From 7008a4ee100830a29a923a05274fd4ca216cd1ea Mon Sep 17 00:00:00 2001 From: Johannes Ranke Date: Fri, 1 Jul 2022 09:08:49 +0200 Subject: Add R version to data in benchmark vignette --- docs/articles/FOCUS_L.html | 210 +++++++++++++++++++++++---------------------- 1 file changed, 109 insertions(+), 101 deletions(-) (limited to 'docs/articles/FOCUS_L.html') diff --git a/docs/articles/FOCUS_L.html b/docs/articles/FOCUS_L.html index 5f41b6a3..d3918ef4 100644 --- a/docs/articles/FOCUS_L.html +++ b/docs/articles/FOCUS_L.html @@ -105,7 +105,7 @@

Example evaluation of FOCUS Laboratory Data L1 to L3

Johannes Ranke

-

Last change 17 November 2016 (rebuilt 2022-05-18)

+

Last change 18 May 2022 (rebuilt 2022-06-30)

Source: vignettes/FOCUS_L.rmd @@ -130,18 +130,18 @@

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)
+summary(m.L1.SFO) 
## mkin version used for fitting:    1.1.0 
-## R version used for fitting:       4.2.0 
-## Date of fit:     Wed May 18 20:42:32 2022 
-## Date of summary: Wed May 18 20:42:32 2022 
+## R version used for fitting:       4.2.1 
+## Date of fit:     Thu Jun 30 10:43:59 2022 
+## Date of summary: Thu Jun 30 10:43:59 2022 
 ## 
 ## Equations:
 ## d_parent/dt = - k_parent * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 133 model solutions performed in 0.031 s
+## Fitted using 133 model solutions performed in 0.032 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -173,9 +173,9 @@
 ## 
 ## Parameter correlation:
 ##                parent_0 log_k_parent      sigma
-## parent_0      1.000e+00    6.186e-01 -1.712e-09
-## log_k_parent  6.186e-01    1.000e+00 -3.237e-09
-## sigma        -1.712e-09   -3.237e-09  1.000e+00
+## parent_0      1.000e+00    6.186e-01 -1.516e-09
+## log_k_parent  6.186e-01    1.000e+00 -3.124e-09
+## sigma        -1.516e-09   -3.124e-09  1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
@@ -217,7 +217,7 @@
 ##    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, show_errmin = TRUE, main = "FOCUS L1 - SFO")
+plot(m.L1.SFO, show_errmin = TRUE, main = "FOCUS L1 - SFO")

The residual plot can be easily obtained by

@@ -225,26 +225,29 @@
 

 
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)
-plot(m.L1.FOMC, show_errmin = TRUE, main = "FOCUS L1 - FOMC")

+m.L1.FOMC <- mkinfit("FOMC", FOCUS_2006_L1_mkin, quiet=TRUE)
+
## Warning in mkinfit("FOMC", FOCUS_2006_L1_mkin, quiet = TRUE): Optimisation did not converge:
+## false convergence (8)
+
+plot(m.L1.FOMC, show_errmin = TRUE, main = "FOCUS L1 - FOMC")

-
-summary(m.L1.FOMC, data = FALSE)
+
+summary(m.L1.FOMC, data = FALSE)
## Warning in sqrt(diag(covar)): NaNs produced
## Warning in sqrt(1/diag(V)): NaNs produced
## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
 ## doubtful
## mkin version used for fitting:    1.1.0 
-## R version used for fitting:       4.2.0 
-## Date of fit:     Wed May 18 20:42:33 2022 
-## Date of summary: Wed May 18 20:42:33 2022 
+## R version used for fitting:       4.2.1 
+## Date of fit:     Thu Jun 30 10:44:00 2022 
+## Date of summary: Thu Jun 30 10:44:00 2022 
 ## 
 ## Equations:
 ## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 357 model solutions performed in 0.072 s
+## Fitted using 369 model solutions performed in 0.082 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -265,34 +268,39 @@
 ## Fixed parameter values:
 ## None
 ## 
+## 
+## Warning(s): 
+## Optimisation did not converge:
+## false convergence (8)
+## 
 ## Results:
 ## 
-##        AIC      BIC    logLik
-##   95.88804 99.44953 -43.94402
+##        AIC      BIC   logLik
+##   95.88781 99.44929 -43.9439
 ## 
 ## Optimised, transformed parameters with symmetric confidence intervals:
 ##           Estimate Std. Error  Lower  Upper
 ## parent_0     92.47     1.2820 89.720 95.220
-## log_alpha    11.37        NaN    NaN    NaN
-## log_beta     13.72        NaN    NaN    NaN
-## sigma         2.78     0.4621  1.789  3.771
+## log_alpha    13.78        NaN    NaN    NaN
+## log_beta     16.13        NaN    NaN    NaN
+## sigma         2.78     0.4598  1.794  3.766
 ## 
 ## Parameter correlation:
 ##            parent_0 log_alpha log_beta     sigma
-## parent_0  1.0000000       NaN      NaN 0.0005548
+## parent_0  1.0000000       NaN      NaN 0.0001671
 ## log_alpha       NaN         1      NaN       NaN
 ## log_beta        NaN       NaN        1       NaN
-## sigma     0.0005548       NaN      NaN 1.0000000
+## sigma     0.0001671       NaN      NaN 1.0000000
 ## 
 ## Backtransformed parameters:
 ## 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     92.47      NA     NA 89.720 95.220
-## alpha     87110.00      NA     NA     NA     NA
-## beta     911100.00      NA     NA     NA     NA
-## sigma         2.78      NA     NA  1.789  3.771
+## parent_0 9.247e+01      NA     NA 89.720 95.220
+## alpha    9.658e+05      NA     NA     NA     NA
+## beta     1.010e+07      NA     NA     NA     NA
+## sigma    2.780e+00      NA     NA  1.794  3.766
 ## 
 ## FOCUS Chi2 error levels in percent:
 ##          err.min n.optim df
@@ -300,8 +308,8 @@
 ## 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

We get a warning that the default optimisation algorithm Port did not converge, which is an indication that the model is overparameterised, i.e. contains too many parameters that are ill-defined as a consequence.

And in fact, 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 excessive confidence intervals, that span more than 25 orders of magnitude (!) when backtransformed to the scale of alpha and beta. Also, the t-test for significant difference from zero does not indicate such a significant difference, with p-values greater than 0.1, and finally, the parameter correlation of log_alpha and log_beta is 1.000, clearly 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 and 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 was the first widely used standard package in this field. Also, the calculation of \(\chi^2\) error levels was compared with KinGUII, CAKE and DegKin manager in a project sponsored by the German Umweltbundesamt (Ranke 2014).

@@ -310,7 +318,7 @@

Laboratory Data L2

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,
@@ -321,9 +329,9 @@
 
SFO fit for L2
 

 
Again, the SFO model is fitted and the result is plotted. The residual plot can be obtained simply by adding the argument show_residuals to the plot command.

-
+
 m.L2.SFO <- mkinfit("SFO", FOCUS_2006_L2_mkin, quiet=TRUE)
-plot(m.L2.SFO, show_residuals = TRUE, show_errmin = TRUE,
+plot(m.L2.SFO, show_residuals = TRUE, show_errmin = TRUE,
      main = "FOCUS L2 - SFO")

 

 
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, in which we have included the residual plot.

@@ -334,24 +342,24 @@
 
FOMC fit for L2
 

 
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)
-plot(m.L2.FOMC, show_residuals = TRUE,
+plot(m.L2.FOMC, show_residuals = TRUE,
      main = "FOCUS L2 - FOMC")

 

-
-summary(m.L2.FOMC, data = FALSE)

+
+summary(m.L2.FOMC, data = FALSE)

 
## mkin version used for fitting:    1.1.0 
-## R version used for fitting:       4.2.0 
-## Date of fit:     Wed May 18 20:42:33 2022 
-## Date of summary: Wed May 18 20:42:33 2022 
+## R version used for fitting:       4.2.1 
+## Date of fit:     Thu Jun 30 10:44:01 2022 
+## Date of summary: Thu Jun 30 10:44:01 2022 
 ## 
 ## Equations:
 ## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 239 model solutions performed in 0.044 s
+## Fitted using 239 model solutions performed in 0.049 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -386,10 +394,10 @@
 ## 
 ## Parameter correlation:
 ##             parent_0  log_alpha   log_beta      sigma
-## parent_0   1.000e+00 -1.151e-01 -2.085e-01 -7.637e-09
-## log_alpha -1.151e-01  1.000e+00  9.741e-01 -1.617e-07
-## log_beta  -2.085e-01  9.741e-01  1.000e+00 -1.387e-07
-## sigma     -7.637e-09 -1.617e-07 -1.387e-07  1.000e+00
+## parent_0   1.000e+00 -1.151e-01 -2.085e-01 -7.828e-09
+## log_alpha -1.151e-01  1.000e+00  9.741e-01 -1.602e-07
+## log_beta  -2.085e-01  9.741e-01  1.000e+00 -1.372e-07
+## sigma     -7.828e-09 -1.602e-07 -1.372e-07  1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
@@ -415,17 +423,17 @@
 
DFOP fit for L2
 

 
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, show_residuals = TRUE, show_errmin = TRUE,
+plot(m.L2.DFOP, show_residuals = TRUE, show_errmin = TRUE,
      main = "FOCUS L2 - DFOP")

 

-
-summary(m.L2.DFOP, data = FALSE)

+
+summary(m.L2.DFOP, data = FALSE)

 
## mkin version used for fitting:    1.1.0 
-## R version used for fitting:       4.2.0 
-## Date of fit:     Wed May 18 20:42:34 2022 
-## Date of summary: Wed May 18 20:42:34 2022 
+## R version used for fitting:       4.2.1 
+## Date of fit:     Thu Jun 30 10:44:01 2022 
+## Date of summary: Thu Jun 30 10:44:01 2022 
 ## 
 ## Equations:
 ## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -434,7 +442,7 @@
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 581 model solutions performed in 0.121 s
+## Fitted using 581 model solutions performed in 0.132 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -465,18 +473,18 @@
 ## Optimised, transformed parameters with symmetric confidence intervals:
 ##          Estimate Std. Error      Lower     Upper
 ## parent_0   93.950  9.998e-01    91.5900   96.3100
-## log_k1      3.113  1.845e+03 -4360.0000 4367.0000
+## log_k1      3.112  1.842e+03 -4353.0000 4359.0000
 ## log_k2     -1.088  6.285e-02    -1.2370   -0.9394
 ## g_qlogis   -0.399  9.946e-02    -0.6342   -0.1638
 ## sigma       1.414  2.886e-01     0.7314    2.0960
 ## 
 ## Parameter correlation:
 ##            parent_0     log_k1     log_k2   g_qlogis      sigma
-## parent_0  1.000e+00  6.784e-07 -5.188e-10  2.665e-01 -5.800e-10
-## log_k1    6.784e-07  1.000e+00  1.114e-04 -2.191e-04 -1.029e-05
-## log_k2   -5.188e-10  1.114e-04  1.000e+00 -7.903e-01  5.080e-09
-## g_qlogis  2.665e-01 -2.191e-04 -7.903e-01  1.000e+00 -7.991e-09
-## sigma    -5.800e-10 -1.029e-05  5.080e-09 -7.991e-09  1.000e+00
+## parent_0  1.000e+00  6.783e-07 -3.390e-10  2.665e-01 -2.967e-10
+## log_k1    6.783e-07  1.000e+00  1.116e-04 -2.196e-04 -1.031e-05
+## log_k2   -3.390e-10  1.116e-04  1.000e+00 -7.903e-01  2.917e-09
+## g_qlogis  2.665e-01 -2.196e-04 -7.903e-01  1.000e+00 -4.408e-09
+## sigma    -2.967e-10 -1.031e-05  2.917e-09 -4.408e-09  1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
@@ -484,7 +492,7 @@
 ## for estimators of untransformed parameters.
 ##          Estimate   t value    Pr(>t)   Lower   Upper
 ## parent_0  93.9500 9.397e+01 2.036e-12 91.5900 96.3100
-## k1        22.4800 5.544e-04 4.998e-01  0.0000     Inf
+## k1        22.4800 5.553e-04 4.998e-01  0.0000     Inf
 ## k2         0.3369 1.591e+01 4.697e-07  0.2904  0.3909
 ## g          0.4016 1.680e+01 3.238e-07  0.3466  0.4591
 ## sigma      1.4140 4.899e+00 8.776e-04  0.7314  2.0960
@@ -496,7 +504,7 @@
 ## 
 ## Estimated disappearance times:
 ##          DT50  DT90 DT50back DT50_k1 DT50_k2
-## parent 0.5335 5.311    1.599 0.03083   2.058

+## parent 0.5335 5.311    1.599 0.03084   2.058

 
Here, the DFOP model is clearly the best-fit model for dataset L2 based on the chi^2 error level criterion.

 

 

@@ -504,7 +512,7 @@
 
Laboratory Data L3
 

 
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))
@@ -513,11 +521,11 @@
 
Fit multiple models
 

 
As of mkin version 0.9-39 (June 2015), we can fit several models to one or more datasets in one call to the function mmkin. The datasets have to be passed in a list, in this case a named list holding only the L3 dataset prepared above.

-
+
 # Only use one core here, not to offend the CRAN checks
 mm.L3 <- mmkin(c("SFO", "FOMC", "DFOP"), cores = 1,
                list("FOCUS L3" = FOCUS_2006_L3_mkin), quiet = TRUE)
-plot(mm.L3)

+plot(mm.L3)

 

 
The \(\chi^2\) error level of 21% as well as the plot suggest that the SFO model does not fit very well. The FOMC model performs better, with an error level at which the \(\chi^2\) test passes of 7%. Fitting the four parameter DFOP model further reduces the \(\chi^2\) error level considerably.

 

@@ -526,12 +534,12 @@
 
 
The objects returned by mmkin are arranged like a matrix, with models as a row index and datasets as a column index.

 
We can extract the summary and plot for e.g. the DFOP fit, using square brackets for indexing which will result in the use of the summary and plot functions working on mkinfit objects.

-
-summary(mm.L3[["DFOP", 1]])

+
+summary(mm.L3[["DFOP", 1]])

 
## mkin version used for fitting:    1.1.0 
-## R version used for fitting:       4.2.0 
-## Date of fit:     Wed May 18 20:42:34 2022 
-## Date of summary: Wed May 18 20:42:35 2022 
+## R version used for fitting:       4.2.1 
+## Date of fit:     Thu Jun 30 10:44:02 2022 
+## Date of summary: Thu Jun 30 10:44:02 2022 
 ## 
 ## Equations:
 ## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -540,7 +548,7 @@
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 376 model solutions performed in 0.073 s
+## Fitted using 376 model solutions performed in 0.08 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -578,11 +586,11 @@
 ## 
 ## Parameter correlation:
 ##            parent_0     log_k1     log_k2   g_qlogis      sigma
-## parent_0  1.000e+00  1.732e-01  2.282e-02  4.009e-01 -9.632e-08
-## log_k1    1.732e-01  1.000e+00  4.945e-01 -5.809e-01  7.145e-07
-## log_k2    2.282e-02  4.945e-01  1.000e+00 -6.812e-01  1.021e-06
-## g_qlogis  4.009e-01 -5.809e-01 -6.812e-01  1.000e+00 -7.925e-07
-## sigma    -9.632e-08  7.145e-07  1.021e-06 -7.925e-07  1.000e+00
+## parent_0  1.000e+00  1.732e-01  2.282e-02  4.009e-01 -9.664e-08
+## log_k1    1.732e-01  1.000e+00  4.945e-01 -5.809e-01  7.147e-07
+## log_k2    2.282e-02  4.945e-01  1.000e+00 -6.812e-01  1.022e-06
+## g_qlogis  4.009e-01 -5.809e-01 -6.812e-01  1.000e+00 -7.926e-07
+## sigma    -9.664e-08  7.147e-07  1.022e-06 -7.926e-07  1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
@@ -614,8 +622,8 @@
 ##    60   parent     22.0     23.26 -1.25919
 ##    91   parent     15.0     15.18 -0.18181
 ##   120   parent     12.0     10.19  1.81395

-
-plot(mm.L3[["DFOP", 1]], show_errmin = TRUE)

+
+plot(mm.L3[["DFOP", 1]], show_errmin = TRUE)

 

 
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.

@@ -625,33 +633,33 @@
 
Laboratory Data L4
 

 
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)

 
Fits of the SFO and FOMC models, plots and summaries are produced below:

-
+
 # Only use one core here, not to offend the CRAN checks
 mm.L4 <- mmkin(c("SFO", "FOMC"), cores = 1,
                list("FOCUS L4" = FOCUS_2006_L4_mkin),
                quiet = TRUE)
-plot(mm.L4)

+plot(mm.L4)

 

 
The \(\chi^2\) error level of 3.3% as well as the plot suggest that the SFO model fits very well. The error level at which the \(\chi^2\) test passes is slightly lower for the FOMC model. However, the difference appears negligible.

-
-summary(mm.L4[["SFO", 1]], data = FALSE)

+
+summary(mm.L4[["SFO", 1]], data = FALSE)

 
## mkin version used for fitting:    1.1.0 
-## R version used for fitting:       4.2.0 
-## Date of fit:     Wed May 18 20:42:35 2022 
-## Date of summary: Wed May 18 20:42:35 2022 
+## R version used for fitting:       4.2.1 
+## Date of fit:     Thu Jun 30 10:44:02 2022 
+## Date of summary: Thu Jun 30 10:44:02 2022 
 ## 
 ## Equations:
 ## d_parent/dt = - k_parent * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 142 model solutions performed in 0.027 s
+## Fitted using 142 model solutions performed in 0.03 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -683,9 +691,9 @@
 ## 
 ## Parameter correlation:
 ##               parent_0 log_k_parent     sigma
-## parent_0     1.000e+00    5.938e-01 3.440e-07
-## log_k_parent 5.938e-01    1.000e+00 5.885e-07
-## sigma        3.440e-07    5.885e-07 1.000e+00
+## parent_0     1.000e+00    5.938e-01 3.387e-07
+## log_k_parent 5.938e-01    1.000e+00 5.830e-07
+## sigma        3.387e-07    5.830e-07 1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
@@ -704,19 +712,19 @@
 ## Estimated disappearance times:
 ##        DT50 DT90
 ## parent  106  352

-
-summary(mm.L4[["FOMC", 1]], data = FALSE)

+
+summary(mm.L4[["FOMC", 1]], data = FALSE)

 
## mkin version used for fitting:    1.1.0 
-## R version used for fitting:       4.2.0 
-## Date of fit:     Wed May 18 20:42:35 2022 
-## Date of summary: Wed May 18 20:42:35 2022 
+## R version used for fitting:       4.2.1 
+## Date of fit:     Thu Jun 30 10:44:02 2022 
+## Date of summary: Thu Jun 30 10:44:03 2022 
 ## 
 ## Equations:
 ## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 224 model solutions performed in 0.041 s
+## Fitted using 224 model solutions performed in 0.045 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -751,10 +759,10 @@
 ## 
 ## Parameter correlation:
 ##             parent_0  log_alpha   log_beta      sigma
-## parent_0   1.000e+00 -4.696e-01 -5.543e-01 -2.563e-07
-## log_alpha -4.696e-01  1.000e+00  9.889e-01  4.066e-08
-## log_beta  -5.543e-01  9.889e-01  1.000e+00  6.818e-08
-## sigma     -2.563e-07  4.066e-08  6.818e-08  1.000e+00
+## parent_0   1.000e+00 -4.696e-01 -5.543e-01 -2.468e-07
+## log_alpha -4.696e-01  1.000e+00  9.889e-01  2.478e-08
+## log_beta  -5.543e-01  9.889e-01  1.000e+00  5.211e-08
+## sigma     -2.468e-07  2.478e-08  5.211e-08  1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
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