Functions to transform and backtransform kinetic parameters for fitting

+ + +

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 parameters 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.

+ +

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.
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.
transparms	Transformed parameters of kinetic models as used in the +fitting procedure.

+ +

Value

+ +

A vector of transformed or backtransformed parameters

Details

+ +

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.

+ +

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)
#> Warning: Observations with value of zero were removed from the data
fit.s <- summary(fit)
+# Transformed and backtransformed parameters
+print(fit.s$par, 3)
#>                Estimate Std. Error   Lower   Upper
+#> parent_0         99.598     1.5702 96.4038 102.793
+#> log_k_parent     -2.316     0.0409 -2.3988  -2.233
+#> log_k_m1         -5.248     0.1332 -5.5184  -4.977
+#> f_parent_ilr_1    0.041     0.0631 -0.0875   0.169
+#> sigma             3.126     0.3585  2.3961   3.855
print(fit.s$bpar, 3)
#>                Estimate se_notrans t value   Pr(>t)    Lower    Upper
+#> parent_0       99.59848    1.57022   63.43 2.30e-36 96.40384 102.7931
+#> k_parent        0.09870    0.00403   24.47 4.96e-23  0.09082   0.1073
+#> k_m1            0.00526    0.00070    7.51 6.16e-09  0.00401   0.0069
+#> f_parent_to_m1  0.51448    0.02230   23.07 3.10e-22  0.46912   0.5596
+#> sigma           3.12550    0.35852    8.72 2.24e-10  2.39609   3.8549

+# \dontrun{
+# Compare to the version without transforming rate parameters
+fit.2 <- mkinfit(SFO_SFO, FOCUS_2006_D, transform_rates = FALSE, quiet = TRUE)
#> Warning: Observations with value of zero were removed from the data
#> Error in if (cost < cost.current) {    assign("cost.current", cost, inherits = TRUE)    if (!quiet)         cat(ifelse(OLS, "Sum of squared residuals", "Negative log-likelihood"),             " at call ", calls, ": ", cost.current, "\n", sep = "")}: missing value where TRUE/FALSE needed
#> Timing stopped at: 0.003 0 0.003
fit.2.s <- summary(fit.2)
#> Error in summary(fit.2): object 'fit.2' not found
print(fit.2.s$par, 3)
#> Error in print(fit.2.s$par, 3): object 'fit.2.s' not found
print(fit.2.s$bpar, 3)
#> Error in print(fit.2.s$bpar, 3): object 'fit.2.s' not found
# }
+
+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       log_k_m1 f_parent_ilr_1 
+#>     100.750000      -2.302585      -2.301586       0.000000 
backtransform_odeparms(transformed, SFO_SFO)
#>       parent_0       k_parent           k_m1 f_parent_to_m1 
+#>       100.7500         0.1000         0.1001         0.5000 

+# \dontrun{
+# 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")
#> Successfully compiled differential equation model from auto-generated C code.

+fit.ff <- mkinfit(SFO_SFO.ff, FOCUS_2006_D, quiet = TRUE)
#> Warning: Observations with value of zero were removed from the data
fit.ff.s <- summary(fit.ff)
+print(fit.ff.s$par, 3)
#>                Estimate Std. Error   Lower   Upper
+#> parent_0         99.598     1.5702 96.4038 102.793
+#> log_k_parent     -2.316     0.0409 -2.3988  -2.233
+#> log_k_m1         -5.248     0.1332 -5.5184  -4.977
+#> f_parent_ilr_1    0.041     0.0631 -0.0875   0.169
+#> sigma             3.126     0.3585  2.3961   3.855
print(fit.ff.s$bpar, 3)
#>                Estimate se_notrans t value   Pr(>t)    Lower    Upper
+#> parent_0       99.59848    1.57022   63.43 2.30e-36 96.40384 102.7931
+#> k_parent        0.09870    0.00403   24.47 4.96e-23  0.09082   0.1073
+#> k_m1            0.00526    0.00070    7.51 6.16e-09  0.00401   0.0069
+#> f_parent_to_m1  0.51448    0.02230   23.07 3.10e-22  0.46912   0.5596
+#> sigma           3.12550    0.35852    8.72 2.24e-10  2.39609   3.8549
initials <- c("f_parent_to_m1" = 0.5)
+transformed <- transform_odeparms(initials, SFO_SFO.ff)
+backtransform_odeparms(transformed, SFO_SFO.ff)
#> f_parent_to_m1 
+#>            0.5 

+# And without sink
+SFO_SFO.ff.2 <- mkinmod(
+  parent = list(type = "SFO", to = "m1", sink = FALSE),
+  m1 = list(type = "SFO"),
+  use_of_ff = "max")
#> Successfully compiled differential equation model from auto-generated C code.

+
+fit.ff.2 <- mkinfit(SFO_SFO.ff.2, FOCUS_2006_D, quiet = TRUE)
#> Warning: Observations with value of zero were removed from the data
fit.ff.2.s <- summary(fit.ff.2)
+print(fit.ff.2.s$par, 3)
#>              Estimate Std. Error Lower Upper
+#> parent_0        84.79      3.012 78.67 90.91
+#> log_k_parent    -2.76      0.082 -2.92 -2.59
+#> log_k_m1        -4.21      0.123 -4.46 -3.96
+#> sigma            8.22      0.943  6.31 10.14
print(fit.ff.2.s$bpar, 3)
#>          Estimate se_notrans t value   Pr(>t)   Lower  Upper
+#> parent_0  84.7916    3.01203   28.15 1.92e-25 78.6704 90.913
+#> k_parent   0.0635    0.00521   12.19 2.91e-14  0.0538  0.075
+#> k_m1       0.0148    0.00182    8.13 8.81e-10  0.0115  0.019
+#> sigma      8.2229    0.94323    8.72 1.73e-10  6.3060 10.140
# }
+
+

+ +