transform_odeparms. mkin 0.9.44.9000

Usage

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. -

- -

Description

- -

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.

- -

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:     Sat Sep 10 05:19:46 2016 
-Date of summary: Sat Sep 10 05:19:46 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 0.681 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) 
-# ## End(Not run)
-
-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)
-# ## End(Not run)
-

- - - -

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