From 03e1598a3c79911a497758fe382461f288bf05e6 Mon Sep 17 00:00:00 2001 From: Johannes Ranke Date: Fri, 16 Sep 2022 10:12:54 +0200 Subject: Diagnostic plots for multistart method --- DESCRIPTION | 5 +- NAMESPACE | 8 +- NEWS.md | 2 +- R/aw.R | 36 ++++++-- R/multistart.R | 59 ++++++++++++- R/saem.R | 8 +- log/test.log | 28 +++--- man/aw.Rd | 6 ++ man/multistart.Rd | 21 ++++- man/saem.Rd | 2 +- tests/testthat/print_sfo_saem_1.txt | 6 +- tests/testthat/summary_hfit_sfo_tc.txt | 2 +- vignettes/FOCUS_L.html | 151 +++++++++++++++++---------------- 13 files changed, 223 insertions(+), 111 deletions(-) diff --git a/DESCRIPTION b/DESCRIPTION index 6734a43c..c653be1c 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -2,7 +2,7 @@ Package: mkin Type: Package Title: Kinetic Evaluation of Chemical Degradation Data Version: 1.1.2 -Date: 2022-09-14 +Date: 2022-09-16 Authors@R: c( person("Johannes", "Ranke", role = c("aut", "cre", "cph"), email = "johannes.ranke@jrwb.de", @@ -24,7 +24,8 @@ Description: Calculation routines based on the FOCUS Kinetics Report (2006, purpose. Depends: R (>= 2.15.1), Imports: stats, graphics, methods, parallel, deSolve, R6, inline (>= 0.3.19), - numDeriv, lmtest, pkgbuild, nlme (>= 3.1-151), saemix (>= 3.1), rlang, vctrs + numDeriv, lmtest, pkgbuild, nlme (>= 3.1-151), saemix (>= 3.1), rlang, vctrs, + KernSmooth Suggests: knitr, rbenchmark, tikzDevice, testthat, rmarkdown, covr, vdiffr, benchmarkme, tibble, stats4 License: GPL diff --git a/NAMESPACE b/NAMESPACE index 1be6d95d..bd12d0db 100644 --- a/NAMESPACE +++ b/NAMESPACE @@ -6,8 +6,10 @@ S3method(AIC,mhmkin) S3method(AIC,mmkin) S3method(BIC,mhmkin) S3method(BIC,mmkin) +S3method(aw,mixed.mmkin) S3method(aw,mkinfit) S3method(aw,mmkin) +S3method(aw,multistart) S3method(confint,mkinfit) S3method(convergence,mhmkin) S3method(convergence,mmkin) @@ -32,6 +34,7 @@ S3method(nlme,mmkin) S3method(nobs,mkinfit) S3method(parms,mkinfit) S3method(parms,mmkin) +S3method(parms,multistart) S3method(parms,saem.mmkin) S3method(plot,mixed.mmkin) S3method(plot,mkinfit) @@ -59,7 +62,6 @@ S3method(residuals,mkinfit) S3method(saem,mmkin) S3method(summary,mkinfit) S3method(summary,mmkin) -S3method(summary,multistart.saem.mmkin) S3method(summary,nlme.mmkin) S3method(summary,saem.mmkin) S3method(update,mkinfit) @@ -85,6 +87,7 @@ export(illparms) export(ilr) export(intervals) export(invilr) +export(llhist) export(loftest) export(logistic.solution) export(lrtest) @@ -115,6 +118,7 @@ export(nafta) export(nlme) export(nlme_data) export(nlme_function) +export(parhist) export(parms) export(plot_err) export(plot_res) @@ -127,6 +131,7 @@ export(transform_odeparms) import(deSolve) import(graphics) import(nlme) +importFrom(KernSmooth,bkde) importFrom(R6,R6Class) importFrom(grDevices,dev.cur) importFrom(lmtest,lrtest) @@ -147,6 +152,7 @@ importFrom(stats,dist) importFrom(stats,dnorm) importFrom(stats,lm) importFrom(stats,logLik) +importFrom(stats,median) importFrom(stats,na.fail) importFrom(stats,nlminb) importFrom(stats,nobs) diff --git a/NEWS.md b/NEWS.md index 0738d54a..d288c32f 100644 --- a/NEWS.md +++ b/NEWS.md @@ -1,6 +1,6 @@ # mkin 1.1.2 -- 'R/multistart.R': New method for testing multiple start parameters for hierarchical model fits. +- 'R/multistart.R': New method for testing multiple start parameters for hierarchical model fits, with diagnostic plotting functions 'llhist' and 'parhist'. - 'R/mhmkin.R': New method for performing multiple hierarchical mkin fits in one function call, optionally in parallel. diff --git a/R/aw.R b/R/aw.R index f46b20ec..b3992f94 100644 --- a/R/aw.R +++ b/R/aw.R @@ -30,6 +30,14 @@ #' @export aw <- function(object, ...) UseMethod("aw") +.aw <- function(all_objects) { + AIC_all <- sapply(all_objects, AIC) + delta_i <- AIC_all - min(AIC_all) + denom <- sum(exp(-delta_i/2)) + w_i <- exp(-delta_i/2) / denom + return(w_i) +} + #' @export #' @rdname aw aw.mkinfit <- function(object, ...) { @@ -43,11 +51,7 @@ aw.mkinfit <- function(object, ...) { } } all_objects <- list(object, ...) - AIC_all <- sapply(all_objects, AIC) - delta_i <- AIC_all - min(AIC_all) - denom <- sum(exp(-delta_i/2)) - w_i <- exp(-delta_i/2) / denom - return(w_i) + .aw(all_objects) } #' @export @@ -56,3 +60,25 @@ aw.mmkin <- function(object, ...) { if (ncol(object) > 1) stop("Please supply an mmkin column object") do.call(aw, object) } + +#' @export +#' @rdname aw +aw.mixed.mmkin <- function(object, ...) { + oo <- list(...) + data_object <- object$data[c("ds", "name", "time", "value")] + for (i in seq_along(oo)) { + if (!inherits(oo[[i]], "mixed.mmkin")) stop("Please supply objects inheriting from mixed.mmkin") + data_other_object <- oo[[i]]$data[c("ds", "name", "time", "value")] + if (!identical(data_object, data_other_object)) { + stop("It seems that the mixed.mmkin objects have not all been fitted to the same data") + } + } + all_objects <- list(object, ...) + .aw(all_objects) +} + +#' @export +#' @rdname aw +aw.multistart <- function(object, ...) { + do.call(aw, object) +} diff --git a/R/multistart.R b/R/multistart.R index a3afa08b..94292e82 100644 --- a/R/multistart.R +++ b/R/multistart.R @@ -14,7 +14,12 @@ #' @param n How many different combinations of starting parameters should be #' used? #' @param cores How many fits should be run in parallel? -#' @param \dots Passed to the update function. +#' @param \dots Passed to the update function, or to the basic plotting +#' function in the case of the graphical function. +#' @param x The multistart object to print +#' @param breaks Passed to [hist] +#' @param main title of the plot +#' @param lpos Positioning of the legend. #' @return A list of [saem.mmkin] objects, with class attributes #' 'multistart.saem.mmkin' and 'multistart'. #' @@ -39,6 +44,7 @@ multistart.saem.mmkin <- function(object, n = 50, cores = 1, ...) { res <- parallel::mclapply(1:n, function(x) { update(object, degparms_start = start_parms[x, ], ...) }, mc.cores = cores) + attr(res, "orig") <- object attr(res, "start_parms") <- start_parms class(res) <- c("multistart.saem.mmkin", "multistart") return(res) @@ -53,8 +59,53 @@ print.multistart <- function(x, ...) { #' @rdname multistart #' @export -summary.multistart.saem.mmkin <- function(object) { +parms.multistart <- function(object, ...) { + t(sapply(object, parms)) +} + +#' @rdname multistart +#' @importFrom stats median +#' @export +parhist <- function(object, lpos = "topleft", ...) { + orig <- attr(object, "orig") + orig_parms <- parms(orig) + start_parms <- orig$mean_dp_start + all_parms <- parms(object) + median_parms <- apply(all_parms, 2, median) + all_scaled_parms <- t(apply(all_parms, 1, function(x) x / median_parms)) + orig_scaled_parms <- orig_parms / median_parms + start_scaled_parms <- rep(NA_real_, length(orig_parms)) + names(start_scaled_parms) <- names(orig_parms) + start_scaled_parms[names(start_parms)] <- + start_parms / median_parms[names(start_parms)] + + boxplot(all_scaled_parms, log = "y", ...) + points(orig_scaled_parms, col = 2, cex = 2) + points(start_scaled_parms, col = 3, cex = 3) + legend(lpos, inset = c(0.05, 0.05), bty = "n", + pch = 1, col = 3:1, lty = c(NA, NA, 1), + legend = c( + "Starting parameters", + "Converged parameters", + "Multistart runs")) +} + +#' @rdname multistart +#' @importFrom KernSmooth bkde +#' @export +llhist <- function(object, breaks = "Sturges", main = "", lpos = "topleft", ...) { + ll <- sapply(object, logLik) + kde <- KernSmooth::bkde(ll) + h <- hist(ll, freq = TRUE, + xlim = range(kde$x), + xlab = "", main = main, + ylab = "Frequency of log likelihoods", breaks = breaks, ...) - parm_matrix <- sapply(object, parms) - parm_matrix + freq_factor <- h$counts[1] / h$density[1] + lines(kde$x, freq_factor * kde$y) + abline(v = logLik(attr(object, "orig")), col = 2) + legend(lpos, inset = c(0.05, 0.05), bty = "n", + lty = 1, col = c(2, 1), + legend = c("original log likelihood", + "kernel density estimate")) } diff --git a/R/saem.R b/R/saem.R index 875456c3..0d0d9b8a 100644 --- a/R/saem.R +++ b/R/saem.R @@ -568,7 +568,7 @@ saemix_data <- function(object, verbose = FALSE, ...) { ds_list <- lapply(object, function(x) x$data[c("time", "variable", "observed")]) names(ds_list) <- ds_names - ds_saemix_all <- purrr::map_dfr(ds_list, function(x) x, .id = "ds") + ds_saemix_all <- vctrs::vec_rbind(!!!ds_list, .names_to = "ds") ds_saemix <- data.frame(ds = ds_saemix_all$ds, name = as.character(ds_saemix_all$variable), time = ds_saemix_all$time, @@ -617,9 +617,9 @@ update.saem.mmkin <- function(object, ..., evaluate = TRUE) { #' @rdname saem #' @param ci Should a matrix with estimates and confidence interval boundaries #' be returned? If FALSE (default), a vector of estimates is returned. -parms.saem.mmkin <- function(x, ci = FALSE, ...) { - conf.int <- x$so@results@conf.int[c("estimate", "lower", "upper")] - rownames(conf.int) <- x$so@results@conf.int[["name"]] +parms.saem.mmkin <- function(object, ci = FALSE, ...) { + conf.int <- object$so@results@conf.int[c("estimate", "lower", "upper")] + rownames(conf.int) <- object$so@results@conf.int[["name"]] conf.int.var <- grepl("^Var\\.", rownames(conf.int)) conf.int <- conf.int[!conf.int.var, ] estimate <- conf.int[, "estimate"] diff --git a/log/test.log b/log/test.log index 8be4a512..cb123776 100644 --- a/log/test.log +++ b/log/test.log @@ -1,23 +1,23 @@ ℹ Testing mkin ✔ | F W S OK | Context ✔ | 5 | AIC calculation -✔ | 5 | Analytical solutions for coupled models [3.4s] +✔ | 5 | Analytical solutions for coupled models [3.3s] ✔ | 5 | Calculation of Akaike weights ✔ | 3 | Export dataset for reading into CAKE -✔ | 12 | Confidence intervals and p-values [1.0s] -✔ | 1 12 | Dimethenamid data from 2018 [32.4s] +✔ | 12 | Confidence intervals and p-values [1.1s] +✔ | 1 12 | Dimethenamid data from 2018 [32.5s] ──────────────────────────────────────────────────────────────────────────────── Skip (test_dmta.R:98:3): Different backends get consistent results for SFO-SFO3+, dimethenamid data Reason: Fitting this ODE model with saemix takes about 15 minutes on my system ──────────────────────────────────────────────────────────────────────────────── -✔ | 14 | Error model fitting [5.0s] +✔ | 14 | Error model fitting [5.1s] ✔ | 5 | Time step normalisation ✔ | 4 | Calculation of FOCUS chi2 error levels [0.6s] ✔ | 14 | Results for FOCUS D established in expertise for UBA (Ranke 2014) [0.8s] ✔ | 4 | Test fitting the decline of metabolites from their maximum [0.4s] ✔ | 1 | Fitting the logistic model [0.2s] -✔ | 5 | Batch fitting and diagnosing hierarchical kinetic models [14.5s] -✔ | 1 12 | Nonlinear mixed-effects models [0.2s] +✔ | 7 | Batch fitting and diagnosing hierarchical kinetic models [14.6s] +✔ | 1 12 | Nonlinear mixed-effects models [0.3s] ──────────────────────────────────────────────────────────────────────────────── Skip (test_mixed.R:68:3): saemix results are reproducible for biphasic fits Reason: Fitting with saemix takes around 10 minutes when using deSolve @@ -26,25 +26,25 @@ Reason: Fitting with saemix takes around 10 minutes when using deSolve ✔ | 10 | Special cases of mkinfit calls [0.4s] ✔ | 3 | mkinfit features [0.7s] ✔ | 8 | mkinmod model generation and printing [0.2s] -✔ | 3 | Model predictions with mkinpredict [0.4s] +✔ | 3 | Model predictions with mkinpredict [0.3s] ✔ | 16 | Evaluations according to 2015 NAFTA guidance [1.8s] -✔ | 9 | Nonlinear mixed-effects models with nlme [8.7s] -✔ | 16 | Plotting [10.1s] +✔ | 9 | Nonlinear mixed-effects models with nlme [8.5s] +✔ | 16 | Plotting [10.0s] ✔ | 4 | Residuals extracted from mkinfit models -✔ | 28 | saemix parent models [181.2s] +✔ | 28 | saemix parent models [183.3s] ✔ | 2 | Complex test case from Schaefer et al. (2007) Piacenza paper [1.4s] ✔ | 7 | Fitting the SFORB model [3.7s] ✔ | 1 | Summaries of old mkinfit objects ✔ | 5 | Summary [0.2s] ✔ | 4 | Results for synthetic data established in expertise for UBA (Ranke 2014) [2.1s] -✔ | 9 | Hypothesis tests [7.8s] -✔ | 4 | Calculation of maximum time weighted average concentrations (TWAs) [2.1s] +✔ | 9 | Hypothesis tests [8.1s] +✔ | 4 | Calculation of maximum time weighted average concentrations (TWAs) [2.2s] ══ Results ═════════════════════════════════════════════════════════════════════ -Duration: 279.6 s +Duration: 282.2 s ── Skipped tests ────────────────────────────────────────────────────────────── • Fitting this ODE model with saemix takes about 15 minutes on my system (1) • Fitting with saemix takes around 10 minutes when using deSolve (1) -[ FAIL 0 | WARN 0 | SKIP 2 | PASS 233 ] +[ FAIL 0 | WARN 0 | SKIP 2 | PASS 235 ] diff --git a/man/aw.Rd b/man/aw.Rd index 40676716..9aad2c37 100644 --- a/man/aw.Rd +++ b/man/aw.Rd @@ -4,6 +4,8 @@ \alias{aw} \alias{aw.mkinfit} \alias{aw.mmkin} +\alias{aw.mixed.mmkin} +\alias{aw.multistart} \title{Calculate Akaike weights for model averaging} \usage{ aw(object, ...) @@ -11,6 +13,10 @@ aw(object, ...) \method{aw}{mkinfit}(object, ...) \method{aw}{mmkin}(object, ...) + +\method{aw}{mixed.mmkin}(object, ...) + +\method{aw}{multistart}(object, ...) } \arguments{ \item{object}{An \link{mmkin} column object, containing two or more diff --git a/man/multistart.Rd b/man/multistart.Rd index 347b12fb..4dd95503 100644 --- a/man/multistart.Rd +++ b/man/multistart.Rd @@ -4,7 +4,9 @@ \alias{multistart} \alias{multistart.saem.mmkin} \alias{print.multistart} -\alias{summary.multistart.saem.mmkin} +\alias{parms.multistart} +\alias{parhist} +\alias{llhist} \title{Perform a hierarchical model fit with multiple starting values} \usage{ multistart(object, n = 50, cores = 1, ...) @@ -13,7 +15,11 @@ multistart(object, n = 50, cores = 1, ...) \method{print}{multistart}(x, ...) -\method{summary}{multistart.saem.mmkin}(object) +\method{parms}{multistart}(object, ...) + +parhist(object, lpos = "topleft", ...) + +llhist(object, breaks = "Sturges", main = "", lpos = "topleft", ...) } \arguments{ \item{object}{The fit object to work with} @@ -23,7 +29,16 @@ used?} \item{cores}{How many fits should be run in parallel?} -\item{\dots}{Passed to the update function.} +\item{\dots}{Passed to the update function, or to the basic plotting +function in the case of the graphical function.} + +\item{x}{The multistart object to print} + +\item{lpos}{Positioning of the legend.} + +\item{breaks}{Passed to \link{hist}} + +\item{main}{title of the plot} } \value{ A list of \link{saem.mmkin} objects, with class attributes diff --git a/man/saem.Rd b/man/saem.Rd index dfb652b6..dd787475 100644 --- a/man/saem.Rd +++ b/man/saem.Rd @@ -42,7 +42,7 @@ saemix_model( saemix_data(object, verbose = FALSE, ...) -\method{parms}{saem.mmkin}(x, ci = FALSE, ...) +\method{parms}{saem.mmkin}(object, ci = FALSE, ...) } \arguments{ \item{object}{An \link{mmkin} row object containing several fits of the same diff --git a/tests/testthat/print_sfo_saem_1.txt b/tests/testthat/print_sfo_saem_1.txt index a11e1e96..34eea058 100644 --- a/tests/testthat/print_sfo_saem_1.txt +++ b/tests/testthat/print_sfo_saem_1.txt @@ -7,13 +7,13 @@ Data: Likelihood computed by importance sampling AIC BIC logLik - 1311 1315 -649 + 1312 1316 -650 Fitted parameters: estimate lower upper -parent_0 1e+02 99.13 1e+02 +parent_0 1e+02 99.28 1e+02 k_parent 4e-02 0.03 4e-02 a.1 9e-01 0.75 1e+00 b.1 5e-02 0.04 5e-02 -SD.parent_0 7e-01 -1.09 3e+00 +SD.parent_0 2e-01 -6.33 7e+00 SD.k_parent 3e-01 0.20 4e-01 diff --git a/tests/testthat/summary_hfit_sfo_tc.txt b/tests/testthat/summary_hfit_sfo_tc.txt index ad701cee..e3e2f7e4 100644 --- a/tests/testthat/summary_hfit_sfo_tc.txt +++ b/tests/testthat/summary_hfit_sfo_tc.txt @@ -45,7 +45,7 @@ SD.log_k_parent 0.3 0.1 0.4 Variance model: est. lower upper -a.1 0.91 0.64 1.17 +a.1 0.90 0.64 1.17 b.1 0.05 0.04 0.06 Backtransformed parameters: diff --git a/vignettes/FOCUS_L.html b/vignettes/FOCUS_L.html index 13d0d9eb..da6c11fe 100644 --- a/vignettes/FOCUS_L.html +++ b/vignettes/FOCUS_L.html @@ -1517,7 +1517,7 @@ div.tocify {

Example evaluation of FOCUS Laboratory Data L1 to L3

Johannes Ranke

-

Last change 18 May 2022 (rebuilt 2022-07-08)

+

Last change 18 May 2022 (rebuilt 2022-09-14)

@@ -1536,17 +1536,17 @@ FOCUS_2006_L1_mkin <- mkin_wide_to_long(FOCUS_2006_L1)

Since mkin version 0.9-32 (July 2014), we can use shorthand notation like "SFO" for parent only degradation models. The following two lines fit the model and produce the summary report of the model fit. This covers the numerical analysis given in the FOCUS report.

m.L1.SFO <- mkinfit("SFO", FOCUS_2006_L1_mkin, quiet = TRUE)
 summary(m.L1.SFO)
-
## mkin version used for fitting:    1.1.0 
+
## mkin version used for fitting:    1.1.2 
 ## R version used for fitting:       4.2.1 
-## Date of fit:     Fri Jul  8 15:44:39 2022 
-## Date of summary: Fri Jul  8 15:44:39 2022 
+## Date of fit:     Wed Sep 14 22:28:35 2022 
+## Date of summary: Wed Sep 14 22:28:35 2022 
 ## 
 ## Equations:
 ## d_parent/dt = - k_parent * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 133 model solutions performed in 0.029 s
+## Fitted using 133 model solutions performed in 0.032 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -1578,9 +1578,9 @@ summary(m.L1.SFO)

 ## 
 ## Parameter correlation:
 ##                parent_0 log_k_parent      sigma
-## parent_0      1.000e+00    6.186e-01 -1.712e-09
-## log_k_parent  6.186e-01    1.000e+00 -3.237e-09
-## sigma        -1.712e-09   -3.237e-09  1.000e+00
+## parent_0      1.000e+00    6.186e-01 -1.516e-09
+## log_k_parent  6.186e-01    1.000e+00 -3.124e-09
+## sigma        -1.516e-09   -3.124e-09  1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
@@ -1627,25 +1627,27 @@ summary(m.L1.SFO)
mkinresplot(m.L1.SFO, ylab = "Observed", xlab = "Time")

For comparison, the FOMC model is fitted as well, and the χ2 error level is checked.

-
m.L1.FOMC <- mkinfit("FOMC", FOCUS_2006_L1_mkin, quiet=TRUE)
-plot(m.L1.FOMC, show_errmin = TRUE, main = "FOCUS L1 - FOMC")
-

+
m.L1.FOMC <- mkinfit("FOMC", FOCUS_2006_L1_mkin, quiet=TRUE)
+
## Warning in mkinfit("FOMC", FOCUS_2006_L1_mkin, quiet = TRUE): Optimisation did not converge:
+## false convergence (8)
+
plot(m.L1.FOMC, show_errmin = TRUE, main = "FOCUS L1 - FOMC")
+

summary(m.L1.FOMC, data = FALSE)
## Warning in sqrt(diag(covar)): NaNs produced
## Warning in sqrt(1/diag(V)): NaNs produced
## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
 ## doubtful
-
## mkin version used for fitting:    1.1.0 
+
## mkin version used for fitting:    1.1.2 
 ## R version used for fitting:       4.2.1 
-## Date of fit:     Fri Jul  8 15:44:39 2022 
-## Date of summary: Fri Jul  8 15:44:40 2022 
+## Date of fit:     Wed Sep 14 22:28:35 2022 
+## Date of summary: Wed Sep 14 22:28:35 2022 
 ## 
 ## Equations:
 ## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 357 model solutions performed in 0.071 s
+## Fitted using 369 model solutions performed in 0.081 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -1666,34 +1668,39 @@ plot(m.L1.FOMC, show_errmin = TRUE, main = "FOCUS L1 - FOMC")

+##        DT50  DT90 DT50back
+## parent 7.25 24.08     7.25

We get a warning that the default optimisation algorithm Port did not converge, which is an indication that the model is overparameterised, i.e. contains too many parameters that are ill-defined as a consequence.

And in fact, due to the higher number of parameters, and the lower number of degrees of freedom of the fit, the χ2 error level is actually higher for the FOMC model (3.6%) than for the SFO model (3.4%). Additionally, the parameters log_alpha and log_beta internally fitted in the model have excessive confidence intervals, that span more than 25 orders of magnitude (!) when backtransformed to the scale of alpha and beta. Also, the t-test for significant difference from zero does not indicate such a significant difference, with p-values greater than 0.1, and finally, the parameter correlation of log_alpha and log_beta is 1.000, clearly indicating that the model is overparameterised.

The χ2 error levels reported in Appendix 3 and Appendix 7 to the FOCUS kinetics report are rounded to integer percentages and partly deviate by one percentage point from the results calculated by mkin. The reason for this is not known. However, mkin gives the same χ2 error levels as the kinfit package and the calculation routines of the kinfit package have been extensively compared to the results obtained by the KinGUI software, as documented in the kinfit package vignette. KinGUI was the first widely used standard package in this field. Also, the calculation of χ2 error levels was compared with KinGUII, CAKE and DegKin manager in a project sponsored by the German Umweltbundesamt (Ranke 2014).

@@ -1735,17 +1742,17 @@ plot(m.L2.FOMC, show_residuals = TRUE, main = "FOCUS L2 - FOMC") 

summary(m.L2.FOMC, data = FALSE)
-
## mkin version used for fitting:    1.1.0 
+
## mkin version used for fitting:    1.1.2 
 ## R version used for fitting:       4.2.1 
-## Date of fit:     Fri Jul  8 15:44:40 2022 
-## Date of summary: Fri Jul  8 15:44:40 2022 
+## Date of fit:     Wed Sep 14 22:28:35 2022 
+## Date of summary: Wed Sep 14 22:28:35 2022 
 ## 
 ## Equations:
 ## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 239 model solutions performed in 0.045 s
+## Fitted using 239 model solutions performed in 0.049 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -1780,10 +1787,10 @@ plot(m.L2.FOMC, show_residuals = TRUE,
 ## 
 ## Parameter correlation:
 ##             parent_0  log_alpha   log_beta      sigma
-## parent_0   1.000e+00 -1.151e-01 -2.085e-01 -7.637e-09
-## log_alpha -1.151e-01  1.000e+00  9.741e-01 -1.617e-07
-## log_beta  -2.085e-01  9.741e-01  1.000e+00 -1.387e-07
-## sigma     -7.637e-09 -1.617e-07 -1.387e-07  1.000e+00
+## parent_0   1.000e+00 -1.151e-01 -2.085e-01 -7.828e-09
+## log_alpha -1.151e-01  1.000e+00  9.741e-01 -1.602e-07
+## log_beta  -2.085e-01  9.741e-01  1.000e+00 -1.372e-07
+## sigma     -7.828e-09 -1.602e-07 -1.372e-07  1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
@@ -1813,10 +1820,10 @@ plot(m.L2.DFOP, show_residuals = TRUE, show_errmin = TRUE,
      main = "FOCUS L2 - DFOP")

 

 
summary(m.L2.DFOP, data = FALSE)

-
## mkin version used for fitting:    1.1.0 
+
## mkin version used for fitting:    1.1.2 
 ## R version used for fitting:       4.2.1 
-## Date of fit:     Fri Jul  8 15:44:40 2022 
-## Date of summary: Fri Jul  8 15:44:40 2022 
+## Date of fit:     Wed Sep 14 22:28:36 2022 
+## Date of summary: Wed Sep 14 22:28:36 2022 
 ## 
 ## Equations:
 ## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -1825,7 +1832,7 @@ plot(m.L2.DFOP, show_residuals = TRUE, show_errmin = TRUE,
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 581 model solutions performed in 0.119 s
+## Fitted using 581 model solutions performed in 0.135 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -1856,18 +1863,18 @@ plot(m.L2.DFOP, show_residuals = TRUE, show_errmin = TRUE,
 ## Optimised, transformed parameters with symmetric confidence intervals:
 ##          Estimate Std. Error      Lower     Upper
 ## parent_0   93.950  9.998e-01    91.5900   96.3100
-## log_k1      3.113  1.845e+03 -4360.0000 4367.0000
+## log_k1      3.112  1.842e+03 -4353.0000 4359.0000
 ## log_k2     -1.088  6.285e-02    -1.2370   -0.9394
 ## g_qlogis   -0.399  9.946e-02    -0.6342   -0.1638
 ## sigma       1.414  2.886e-01     0.7314    2.0960
 ## 
 ## Parameter correlation:
 ##            parent_0     log_k1     log_k2   g_qlogis      sigma
-## parent_0  1.000e+00  6.784e-07 -5.188e-10  2.665e-01 -5.800e-10
-## log_k1    6.784e-07  1.000e+00  1.114e-04 -2.191e-04 -1.029e-05
-## log_k2   -5.188e-10  1.114e-04  1.000e+00 -7.903e-01  5.080e-09
-## g_qlogis  2.665e-01 -2.191e-04 -7.903e-01  1.000e+00 -7.991e-09
-## sigma    -5.800e-10 -1.029e-05  5.080e-09 -7.991e-09  1.000e+00
+## parent_0  1.000e+00  6.783e-07 -3.390e-10  2.665e-01 -2.967e-10
+## log_k1    6.783e-07  1.000e+00  1.116e-04 -2.196e-04 -1.031e-05
+## log_k2   -3.390e-10  1.116e-04  1.000e+00 -7.903e-01  2.917e-09
+## g_qlogis  2.665e-01 -2.196e-04 -7.903e-01  1.000e+00 -4.408e-09
+## sigma    -2.967e-10 -1.031e-05  2.917e-09 -4.408e-09  1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
@@ -1875,7 +1882,7 @@ plot(m.L2.DFOP, show_residuals = TRUE, show_errmin = TRUE,
 ## for estimators of untransformed parameters.
 ##          Estimate   t value    Pr(>t)   Lower   Upper
 ## parent_0  93.9500 9.397e+01 2.036e-12 91.5900 96.3100
-## k1        22.4800 5.544e-04 4.998e-01  0.0000     Inf
+## k1        22.4800 5.553e-04 4.998e-01  0.0000     Inf
 ## k2         0.3369 1.591e+01 4.697e-07  0.2904  0.3909
 ## g          0.4016 1.680e+01 3.238e-07  0.3466  0.4591
 ## sigma      1.4140 4.899e+00 8.776e-04  0.7314  2.0960
@@ -1887,7 +1894,7 @@ plot(m.L2.DFOP, show_residuals = TRUE, show_errmin = TRUE,
 ## 
 ## Estimated disappearance times:
 ##          DT50  DT90 DT50back DT50_k1 DT50_k2
-## parent 0.5335 5.311    1.599 0.03083   2.058

+## parent 0.5335 5.311    1.599 0.03084   2.058

 
Here, the DFOP model is clearly the best-fit model for dataset L2 based on the chi^2 error level criterion.

 
 
@@ -1913,10 +1920,10 @@ plot(mm.L3)

The objects returned by mmkin are arranged like a matrix, with models as a row index and datasets as a column index.

We can extract the summary and plot for e.g. the DFOP fit, using square brackets for indexing which will result in the use of the summary and plot functions working on mkinfit objects.

summary(mm.L3[["DFOP", 1]])
-
## mkin version used for fitting:    1.1.0 
+
## mkin version used for fitting:    1.1.2 
 ## R version used for fitting:       4.2.1 
-## Date of fit:     Fri Jul  8 15:44:40 2022 
-## Date of summary: Fri Jul  8 15:44:41 2022 
+## Date of fit:     Wed Sep 14 22:28:36 2022 
+## Date of summary: Wed Sep 14 22:28:36 2022 
 ## 
 ## Equations:
 ## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -1925,7 +1932,7 @@ plot(mm.L3)

 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 376 model solutions performed in 0.072 s
+## Fitted using 376 model solutions performed in 0.081 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -1963,11 +1970,11 @@ plot(mm.L3)
## ## Parameter correlation: ## parent_0 log_k1 log_k2 g_qlogis sigma -## parent_0 1.000e+00 1.732e-01 2.282e-02 4.009e-01 -9.632e-08 -## log_k1 1.732e-01 1.000e+00 4.945e-01 -5.809e-01 7.145e-07 -## log_k2 2.282e-02 4.945e-01 1.000e+00 -6.812e-01 1.021e-06 -## g_qlogis 4.009e-01 -5.809e-01 -6.812e-01 1.000e+00 -7.925e-07 -## sigma -9.632e-08 7.145e-07 1.021e-06 -7.925e-07 1.000e+00 +## parent_0 1.000e+00 1.732e-01 2.282e-02 4.009e-01 -9.664e-08 +## log_k1 1.732e-01 1.000e+00 4.945e-01 -5.809e-01 7.147e-07 +## log_k2 2.282e-02 4.945e-01 1.000e+00 -6.812e-01 1.022e-06 +## g_qlogis 4.009e-01 -5.809e-01 -6.812e-01 1.000e+00 -7.926e-07 +## sigma -9.664e-08 7.147e-07 1.022e-06 -7.926e-07 1.000e+00 ## ## Backtransformed parameters: ## Confidence intervals for internally transformed parameters are asymmetric. @@ -2021,17 +2028,17 @@ plot(mm.L4)

The χ2 error level of 3.3% as well as the plot suggest that the SFO model fits very well. The error level at which the χ2 test passes is slightly lower for the FOMC model. However, the difference appears negligible.

summary(mm.L4[["SFO", 1]], data = FALSE)
-
## mkin version used for fitting:    1.1.0 
+
## mkin version used for fitting:    1.1.2 
 ## R version used for fitting:       4.2.1 
-## Date of fit:     Fri Jul  8 15:44:41 2022 
-## Date of summary: Fri Jul  8 15:44:41 2022 
+## Date of fit:     Wed Sep 14 22:28:36 2022 
+## Date of summary: Wed Sep 14 22:28:37 2022 
 ## 
 ## Equations:
 ## d_parent/dt = - k_parent * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 142 model solutions performed in 0.027 s
+## Fitted using 142 model solutions performed in 0.034 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -2063,9 +2070,9 @@ plot(mm.L4)

 ## 
 ## Parameter correlation:
 ##               parent_0 log_k_parent     sigma
-## parent_0     1.000e+00    5.938e-01 3.440e-07
-## log_k_parent 5.938e-01    1.000e+00 5.885e-07
-## sigma        3.440e-07    5.885e-07 1.000e+00
+## parent_0     1.000e+00    5.938e-01 3.387e-07
+## log_k_parent 5.938e-01    1.000e+00 5.830e-07
+## sigma        3.387e-07    5.830e-07 1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
@@ -2085,17 +2092,17 @@ plot(mm.L4)
## DT50 DT90 ## parent 106 352 
summary(mm.L4[["FOMC", 1]], data = FALSE)
-
## mkin version used for fitting:    1.1.0 
+
## mkin version used for fitting:    1.1.2 
 ## R version used for fitting:       4.2.1 
-## Date of fit:     Fri Jul  8 15:44:41 2022 
-## Date of summary: Fri Jul  8 15:44:41 2022 
+## Date of fit:     Wed Sep 14 22:28:37 2022 
+## Date of summary: Wed Sep 14 22:28:37 2022 
 ## 
 ## Equations:
 ## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 224 model solutions performed in 0.041 s
+## Fitted using 224 model solutions performed in 0.045 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -2130,10 +2137,10 @@ plot(mm.L4)

 ## 
 ## Parameter correlation:
 ##             parent_0  log_alpha   log_beta      sigma
-## parent_0   1.000e+00 -4.696e-01 -5.543e-01 -2.563e-07
-## log_alpha -4.696e-01  1.000e+00  9.889e-01  4.066e-08
-## log_beta  -5.543e-01  9.889e-01  1.000e+00  6.818e-08
-## sigma     -2.563e-07  4.066e-08  6.818e-08  1.000e+00
+## parent_0   1.000e+00 -4.696e-01 -5.543e-01 -2.468e-07
+## log_alpha -4.696e-01  1.000e+00  9.889e-01  2.478e-08
+## log_beta  -5.543e-01  9.889e-01  1.000e+00  5.211e-08
+## sigma     -2.468e-07  2.478e-08  5.211e-08  1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
-- 
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