confint.mkinfit.RdThe default method 'profile' is based on the profile likelihood for each parameter. The method uses two nested optimisations. The speed of the method could likely be improved by using the method of Venzon and Moolgavkar (1988).
# S3 method for mkinfit confint(object, parm, level = 0.95, alpha = 1 - level, cutoff, method = c("profile", "quadratic"), transformed = TRUE, backtransform = TRUE, cores = round(detectCores()/2), quiet = FALSE, ...)
| object | An |
|---|---|
| parm | A vector of names of the parameters which are to be given confidence intervals. If missing, all parameters are considered. |
| level | The confidence level required |
| alpha | The allowed error probability, overrides 'level' if specified. |
| cutoff | Possibility to specify an alternative cutoff for the difference in the log-likelihoods at the confidence boundary. Specifying an explicit cutoff value overrides arguments 'level' and 'alpha' |
| method | The 'profile' method searches the parameter space for the cutoff of the confidence intervals by means of a likelihood ratio test. The 'quadratic' method approximates the likelihood function at the optimised parameters using the second term of the Taylor expansion, using a second derivative (hessian) contained in the object. |
| transformed | If the quadratic approximation is used, should it be applied to the likelihood based on the transformed parameters? |
| backtransform | If we approximate the likelihood in terms of the transformed parameters, should we backtransform the parameters with their confidence intervals? |
| cores | The number of cores to be used for multicore processing. This
is only used when the |
| quiet | Should we suppress the message "Profiling the likelihood" |
| ... | Not used |
A matrix with columns giving lower and upper confidence limits for each parameter.
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.
Venzon DJ and Moolgavkar SH (1988) A Method for Computing Profile-Likelihood Based Confidence Intervals, Applied Statistics, 37, 87–94.
#> 2.5% 97.5% #> parent_0 71.8242430 93.1600766 #> k_parent_sink 0.2109541 0.4440528 #> sigma 1.9778868 7.3681380#>#> 2.5% 97.5% #> parent_0 73.0641834 92.1392181 #> k_parent_sink 0.2170293 0.4235348 #> sigma 3.1307772 8.0628314SFO_SFO <- mkinmod(parent = mkinsub("SFO", "m1"), m1 = mkinsub("SFO"), quiet = TRUE) 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, cores = 1, quiet = TRUE))#> User System verstrichen #> 50.987 0.008 51.023# The following does not save much time, as parent_0 takes up most of the time # system.time(ci_profile <- confint(f_d_1, cores = 5)) # system.time(ci_profile <- confint(f_d_1, # c("k_parent_sink", "k_parent_m1", "k_m1_sink", "sigma"), cores = 1)) # If we exclude parent_0 (the confidence of which is often of minor interest), we get a nice # performance improvement from about 30 seconds to about 12 seconds # system.time(ci_profile_no_parent_0 <- confint(f_d_1, # c("k_parent_sink", "k_parent_m1", "k_m1_sink", "sigma"), cores = 4)) ci_profile#> 2.5% 97.5% #> parent_0 96.456003650 1.027703e+02 #> k_parent_sink 0.040762501 5.549764e-02 #> k_parent_m1 0.046786482 5.500879e-02 #> k_m1_sink 0.003892605 6.702778e-03 #> sigma 2.535612399 3.985263e+00#> 2.5% 97.5% #> parent_0 96.403841649 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+00ci_quadratic_untransformed <- confint(f_d_1, method = "quadratic", transformed = FALSE) ci_quadratic_untransformed#> 2.5% 97.5% #> parent_0 96.403841653 102.79312450 #> k_parent_sink 0.040485331 0.05535491 #> k_parent_m1 0.046611581 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 # 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) rel_diffs_untransformed <- abs((ci_quadratic_untransformed - ci_profile)/ci_profile) rel_diffs_transformed#> 2.5% 97.5% #> parent_0 0.0005407854 0.0002218012 #> k_parent_sink 0.0066452394 0.0083795930 #> k_parent_m1 0.0001833903 0.0020092090 #> k_m1_sink 0.0307278240 0.0290580487 #> sigma 0.0550252516 0.0327066836rel_diffs_untransformed#> 2.5% 97.5% #> parent_0 0.0005407854 0.0002218011 #> k_parent_sink 0.0067996407 0.0025717594 #> k_parent_m1 0.0037382781 0.0011843074 #> k_m1_sink 0.0146745610 0.0025299672 #> sigma 0.0550252516 0.0327066836# Set the number of cores for further examples if (identical(Sys.getenv("NOT_CRAN"), "true")) { n_cores <- parallel::detectCores() - 1 } else { n_cores <- 1 } if (Sys.getenv("TRAVIS") != "") n_cores = 1 if (Sys.info()["sysname"] == "Windows") n_cores = 1 # 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, cores = n_cores)#>ci_profile_ff#> 2.5% 97.5% #> parent_0 96.456003650 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#> 2.5% 97.5% #> parent_0 96.403840123 1.027931e+02 #> k_parent 0.090823791 1.072543e-01 #> k_m1 0.004012216 6.897547e-03 #> f_parent_to_m1 0.469118710 5.595960e-01 #> sigma 2.396089689 3.854918e+00ci_quadratic_untransformed_ff <- confint(f_d_2, method = "quadratic", transformed = FALSE) ci_quadratic_untransformed_ff#> 2.5% 97.5% #> parent_0 96.403840057 1.027931e+02 #> k_parent 0.090491932 1.069035e-01 #> k_m1 0.003835483 6.685819e-03 #> f_parent_to_m1 0.469113361 5.598386e-01 #> sigma 2.396089689 3.854918e+00rel_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 # the profile based interval when using the internal parameter # transformation, the intervals for the other parameters are 'better # without internal parameter transformation. rel_diffs_transformed_ff#> 2.5% 97.5% #> parent_0 0.0005408012 0.0002217857 #> k_parent 0.0009596303 0.0009003981 #> k_m1 0.0307277425 0.0290579163 #> f_parent_to_m1 0.0046884178 0.0027782643 #> sigma 0.0550252516 0.0327066836rel_diffs_untransformed_ff#> 2.5% 97.5% #> parent_0 0.0005408019 0.0002217863 #> k_parent 0.0046099989 0.0023730118 #> k_m1 0.0146746451 0.0025300990 #> f_parent_to_m1 0.0046997668 0.0023460293 #> sigma 0.0550252516 0.0327066836# The profiling for the following fit does not finish in a reasonable time, # therefore we use the quadratic approximation m_synth_DFOP_par <- mkinmod(parent = mkinsub("DFOP", c("M1", "M2")), M1 = mkinsub("SFO"), M2 = mkinsub("SFO"), use_of_ff = "max", quiet = TRUE) 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 94.596183241 106.19937044 #> k_M1 0.037605436 0.04490758 #> k_M2 0.008568746 0.01087675 #> f_parent_to_M1 0.021464277 0.62023879 #> f_parent_to_M2 0.015166876 0.37975352 #> k1 0.273897622 0.33388081 #> k2 0.018614564 0.02250380 #> g 0.671943572 0.73583247 #> sigma_low 0.251284138 0.83992136 #> rsd_high 0.040410998 0.07661999#> 2.5% 97.5% #> parent_0 94.59618 106.1994# }