ((time/beta) + 1)^-1 * parent
+## 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 0.201 s
+## Fitted with method Port using 81 model solutions performed in 0.191 s
 ## 
 ## Weighting: none
 ## 
@@ -581,11 +585,11 @@ mkinresplot(m.L2.FOMC)
 ## Fixed parameter values:
 ## None
 ## 
-## Optimised, transformed parameters:
-##           Estimate Std. Error   Lower   Upper t value  Pr(>|t|)    Pr(>t)
-## parent_0   93.7700     1.8560 89.5700 97.9700 50.5100 2.345e-12 1.173e-12
-## log_alpha   0.3180     0.1867 -0.1044  0.7405  1.7030 1.227e-01 6.137e-02
-## log_beta    0.2102     0.2943 -0.4555  0.8759  0.7142 4.932e-01 2.466e-01
+## Optimised, transformed parameters with symmetric confidence intervals:
+##           Estimate Std. Error   Lower   Upper
+## parent_0   93.7700     1.8560 89.5700 97.9700
+## log_alpha   0.3180     0.1867 -0.1044  0.7405
+## log_beta    0.2102     0.2943 -0.4555  0.8759
 ## 
 ## Parameter correlation:
 ##           parent_0 log_alpha log_beta
@@ -596,10 +600,13 @@ mkinresplot(m.L2.FOMC)
 ## Residual standard error: 2.628 on 9 degrees of freedom
 ## 
 ## Backtransformed parameters:
-##          Estimate   Lower  Upper
-## parent_0   93.770 89.5700 97.970
-## alpha       1.374  0.9009  2.097
-## beta        1.234  0.6341  2.401
+##   Confidence intervals for internally transformed parameters are asymmetric.
+##   t-test (unrealistically) based on the assumption of normal distribution
+##   for estimators of untransformed parameters.
+##          Estimate t value    Pr(>t)   Lower  Upper
+## parent_0   93.770  50.510 1.173e-12 89.5700 97.970
+## alpha       1.374   5.355 2.296e-04  0.9009  2.097
+## beta        1.234   3.398 3.949e-03  0.6341  2.401
 ## 
 ## Chi2 error levels in percent:
 ##          err.min n.optim df
@@ -638,10 +645,10 @@ plot(m.L2.DFOP)
 
summary(m.L2.DFOP, data = FALSE)
 

 
-
## mkin version:    0.9.35 
-## R version:       3.1.2 
-## Date of fit:     Sat Feb 21 14:44:57 2015 
-## Date of summary: Sat Feb 21 14:44:57 2015 
+
## mkin version:    0.9.36 
+## R version:       3.2.1 
+## Date of fit:     Sun Jun 21 01:48:02 2015 
+## Date of summary: Sun Jun 21 01:48:02 2015 
 ## 
 ## Equations:
 ## d_parent = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -650,7 +657,7 @@ plot(m.L2.DFOP)
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted with method Port using 336 model solutions performed in 0.856 s
+## Fitted with method Port using 336 model solutions performed in 0.835 s
 ## 
 ## Weighting: none
 ## 
@@ -671,12 +678,12 @@ plot(m.L2.DFOP)
 ## Fixed parameter values:
 ## None
 ## 
-## Optimised, transformed parameters:
-##          Estimate Std. Error Lower Upper t value Pr(>|t|) Pr(>t)
-## parent_0  93.9500         NA    NA    NA      NA       NA     NA
-## log_k1     3.1210         NA    NA    NA      NA       NA     NA
-## log_k2    -1.0880         NA    NA    NA      NA       NA     NA
-## g_ilr     -0.2821         NA    NA    NA      NA       NA     NA
+## Optimised, transformed parameters with symmetric confidence intervals:
+##          Estimate Std. Error Lower Upper
+## parent_0  93.9500         NA    NA    NA
+## log_k1     3.1210         NA    NA    NA
+## log_k2    -1.0880         NA    NA    NA
+## g_ilr     -0.2821         NA    NA    NA
 ## 
 ## Parameter correlation:
 ## Could not estimate covariance matrix; singular system:
@@ -684,11 +691,14 @@ plot(m.L2.DFOP)
 ## Residual standard error: 1.732 on 8 degrees of freedom
 ## 
 ## Backtransformed parameters:
-##          Estimate Lower Upper
-## parent_0  93.9500    NA    NA
-## k1        22.6700    NA    NA
-## k2         0.3369    NA    NA
-## g          0.4016    NA    NA
+##   Confidence intervals for internally transformed parameters are asymmetric.
+##   t-test (unrealistically) based on the assumption of normal distribution
+##   for estimators of untransformed parameters.
+##          Estimate t value Pr(>t) Lower Upper
+## parent_0  93.9500      NA     NA    NA    NA
+## k1        22.6700      NA     NA    NA    NA
+## k2         0.3369      NA     NA    NA    NA
+## g          0.4016      NA     NA    NA    NA
 ## 
 ## Chi2 error levels in percent:
 ##          err.min n.optim df
@@ -727,17 +737,17 @@ plot(m.L3.SFO)
 
summary(m.L3.SFO)
 

 
-
## mkin version:    0.9.35 
-## R version:       3.1.2 
-## Date of fit:     Sat Feb 21 14:44:57 2015 
-## Date of summary: Sat Feb 21 14:44:57 2015 
+
## mkin version:    0.9.36 
+## R version:       3.2.1 
+## Date of fit:     Sun Jun 21 01:48:03 2015 
+## Date of summary: Sun Jun 21 01:48:03 2015 
 ## 
 ## Equations:
 ## d_parent = - k_parent_sink * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted with method Port using 43 model solutions performed in 0.109 s
+## Fitted with method Port using 43 model solutions performed in 0.104 s
 ## 
 ## Weighting: none
 ## 
@@ -754,13 +764,10 @@ plot(m.L3.SFO)
 ## Fixed parameter values:
 ## None
 ## 
-## Optimised, transformed parameters:
-##                   Estimate Std. Error  Lower Upper t value  Pr(>|t|)
-## parent_0            74.870     8.4570 54.180 95.57   8.853 1.155e-04
-## log_k_parent_sink   -3.678     0.3261 -4.476 -2.88 -11.280 2.903e-05
-##                      Pr(>t)
-## parent_0          5.776e-05
-## log_k_parent_sink 1.451e-05
+## Optimised, transformed parameters with symmetric confidence intervals:
+##                   Estimate Std. Error  Lower Upper
+## parent_0            74.870     8.4570 54.180 95.57
+## log_k_parent_sink   -3.678     0.3261 -4.476 -2.88
 ## 
 ## Parameter correlation:
 ##                   parent_0 log_k_parent_sink
@@ -770,9 +777,12 @@ plot(m.L3.SFO)
 ## Residual standard error: 12.91 on 6 degrees of freedom
 ## 
 ## Backtransformed parameters:
-##               Estimate    Lower    Upper
-## parent_0      74.87000 54.18000 95.57000
-## k_parent_sink  0.02527  0.01138  0.05612
+##   Confidence intervals for internally transformed parameters are asymmetric.
+##   t-test (unrealistically) based on the assumption of normal distribution
+##   for estimators of untransformed parameters.
+##               Estimate t value    Pr(>t)    Lower    Upper
+## parent_0      74.87000   8.853 5.776e-05 54.18000 95.57000
+## k_parent_sink  0.02527   3.067 1.102e-02  0.01138  0.05612
 ## 
 ## Chi2 error levels in percent:
 ##          err.min n.optim df
@@ -813,17 +823,17 @@ plot(m.L3.FOMC)
 
summary(m.L3.FOMC, data = FALSE)
 

 
-
## mkin version:    0.9.35 
-## R version:       3.1.2 
-## Date of fit:     Sat Feb 21 14:44:58 2015 
-## Date of summary: Sat Feb 21 14:44:58 2015 
+
## mkin version:    0.9.36 
+## R version:       3.2.1 
+## Date of fit:     Sun Jun 21 01:48:03 2015 
+## Date of summary: Sun Jun 21 01:48:03 2015 
 ## 
 ## Equations:
-## d_parent = - (alpha/beta) * ((time/beta) + 1)^-1 * parent
+## 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 0.203 s
+## Fitted with method Port using 83 model solutions performed in 0.196 s
 ## 
 ## Weighting: none
 ## 
@@ -842,11 +852,11 @@ plot(m.L3.FOMC)
 ## Fixed parameter values:
 ## None
 ## 
-## Optimised, transformed parameters:
-##           Estimate Std. Error   Lower    Upper t value  Pr(>|t|)    Pr(>t)
-## parent_0   96.9700     4.5500 85.2800 108.7000  21.310 4.216e-06 2.108e-06
-## log_alpha  -0.8619     0.1704 -1.3000  -0.4238  -5.057 3.911e-03 1.955e-03
-## log_beta    0.6193     0.4744 -0.6003   1.8390   1.305 2.486e-01 1.243e-01
+## Optimised, transformed parameters with symmetric confidence intervals:
+##           Estimate Std. Error   Lower    Upper
+## parent_0   96.9700     4.5500 85.2800 108.7000
+## log_alpha  -0.8619     0.1704 -1.3000  -0.4238
+## log_beta    0.6193     0.4744 -0.6003   1.8390
 ## 
 ## Parameter correlation:
 ##           parent_0 log_alpha log_beta
@@ -857,10 +867,13 @@ plot(m.L3.FOMC)
 ## Residual standard error: 4.572 on 5 degrees of freedom
 ## 
 ## Backtransformed parameters:
-##          Estimate   Lower    Upper
-## parent_0  96.9700 85.2800 108.7000
-## alpha      0.4224  0.2725   0.6546
-## beta       1.8580  0.5487   6.2890
+##   Confidence intervals for internally transformed parameters are asymmetric.
+##   t-test (unrealistically) based on the assumption of normal distribution
+##   for estimators of untransformed parameters.
+##          Estimate t value    Pr(>t)   Lower    Upper
+## parent_0  96.9700  21.310 2.108e-06 85.2800 108.7000
+## alpha      0.4224   5.867 1.020e-03  0.2725   0.6546
+## beta       1.8580   2.108 4.444e-02  0.5487   6.2890
 ## 
 ## Chi2 error levels in percent:
 ##          err.min n.optim df
@@ -886,10 +899,10 @@ plot(m.L3.DFOP)
 
summary(m.L3.DFOP, data = FALSE)
 

 
-
## mkin version:    0.9.35 
-## R version:       3.1.2 
-## Date of fit:     Sat Feb 21 14:44:58 2015 
-## Date of summary: Sat Feb 21 14:44:58 2015 
+
## mkin version:    0.9.36 
+## R version:       3.2.1 
+## Date of fit:     Sun Jun 21 01:48:03 2015 
+## Date of summary: Sun Jun 21 01:48:03 2015 
 ## 
 ## Equations:
 ## d_parent = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -898,7 +911,7 @@ plot(m.L3.DFOP)
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted with method Port using 137 model solutions performed in 0.346 s
+## Fitted with method Port using 137 model solutions performed in 0.35 s
 ## 
 ## Weighting: none
 ## 
@@ -919,12 +932,12 @@ plot(m.L3.DFOP)
 ## Fixed parameter values:
 ## None
 ## 
-## Optimised, transformed parameters:
-##          Estimate Std. Error   Lower     Upper t value  Pr(>|t|)    Pr(>t)
-## parent_0  97.7500    1.43800 93.7500 101.70000  67.970 2.808e-07 1.404e-07
-## log_k1    -0.6612    0.13340 -1.0310  -0.29100  -4.958 7.715e-03 3.858e-03
-## log_k2    -4.2860    0.05902 -4.4500  -4.12200 -72.620 2.155e-07 1.077e-07
-## g_ilr     -0.1229    0.05121 -0.2651   0.01925  -2.401 7.431e-02 3.716e-02
+## Optimised, transformed parameters with symmetric confidence intervals:
+##          Estimate Std. Error   Lower     Upper
+## parent_0  97.7500    1.43800 93.7500 101.70000
+## log_k1    -0.6612    0.13340 -1.0310  -0.29100
+## log_k2    -4.2860    0.05902 -4.4500  -4.12200
+## g_ilr     -0.1229    0.05121 -0.2651   0.01925
 ## 
 ## Parameter correlation:
 ##          parent_0  log_k1   log_k2   g_ilr
@@ -936,11 +949,14 @@ plot(m.L3.DFOP)
 ## Residual standard error: 1.439 on 4 degrees of freedom
 ## 
 ## Backtransformed parameters:
-##          Estimate    Lower     Upper
-## parent_0 97.75000 93.75000 101.70000
-## k1        0.51620  0.35650   0.74750
-## k2        0.01376  0.01168   0.01621
-## g         0.45660  0.40730   0.50680
+##   Confidence intervals for internally transformed parameters are asymmetric.
+##   t-test (unrealistically) based on the assumption of normal distribution
+##   for estimators of untransformed parameters.
+##          Estimate t value    Pr(>t)    Lower     Upper
+## parent_0 97.75000  67.970 1.404e-07 93.75000 101.70000
+## k1        0.51620   7.499 8.460e-04  0.35650   0.74750
+## k2        0.01376  16.940 3.557e-05  0.01168   0.01621
+## g         0.45660  25.410 7.121e-06  0.40730   0.50680
 ## 
 ## Chi2 error levels in percent:
 ##          err.min n.optim df
@@ -984,17 +1000,17 @@ plot(m.L4.SFO)
 
summary(m.L4.SFO, data = FALSE)
 

 
-
## mkin version:    0.9.35 
-## R version:       3.1.2 
-## Date of fit:     Sat Feb 21 14:44:58 2015 
-## Date of summary: Sat Feb 21 14:44:58 2015 
+
## mkin version:    0.9.36 
+## R version:       3.2.1 
+## Date of fit:     Sun Jun 21 01:48:04 2015 
+## Date of summary: Sun Jun 21 01:48:04 2015 
 ## 
 ## Equations:
 ## d_parent = - k_parent_sink * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted with method Port using 46 model solutions performed in 0.109 s
+## Fitted with method Port using 46 model solutions performed in 0.105 s
 ## 
 ## Weighting: none
 ## 
@@ -1011,13 +1027,10 @@ plot(m.L4.SFO)
 ## Fixed parameter values:
 ## None
 ## 
-## Optimised, transformed parameters:
-##                   Estimate Std. Error  Lower   Upper t value  Pr(>|t|)
-## parent_0             96.44    1.94900 91.670 101.200   49.49 4.566e-09
-## log_k_parent_sink    -5.03    0.07999 -5.225  -4.834  -62.88 1.088e-09
-##                      Pr(>t)
-## parent_0          2.283e-09
-## log_k_parent_sink 5.438e-10
+## Optimised, transformed parameters with symmetric confidence intervals:
+##                   Estimate Std. Error  Lower   Upper
+## parent_0             96.44    1.94900 91.670 101.200
+## log_k_parent_sink    -5.03    0.07999 -5.225  -4.834
 ## 
 ## Parameter correlation:
 ##                   parent_0 log_k_parent_sink
@@ -1027,9 +1040,12 @@ plot(m.L4.SFO)
 ## Residual standard error: 3.651 on 6 degrees of freedom
 ## 
 ## Backtransformed parameters:
-##                Estimate     Lower     Upper
-## parent_0      96.440000 91.670000 1.012e+02
-## k_parent_sink  0.006541  0.005378 7.955e-03
+##   Confidence intervals for internally transformed parameters are asymmetric.
+##   t-test (unrealistically) based on the assumption of normal distribution
+##   for estimators of untransformed parameters.
+##                Estimate t value    Pr(>t)     Lower     Upper
+## parent_0      96.440000   49.49 2.283e-09 91.670000 1.012e+02
+## k_parent_sink  0.006541   12.50 8.008e-06  0.005378 7.955e-03
 ## 
 ## Chi2 error levels in percent:
 ##          err.min n.optim df
@@ -1059,17 +1075,17 @@ plot(m.L4.FOMC)
 
summary(m.L4.FOMC, data = FALSE)
 

 
-
## mkin version:    0.9.35 
-## R version:       3.1.2 
-## Date of fit:     Sat Feb 21 14:44:58 2015 
-## Date of summary: Sat Feb 21 14:44:58 2015 
+
## mkin version:    0.9.36 
+## R version:       3.2.1 
+## Date of fit:     Sun Jun 21 01:48:04 2015 
+## Date of summary: Sun Jun 21 01:48:04 2015 
 ## 
 ## Equations:
-## d_parent = - (alpha/beta) * ((time/beta) + 1)^-1 * parent
+## 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 0.161 s
+## Fitted with method Port using 66 model solutions performed in 0.159 s
 ## 
 ## Weighting: none
 ## 
@@ -1088,11 +1104,11 @@ plot(m.L4.FOMC)
 ## Fixed parameter values:
 ## None
 ## 
-## Optimised, transformed parameters:
-##           Estimate Std. Error  Lower    Upper t value  Pr(>|t|)    Pr(>t)
-## parent_0   99.1400     1.6800 94.820 103.5000 59.0200 2.643e-08 1.322e-08
-## log_alpha  -0.3506     0.3725 -1.308   0.6068 -0.9414 3.897e-01 1.949e-01
-## log_beta    4.1740     0.5635  2.726   5.6230  7.4070 7.059e-04 3.530e-04
+## Optimised, transformed parameters with symmetric confidence intervals:
+##           Estimate Std. Error  Lower    Upper
+## parent_0   99.1400     1.6800 94.820 103.5000
+## log_alpha  -0.3506     0.3725 -1.308   0.6068
+## log_beta    4.1740     0.5635  2.726   5.6230
 ## 
 ## Parameter correlation:
 ##           parent_0 log_alpha log_beta
@@ -1103,10 +1119,13 @@ plot(m.L4.FOMC)
 ## Residual standard error: 2.315 on 5 degrees of freedom
 ## 
 ## Backtransformed parameters:
-##          Estimate   Lower   Upper
-## parent_0  99.1400 94.8200 103.500
-## alpha      0.7042  0.2703   1.835
-## beta      64.9800 15.2600 276.600
+##   Confidence intervals for internally transformed parameters are asymmetric.
+##   t-test (unrealistically) based on the assumption of normal distribution
+##   for estimators of untransformed parameters.
+##          Estimate t value    Pr(>t)   Lower   Upper
+## parent_0  99.1400  59.020 1.322e-08 94.8200 103.500
+## alpha      0.7042   2.685 2.178e-02  0.2703   1.835
+## beta      64.9800   1.775 6.807e-02 15.2600 276.600
 ## 
 ## Chi2 error levels in percent:
 ##          err.min n.optim df
diff --git a/vignettes/FOCUS_Z.Rnw b/vignettes/FOCUS_Z.Rnw
index 5e2e0251..1df0ee9c 100644
--- a/vignettes/FOCUS_Z.Rnw
+++ b/vignettes/FOCUS_Z.Rnw
@@ -265,11 +265,13 @@ summary(m.Z.mkin.5a, data = FALSE)$bpar
 @
 
 A graphical representation of the confidence intervals can finally be obtained.
+
 <>=
 mkinparplot(m.Z.mkin.5a)
 @
 
 The endpoints obtained with this model are
+
 <>=
 endpoints(m.Z.mkin.5a)
 @
diff --git a/vignettes/FOCUS_Z.pdf b/vignettes/FOCUS_Z.pdf
index 3174a23a..36f3dc14 100644
Binary files a/vignettes/FOCUS_Z.pdf and b/vignettes/FOCUS_Z.pdf differ
diff --git a/vignettes/compiled_models.html b/vignettes/compiled_models.html
index 2f2a6edb..e6f21b09 100644
--- a/vignettes/compiled_models.html
+++ b/vignettes/compiled_models.html
@@ -77,7 +77,7 @@ img {
 -->
 

 
Benchmark for a model that can also be solved with Eigenvalues

-
This evaluation is taken from the example section of mkinfit. When using an mkin version greater than 0.9-36 and the ccSolve package is installed and functional, you will get a message that the model is being compiled when defining a model using mkinmod.

+
This evaluation is taken from the example section of mkinfit. When using an mkin version equal to or greater than 0.9-36 and a compiler (gcc) is installed, you will see a message that the model is being compiled from autogenerated C code when defining a model using mkinmod.

 
library("mkin")
 SFO_SFO <- mkinmod(
   parent = list(type = "SFO", to = "m1", sink = TRUE),
@@ -94,20 +94,20 @@ mb.1 <- microbenchmark(
 smb.1 <- summary(mb.1)[-1]
 rownames(smb.1) <- c("deSolve, not compiled", "Eigenvalue based", "deSolve, compiled")
 print(smb.1)

-
##                             min        lq      mean    median        uq
-## deSolve, not compiled 6192.0125 6195.3470 6211.0309 6198.6816 6220.5401
-## Eigenvalue based       956.7604 1008.7224 1026.2572 1060.6844 1061.0055
-## deSolve, compiled      869.6880  871.9315  883.4929  874.1751  890.3953
+
##                            min        lq      mean    median        uq
+## deSolve, not compiled 4969.585 5033.7311 5092.7389 5097.8773 5154.3160
+## Eigenvalue based       868.731  891.7239  909.6449  914.7169  930.1018
+## deSolve, compiled     4935.049 4935.4796 4968.2150 4935.9097 4984.7978
 ##                             max neval
-## deSolve, not compiled 6242.3986     3
-## Eigenvalue based      1061.3266     3
-## deSolve, compiled      906.6155     3

+## deSolve, not compiled 5210.7547     3
+## Eigenvalue based       945.4867     3
+## deSolve, compiled     5033.6858     3

 
We see that using the compiled model is almost a factor of 8 faster than using the R version with the default ode solver, and it is even faster than the Eigenvalue based solution implemented in R which does not need iterative solution of the ODEs:

 
smb.1["median"]/smb.1["deSolve, compiled", "median"]

-
##                         median
-## deSolve, not compiled 7.120877
-## Eigenvalue based      1.205328
-## deSolve, compiled     1.000000

+
##                          median
+## deSolve, not compiled 1.0328141
+## Eigenvalue based      0.1853188
+## deSolve, compiled     1.0000000

 

 

 
Benchmark for a model that can not be solved with Eigenvalues

@@ -124,16 +124,16 @@ smb.2 <- summary(mb.2)[-1]
 rownames(smb.2) <- c("deSolve, not compiled", "deSolve, compiled")
 print(smb.2)

 
##                             min        lq      mean    median        uq
-## deSolve, not compiled 13.297283 13.427702 13.481155 13.558121 13.573092
-## deSolve, compiled      1.486926  1.526887  1.546851  1.566848  1.576813
-##                             max neval
-## deSolve, not compiled 13.588063     3
-## deSolve, compiled      1.586778     3

+## deSolve, not compiled 11.745276 11.754288 11.820726 11.763300 11.858451
+## deSolve, compiled      1.385829  1.386407  1.400841  1.386985  1.408347
+##                            max neval
+## deSolve, not compiled 11.95360     3
+## deSolve, compiled      1.42971     3

 
smb.2["median"]/smb.2["deSolve, compiled", "median"]

-
##                         median
-## deSolve, not compiled 8.653119
-## deSolve, compiled     1.000000

-
Here we get a performance benefit of more than a factor of 8 using the version of the differential equation model compiled from C code using the ccSolve package!

+
##                       median
+## deSolve, not compiled 8.4812
+## deSolve, compiled     1.0000

+
Here we get a performance benefit of more than a factor of 10 using the version of the differential equation model compiled from C code using the inline package!

 
 
 
diff --git a/vignettes/mkin.pdf b/vignettes/mkin.pdf
index 8f1e0884..5786c5bf 100644
Binary files a/vignettes/mkin.pdf and b/vignettes/mkin.pdf differ
-- 
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