@@ -212,7 +220,7 @@ their confidence intervals?
cores -
The number of cores to be used for multicore processing. +
The number of cores to be used for multicore processing. On Windows machines, cores > 1 is currently not supported.
@@ -228,15 +236,15 @@ On Windows machines, cores > 1 is currently not supported.
Value

A matrix with columns giving lower and upper confidence limits for - each parameter.
+each parameter.
References

Bates DM and Watts GW (1988) Nonlinear regression analysis & its applications
Pawitan Y (2013) In all likelihood - Statistical modelling and - inference using likelihood. Clarendon Press, Oxford.
+inference using likelihood. Clarendon Press, Oxford.
Venzon DJ and Moolgavkar SH (1988) A Method for Computing - Profile-Likelihood Based Confidence Intervals, Applied Statistics, 37, - 87–94.
+Profile-Likelihood Based Confidence Intervals, Applied Statistics, 37, +87–94.
Examples

f <- mkinfit("SFO", FOCUS_2006_C, quiet = TRUE)
@@ -262,50 +270,71 @@ On Windows machines, cores > 1 is currently not supported.
 SFO_SFO.ff <- mkinmod(parent = mkinsub("SFO", "m1"), m1 = mkinsub("SFO"),
   use_of_ff = "max", quiet = TRUE)
 f_d_1 <- mkinfit(SFO_SFO, subset(FOCUS_2006_D, value != 0), quiet = TRUE)
-system.time(ci_profile <- confint(f_d_1, method = "profile", cores = 1, quiet = TRUE))
#> Error in mkinpredict.mkinmod(mkinmod, parms, odeini, outtimes, solution_type = solution_type,     use_compiled = use_compiled, method.ode = method.ode, atol = atol,     rtol = rtol, ...): Differential equations were not integrated for all output times because
-#> NaN values occurred in output from ode()
#> Timing stopped at: 11.39 0 11.4
# Using more cores does not save much time here, as parent_0 takes up most of the time
+system.time(ci_profile <- confint(f_d_1, method = "profile", cores = 1, quiet = TRUE))
#>        User      System verstrichen 
+#>       3.362       0.000       3.364 
# Using more cores does not save much time here, as parent_0 takes up most of the time
 # If we additionally exclude parent_0 (the confidence of which is often of
 # minor interest), we get a nice performance improvement from about 50
 # seconds to about 12 seconds if we use at least four cores
 system.time(ci_profile_no_parent_0 <- confint(f_d_1, method = "profile",
-  c("k_parent_sink", "k_parent_m1", "k_m1_sink", "sigma"), cores = n_cores))
#> Profiling the likelihood
#>        User      System verstrichen 
-#>      20.058       0.122      11.784 
ci_profile
#> Error in eval(expr, envir, enclos): Objekt 'ci_profile' nicht gefunden
ci_quadratic_transformed <- confint(f_d_1, method = "quadratic")
-ci_quadratic_transformed
#>                       2.5%        97.5%
-#> parent_0      96.403841641 1.027931e+02
-#> k_parent_sink  0.041033378 5.596269e-02
-#> k_parent_m1    0.046777902 5.511931e-02
-#> k_m1_sink      0.004012217 6.897547e-03
-#> sigma          2.396089689 3.854918e+00
ci_quadratic_untransformed <- confint(f_d_1, method = "quadratic", transformed = FALSE)
-ci_quadratic_untransformed
#>                       2.5%        97.5%
-#> parent_0      96.403841648 102.79312450
-#> k_parent_sink  0.040485331   0.05535491
-#> k_parent_m1    0.046611582   0.05494364
-#> k_m1_sink      0.003835483   0.00668582
-#> sigma          2.396089689   3.85491806
# Against the expectation based on Bates and Watts (1988), the confidence
+  c("k_parent_sink", "k_parent_m1", "k_m1_sink", "sigma"), cores = n_cores))
#> Profiling the likelihood
#> Warning: scheduled cores 1, 2, 3 encountered errors in user code, all values of the jobs will be affected
#> Error in dimnames(x) <- dn: Länge von 'dimnames' [2] ungleich der Arrayausdehnung
#> Timing stopped at: 0.011 0.045 0.201
ci_profile
#>                        2.5%        97.5%
+#> parent_0       96.456003640 1.027703e+02
+#> k_parent        0.090911032 1.071578e-01
+#> k_m1            0.003892605 6.702778e-03
+#> f_parent_to_m1  0.471328495 5.611550e-01
+#> sigma           2.535612399 3.985263e+00
ci_quadratic_transformed <- confint(f_d_1, method = "quadratic")
+ci_quadratic_transformed
#>                        2.5%        97.5%
+#> parent_0       96.403839460 1.027931e+02
+#> k_parent        0.090823790 1.072543e-01
+#> k_m1            0.004012216 6.897547e-03
+#> f_parent_to_m1  0.469118713 5.595960e-01
+#> sigma           2.396089689 3.854918e+00
ci_quadratic_untransformed <- confint(f_d_1, method = "quadratic", transformed = FALSE)
+ci_quadratic_untransformed
#>                        2.5%        97.5%
+#> parent_0       96.403839413 1.027931e+02
+#> k_parent        0.090491931 1.069035e-01
+#> k_m1            0.003835483 6.685819e-03
+#> f_parent_to_m1  0.469113365 5.598386e-01
+#> sigma           2.396089689 3.854918e+00
# Against the expectation based on Bates and Watts (1988), the confidence
 # intervals based on the internal parameter transformation are less
 # congruent with the likelihood based intervals. Note the superiority of the
 # interval based on the untransformed fit for k_m1_sink
-rel_diffs_transformed <- abs((ci_quadratic_transformed - ci_profile)/ci_profile)
#> Error in eval(expr, envir, enclos): Objekt 'ci_profile' nicht gefunden
rel_diffs_untransformed <- abs((ci_quadratic_untransformed - ci_profile)/ci_profile)
#> Error in eval(expr, envir, enclos): Objekt 'ci_profile' nicht gefunden
rel_diffs_transformed < rel_diffs_untransformed
#> Error in eval(expr, envir, enclos): Objekt 'rel_diffs_transformed' nicht gefunden
signif(rel_diffs_transformed, 3)
#> Error in eval(expr, envir, enclos): Objekt 'rel_diffs_transformed' nicht gefunden
signif(rel_diffs_untransformed, 3)
#> Error in eval(expr, envir, enclos): Objekt 'rel_diffs_untransformed' nicht gefunden

+rel_diffs_transformed <- abs((ci_quadratic_transformed - ci_profile)/ci_profile)
+rel_diffs_untransformed <- abs((ci_quadratic_untransformed - ci_profile)/ci_profile)
+rel_diffs_transformed < rel_diffs_untransformed
#>                 2.5% 97.5%
+#> parent_0        TRUE  TRUE
+#> k_parent        TRUE  TRUE
+#> k_m1           FALSE FALSE
+#> f_parent_to_m1  TRUE FALSE
+#> sigma          FALSE FALSE
signif(rel_diffs_transformed, 3)
#>                    2.5%    97.5%
+#> parent_0       0.000541 0.000222
+#> k_parent       0.000960 0.000900
+#> k_m1           0.030700 0.029100
+#> f_parent_to_m1 0.004690 0.002780
+#> sigma          0.055000 0.032700
signif(rel_diffs_untransformed, 3)
#>                    2.5%    97.5%
+#> parent_0       0.000541 0.000222
+#> k_parent       0.004610 0.002370
+#> k_m1           0.014700 0.002530
+#> f_parent_to_m1 0.004700 0.002350
+#> sigma          0.055000 0.032700

 
 # Investigate a case with formation fractions
 f_d_2 <- mkinfit(SFO_SFO.ff, subset(FOCUS_2006_D, value != 0), quiet = TRUE)
 ci_profile_ff <- confint(f_d_2, method = "profile", cores = n_cores)
#> Profiling the likelihood
ci_profile_ff
#>                        2.5%        97.5%
-#> parent_0       96.456003650 1.027703e+02
+#> parent_0       96.456003640 1.027703e+02
 #> k_parent        0.090911032 1.071578e-01
 #> k_m1            0.003892605 6.702778e-03
 #> f_parent_to_m1  0.471328495 5.611550e-01
 #> sigma           2.535612399 3.985263e+00
ci_quadratic_transformed_ff <- confint(f_d_2, method = "quadratic")
 ci_quadratic_transformed_ff
#>                        2.5%        97.5%
-#> parent_0       96.403839992 1.027931e+02
+#> parent_0       96.403839460 1.027931e+02
 #> k_parent        0.090823790 1.072543e-01
 #> k_m1            0.004012216 6.897547e-03
-#> f_parent_to_m1  0.469118711 5.595960e-01
+#> f_parent_to_m1  0.469118713 5.595960e-01
 #> sigma           2.396089689 3.854918e+00
ci_quadratic_untransformed_ff <- confint(f_d_2, method = "quadratic", transformed = FALSE)
 ci_quadratic_untransformed_ff
#>                        2.5%        97.5%
-#> parent_0       96.403839944 1.027931e+02
+#> parent_0       96.403839413 1.027931e+02
 #> k_parent        0.090491931 1.069035e-01
 #> k_m1            0.003835483 6.685819e-03
-#> f_parent_to_m1  0.469113362 5.598386e-01
+#> f_parent_to_m1  0.469113365 5.598386e-01
 #> sigma           2.396089689 3.854918e+00
rel_diffs_transformed_ff <- abs((ci_quadratic_transformed_ff - ci_profile_ff)/ci_profile_ff)
 rel_diffs_untransformed_ff <- abs((ci_quadratic_untransformed_ff - ci_profile_ff)/ci_profile_ff)
 # While the confidence interval for the parent rate constant is closer to
@@ -318,15 +347,15 @@ On Windows machines, cores > 1 is currently not supported.
 #> k_m1           FALSE FALSE
 #> f_parent_to_m1  TRUE FALSE
 #> sigma          FALSE FALSE
rel_diffs_transformed_ff
#>                        2.5%        97.5%
-#> parent_0       0.0005408026 0.0002217846
-#> k_parent       0.0009596414 0.0009003877
-#> k_m1           0.0307277403 0.0290579212
-#> f_parent_to_m1 0.0046884168 0.0027782604
+#> parent_0       0.0005408080 0.0002217794
+#> k_parent       0.0009596417 0.0009003876
+#> k_m1           0.0307277370 0.0290579182
+#> f_parent_to_m1 0.0046884130 0.0027782556
 #> sigma          0.0550252516 0.0327066836
rel_diffs_untransformed_ff
#>                        2.5%        97.5%
-#> parent_0       0.0005408031 0.0002217851
-#> k_parent       0.0046100089 0.0023730230
-#> k_m1           0.0146746442 0.0025300972
-#> f_parent_to_m1 0.0046997642 0.0023460268
+#> parent_0       0.0005408085 0.0002217799
+#> k_parent       0.0046100096 0.0023730229
+#> k_m1           0.0146746469 0.0025301011
+#> f_parent_to_m1 0.0046997599 0.0023460223
 #> sigma          0.0550252516 0.0327066836

 # The profiling for the following fit does not finish in a reasonable time,
 # therefore we use the quadratic approximation
@@ -337,29 +366,24 @@ On Windows machines, cores > 1 is currently not supported.
 DFOP_par_c <- synthetic_data_for_UBA_2014[[12]]$data
 f_tc_2 <- mkinfit(m_synth_DFOP_par, DFOP_par_c, error_model = "tc",
   error_model_algorithm = "direct", quiet = TRUE)
-confint(f_tc_2, method = "quadratic")
#>                        2.5%        97.5%
-#> parent_0       94.596218141 106.19934683
-#> k_M1            0.037605440   0.04490756
-#> k_M2            0.008568747   0.01087674
-#> f_parent_to_M1  0.021466788   0.62023878
-#> f_parent_to_M2  0.015168650   0.37975352
-#> k1              0.273897581   0.33388066
-#> k2              0.018614556   0.02250379
-#> g               0.671943831   0.73583255
-#> sigma_low       0.251283700   0.83992071
-#> rsd_high        0.040411017   0.07662005
confint(f_tc_2, "parent_0", method = "quadratic")
#>              2.5%    97.5%
-#> parent_0 94.59622 106.1993
# }
+confint(f_tc_2, method = "quadratic")
#>                       2.5%        97.5%
+#> parent_0       94.59613833 106.19939215
+#> k_M1            0.03760542   0.04490759
+#> k_M2            0.00856874   0.01087675
+#> f_parent_to_M1  0.02146166   0.62023888
+#> f_parent_to_M2  0.01516502   0.37975343
+#> k1              0.27389751   0.33388078
+#> k2              0.01861456   0.02250379
+#> g               0.67194349   0.73583256
+#> sigma_low       0.25128383   0.83992146
+#> rsd_high        0.04041100   0.07662001
confint(f_tc_2, "parent_0", method = "quadratic")
#>              2.5%    97.5%
+#> parent_0 94.59614 106.1994
# }
Confidence intervals for parameters of mkinfit objects

Value

References

Examples

Contents
