transform_odeparms. mkin

+ +

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)

+ +

Arguments

parms: + Parameters of kinetic models as used in the differential equations. +
transparms: + Transformed parameters of kinetic models as used in the fitting procedure. +
mkinmod: + The kinetic model of class 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. +
transform_rates: + Boolean specifying if kinetic rate constants should be transformed in the + model specification used in the fitting for better compliance with the + assumption of normal distribution of the estimator. If TRUE, also + alpha and beta parameters of the FOMC model are log-transformed, as well + as k1 and k2 rate constants for the DFOP and HS models and the break point tb + of the HS model. +
transform_fractions: + Boolean specifying if formation fractions constants should be transformed in the + model specification used in the fitting for better compliance with the + assumption of normal distribution of the estimator. The default (TRUE) is + to do transformations. The g parameter of the DFOP and HS models are also + transformed, as they can also be seen as compositional data. The + transformation used for these transformations is the ilr + transformation. +

+ +

Value

+ +

A vector of transformed or backtransformed parameters with the same names + as the original parameters.

+ +

Examples

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 09:18:08 2016 
+#> Date of summary: Thu Oct  6 09:18:08 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 0.636 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)
+## ---------------------------------------------

Author

+ + Johannes Ranke + +