Further arguments that will be passed on to
@@ -409,7 +413,8 @@ internal rate transformation.
for measurement error in analytical chemistry. Technometrics 37(2), 176-184.
Ranke J and Meinecke S (2019) Error Models for the Kinetic Evaluation of Chemical
Degradation Data. Environments 6(12) 124
-doi:10.3390/environments6120124.
+doi: 10.3390/environments6120124
+.
See also
summary.mkinfit, plot.mkinfit, parms and lrtest.
@@ -426,17 +431,17 @@ Degradation Data. Environments 6(12) 124
# Use shorthand notation for parent only degradation
fit <- mkinfit("FOMC", FOCUS_2006_C, quiet = TRUE)
summary(fit)
- #> mkin version used for fitting: 0.9.50.3
+ #> mkin version used for fitting: 1.0.0
#> R version used for fitting: 4.0.3
-#> Date of fit: Thu Oct 15 12:40:10 2020
-#> Date of summary: Thu Oct 15 12:40:10 2020
+#> Date of fit: Wed Feb 3 17:28:58 2021
+#> Date of summary: Wed Feb 3 17:28:58 2021
#>
#> Equations:
#> d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
#>
#> Model predictions using solution type analytical
#>
-#> Fitted using 222 model solutions performed in 0.045 s
+#> Fitted using 222 model solutions performed in 0.046 s
#>
#> Error model: Constant variance
#>
@@ -511,13 +516,13 @@ Degradation Data. Environments 6(12) 124
FOCUS_D <- subset(FOCUS_2006_D, value != 0)
# Use mkinsub for convenience in model formulation. Pathway to sink included per default.
SFO_SFO <- mkinmod(
- parent = mkinsub("SFO", "m1"),
- m1 = mkinsub("SFO"))
- #> Successfully compiled differential equation model from auto-generated C code. #> Temporary DLL for differentials generated and loaded
# Fit the model quietly to the FOCUS example dataset D using defaults
fit <- mkinfit(SFO_SFO, FOCUS_D, quiet = TRUE)
- #> Warning: Shapiro-Wilk test for standardized residuals: p = 0.0165 #> Likelihood ratio test
#>
@@ -544,9 +548,9 @@ Degradation Data. Environments 6(12) 124
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 #> parent_0 k_parent k_m1 f_parent_to_m1 sigma_low
-#> 1.007343e+02 1.005562e-01 5.166712e-03 5.083933e-01 3.049891e-03
+#> 1.007343e+02 1.005562e-01 5.166712e-03 5.083933e-01 3.049884e-03
#> rsd_high
-#> 7.928117e-02 #> $ff
#> parent_m1 parent_sink
#> 0.5083933 0.4916067
@@ -554,7 +558,7 @@ Degradation Data. Environments 6(12) 124
#> $distimes
#> DT50 DT90
#> parent 6.89313 22.89848
-#> m1 134.15635 445.65776
+#> m1 134.15634 445.65772
#>
# We can show a quick (only one replication) benchmark for this case, as we
# have several alternative solution methods for the model. We skip
@@ -571,33 +575,34 @@ Degradation Data. Environments 6(12) 124
solution_type = "analytical"))
}
#> test relative elapsed
-#> 3 analytical 1.000 0.752
-#> 1 deSolve_compiled 2.294 1.725
-#> 2 eigen 2.727 2.051 # }
+#> 3 analytical 1.000 0.542
+#> 1 deSolve_compiled 1.812 0.982
+#> 2 eigen 2.234 1.211 #> Successfully compiled differential equation model from auto-generated C code. fit.FOMC_SFO <- mkinfit(FOMC_SFO, FOCUS_D, quiet = TRUE)
- #> Warning: Shapiro-Wilk test for standardized residuals: p = 0.0499 #> Temporary DLL for differentials generated and loaded fit.FOMC_SFO <- mkinfit(FOMC_SFO, FOCUS_D, quiet = TRUE)
+# Again, we get a warning and try a more sophisticated error model
fit.FOMC_SFO.tc <- mkinfit(FOMC_SFO, FOCUS_D, quiet = TRUE, error_model = "tc")
-# This model has a higher likelihood, but not significantly so
+ #> Warning: Optimisation did not converge:
+#> iteration limit reached without convergence (10) #> Likelihood ratio test
#>
#> Model 1: FOMC_SFO with error model tc and fixed parameter(s) m1_0
#> Model 2: SFO_SFO with error model tc and fixed parameter(s) m1_0
#> #Df LogLik Df Chisq Pr(>Chisq)
-#> 1 7 -64.829
-#> 2 6 -64.983 -1 0.3075 0.5792 # Also, the missing standard error for log_beta and the t-tests for alpha
+#> 1 7 -64.870
+#> 2 6 -64.983 -1 0.2259 0.6346 #> Warning: NaNs produced #> Warning: NaNs produced #> Warning: diag(.) had 0 or NA entries; non-finite result is doubtful #> mkin version used for fitting: 0.9.50.3
+ #> Warning: NaNs produced #> Warning: NaNs produced #> Warning: NaNs produced #> Warning: diag(.) had 0 or NA entries; non-finite result is doubtful #> mkin version used for fitting: 1.0.0
#> R version used for fitting: 4.0.3
-#> Date of fit: Thu Oct 15 12:40:24 2020
-#> Date of summary: Thu Oct 15 12:40:24 2020
+#> Date of fit: Wed Feb 3 17:29:09 2021
+#> Date of summary: Wed Feb 3 17:29:09 2021
#>
#> Equations:
#> d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
@@ -606,7 +611,7 @@ Degradation Data. Environments 6(12) 124
#>
#> Model predictions using solution type deSolve
#>
-#> Fitted using 3611 model solutions performed in 2.669 s
+#> Fitted using 4273 model solutions performed in 3.195 s
#>
#> Error model: Two-component variance function
#>
@@ -624,80 +629,85 @@ Degradation Data. Environments 6(12) 124
#> rsd_high 0.10 error
#>
#> Starting values for the transformed parameters actually optimised:
-#> value lower upper
-#> parent_0 100.750000 -Inf Inf
-#> log_k_m1 -2.302585 -Inf Inf
-#> f_parent_ilr_1 0.000000 -Inf Inf
-#> log_alpha 0.000000 -Inf Inf
-#> log_beta 2.302585 -Inf Inf
-#> sigma_low 0.100000 0 Inf
-#> rsd_high 0.100000 0 Inf
+#> value lower upper
+#> parent_0 100.750000 -Inf Inf
+#> log_k_m1 -2.302585 -Inf Inf
+#> f_parent_qlogis 0.000000 -Inf Inf
+#> log_alpha 0.000000 -Inf Inf
+#> log_beta 2.302585 -Inf Inf
+#> sigma_low 0.100000 0 Inf
+#> rsd_high 0.100000 0 Inf
#>
#> Fixed parameter values:
#> value type
#> m1_0 0 state
#>
+#>
+#> Warning(s):
+#> Optimisation did not converge:
+#> iteration limit reached without convergence (10)
+#>
#> Results:
#>
-#> AIC BIC logLik
-#> 143.658 155.1211 -64.82902
+#> AIC BIC logLik
+#> 143.7396 155.2027 -64.86982
#>
#> Optimised, transformed parameters with symmetric confidence intervals:
-#> Estimate Std. Error Lower Upper
-#> parent_0 101.600000 2.6390000 96.240000 107.000000
-#> log_k_m1 -5.284000 0.0928900 -5.473000 -5.095000
-#> f_parent_ilr_1 0.001008 0.0541900 -0.109500 0.111500
-#> log_alpha 5.522000 0.0077300 5.506000 5.538000
-#> log_beta 7.806000 NaN NaN NaN
-#> sigma_low 0.002488 0.0002431 0.001992 0.002984
-#> rsd_high 0.079210 0.0093280 0.060180 0.098230
+#> Estimate Std. Error Lower Upper
+#> parent_0 1.016e+02 1.90600 97.7400 105.5000
+#> log_k_m1 -5.285e+00 0.09286 -5.4740 -5.0950
+#> f_parent_qlogis 6.482e-04 0.06164 -0.1251 0.1264
+#> log_alpha 5.467e+00 NaN NaN NaN
+#> log_beta 7.750e+00 NaN NaN NaN
+#> sigma_low 0.000e+00 NaN NaN NaN
+#> rsd_high 7.989e-02 NaN NaN NaN
#>
#> Parameter correlation:
-#> parent_0 log_k_m1 f_parent_ilr_1 log_alpha log_beta sigma_low
-#> parent_0 1.000000 -0.094697 -0.76654 0.70525 NaN 0.016099
-#> log_k_m1 -0.094697 1.000000 0.51404 -0.14347 NaN 0.001576
-#> f_parent_ilr_1 -0.766543 0.514038 1.00000 -0.61368 NaN 0.015465
-#> log_alpha 0.705247 -0.143468 -0.61368 1.00000 NaN 5.871780
-#> log_beta NaN NaN NaN NaN 1 NaN
-#> sigma_low 0.016099 0.001576 0.01546 5.87178 NaN 1.000000
-#> rsd_high 0.006566 -0.011662 -0.05353 0.04845 NaN -0.652554
-#> rsd_high
-#> parent_0 0.006566
-#> log_k_m1 -0.011662
-#> f_parent_ilr_1 -0.053525
-#> log_alpha 0.048451
-#> log_beta NaN
-#> sigma_low -0.652554
-#> rsd_high 1.000000
+#> parent_0 log_k_m1 f_parent_qlogis log_alpha log_beta
+#> parent_0 1.0000000 -0.0002167 -0.6060 NaN NaN
+#> log_k_m1 -0.0002167 1.0000000 0.5474 NaN NaN
+#> f_parent_qlogis -0.6060320 0.5474423 1.0000 NaN NaN
+#> log_alpha NaN NaN NaN 1 NaN
+#> log_beta NaN NaN NaN NaN 1
+#> sigma_low NaN NaN NaN NaN NaN
+#> rsd_high NaN NaN NaN NaN NaN
+#> sigma_low rsd_high
+#> parent_0 NaN NaN
+#> log_k_m1 NaN NaN
+#> f_parent_qlogis NaN NaN
+#> log_alpha NaN NaN
+#> log_beta NaN NaN
+#> sigma_low 1 NaN
+#> rsd_high NaN 1
#>
#> 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 1.016e+02 32.7800 6.312e-26 9.624e+01 1.070e+02
-#> k_m1 5.072e-03 10.1200 1.216e-11 4.197e-03 6.130e-03
-#> f_parent_to_m1 5.004e-01 20.8300 4.318e-20 4.614e-01 5.394e-01
-#> alpha 2.502e+02 0.5624 2.889e-01 2.463e+02 2.542e+02
-#> beta 2.455e+03 0.5549 2.915e-01 NA NA
-#> sigma_low 2.488e-03 0.4843 3.158e-01 1.992e-03 2.984e-03
-#> rsd_high 7.921e-02 8.4300 8.001e-10 6.018e-02 9.823e-02
+#> parent_0 1.016e+02 32.5400 7.812e-26 97.740000 1.055e+02
+#> k_m1 5.069e-03 10.0400 1.448e-11 0.004194 6.126e-03
+#> f_parent_to_m1 5.002e-01 20.7300 5.001e-20 0.468800 5.315e-01
+#> alpha 2.367e+02 0.6205 2.697e-01 NA NA
+#> beta 2.322e+03 0.6114 2.727e-01 NA NA
+#> sigma_low 0.000e+00 NaN NaN NaN NaN
+#> rsd_high 7.989e-02 8.6630 4.393e-10 NaN NaN
#>
#> FOCUS Chi2 error levels in percent:
#> err.min n.optim df
-#> All data 6.781 5 14
-#> parent 7.141 3 6
-#> m1 4.640 2 8
+#> All data 6.782 5 14
+#> parent 7.142 3 6
+#> m1 4.639 2 8
#>
#> Resulting formation fractions:
#> ff
-#> parent_m1 0.5004
-#> parent_sink 0.4996
+#> parent_m1 0.5002
+#> parent_sink 0.4998
#>
#> Estimated disappearance times:
-#> DT50 DT90 DT50back
-#> parent 6.812 22.7 6.834
-#> m1 136.661 454.0 NA
+#> DT50 DT90 DT50back
+#> parent 6.81 22.7 6.833
+#> m1 136.74 454.2 NA
# We can easily use starting parameters from the parent only fit (only for illustration)
fit.FOMC = mkinfit("FOMC", FOCUS_2006_D, quiet = TRUE, error_model = "tc")
fit.FOMC_SFO <- mkinfit(FOMC_SFO, FOCUS_D, quiet = TRUE,
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