The transformations are intended to map parameters that should only take
on restricted values to the full scale of real numbers. For kinetic rate
constants and other paramters that can only take on positive values, a
simple log transformation is used. For compositional parameters, such as
the formations fractions that should always sum up to 1 and can not be
negative, the ilr transformation is used.
The transformation of sets of formation fractions is fragile, as it supposes
the same ordering of the components in forward and backward transformation.
This is no problem for the internal use in mkinfit.
transform_odeparms(parms, mkinmod, transform_rates = TRUE, transform_fractions = TRUE) backtransform_odeparms(transparms, mkinmod, transform_rates = TRUE, transform_fractions = TRUE)
mkinmod, containing the names of
the model variables that are needed for grouping the formation fractions
before ilr transformation, the parameter names and
the information if the pathway to sink is included in the model.
ilr
transformation.
A vector of transformed or backtransformed parameters with the same names as the original parameters.
SFO_SFO <- mkinmod( parent = list(type = "SFO", to = "m1", sink = TRUE), m1 = list(type = "SFO"))Successfully compiled differential equation model from auto-generated C code.# Fit the model to the FOCUS example dataset D using defaults fit <- mkinfit(SFO_SFO, FOCUS_2006_D, quiet = TRUE) summary(fit, data=FALSE) # See transformed and backtransformed parameters#> mkin version: 0.9.44.9000 #> R version: 3.3.1 #> Date of fit: Thu Oct 6 09:39:23 2016 #> Date of summary: Thu Oct 6 09:39:23 2016 #> #> Equations: #> d_parent = - k_parent_sink * parent - k_parent_m1 * parent #> d_m1 = + k_parent_m1 * parent - k_m1_sink * m1 #> #> Model predictions using solution type deSolve #> #> Fitted with method Port using 153 model solutions performed in 0.63 s #> #> Weighting: none #> #> Starting values for parameters to be optimised: #> value type #> parent_0 100.7500 state #> k_parent_sink 0.1000 deparm #> k_parent_m1 0.1001 deparm #> k_m1_sink 0.1002 deparm #> #> Starting values for the transformed parameters actually optimised: #> value lower upper #> parent_0 100.750000 -Inf Inf #> log_k_parent_sink -2.302585 -Inf Inf #> log_k_parent_m1 -2.301586 -Inf Inf #> log_k_m1_sink -2.300587 -Inf Inf #> #> Fixed parameter values: #> value type #> m1_0 0 state #> #> 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 #> parent_0 1.00000 0.6075 -0.06625 -0.1701 #> log_k_parent_sink 0.60752 1.0000 -0.08740 -0.6253 #> log_k_parent_m1 -0.06625 -0.0874 1.00000 0.4716 #> log_k_m1_sink -0.17006 -0.6253 0.47163 1.0000 #> #> Residual standard error: 3.211 on 36 degrees of freedom #> #> 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 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 #> All data 6.398 4 15 #> parent 6.827 3 6 #> m1 4.490 1 9 #> #> Resulting formation fractions: #> ff #> parent_sink 0.4855 #> parent_m1 0.5145 #> m1_sink 1.0000 #> #> Estimated disappearance times: #> DT50 DT90 #> parent 7.023 23.33 #> m1 131.761 437.70 #>## Not run: ------------------------------------ # fit.2 <- mkinfit(SFO_SFO, FOCUS_2006_D, transform_rates = FALSE) # summary(fit.2, data=FALSE) ## --------------------------------------------- initials <- fit$start$value names(initials) <- rownames(fit$start) transformed <- fit$start_transformed$value names(transformed) <- rownames(fit$start_transformed) transform_odeparms(initials, SFO_SFO)#> parent_0 log_k_parent_sink log_k_parent_m1 log_k_m1_sink #> 100.750000 -2.302585 -2.301586 -2.300587 #>backtransform_odeparms(transformed, SFO_SFO)#> parent_0 k_parent_sink k_parent_m1 k_m1_sink #> 100.7500 0.1000 0.1001 0.1002 #>## Not run: ------------------------------------ # # The case of formation fractions # SFO_SFO.ff <- mkinmod( # parent = list(type = "SFO", to = "m1", sink = TRUE), # m1 = list(type = "SFO"), # use_of_ff = "max") # # fit.ff <- mkinfit(SFO_SFO.ff, FOCUS_2006_D) # summary(fit.ff, data = FALSE) # initials <- c("f_parent_to_m1" = 0.5) # transformed <- transform_odeparms(initials, SFO_SFO.ff) # backtransform_odeparms(transformed, SFO_SFO.ff) # # # And without sink # SFO_SFO.ff.2 <- mkinmod( # parent = list(type = "SFO", to = "m1", sink = FALSE), # m1 = list(type = "SFO"), # use_of_ff = "max") # # # fit.ff.2 <- mkinfit(SFO_SFO.ff.2, FOCUS_2006_D) # summary(fit.ff.2, data = FALSE) ## ---------------------------------------------