![[Stable]](figures/lifecycle-stable.svg)
Contains final cycle information from run.
Details
The PM_final object is both a data field within a PM_result, and itself an R6 object comprising data fields and associated methods suitable for analysis and plotting of final cycle parameters.
Because PM_final objects are automatically added to the PM_result at the end of a successful run, it is generally not necessary for users to generate PM_final objects themselves.
The main results are contained in the $data field,
and it is this field which is passed to the $plot and $summary methods.
You can use this $data field for custom manipulations, e.g. probs <- run1$final$data$popPoints %>% select(prob).
This will select the probabilities of the support points.
If you are unfamiliar with the %>% pipe function, please type help("%>%", "magrittr")
into the R console and look online for instructions/tutorials in tidyverse, a
powerful approach to data manipulation upon which Pmetrics is built.
To provide a more traditional experience in R,
the $data field is also separated by list items into the other data fields within the R6 object,
e.g. popMean or nsub. This
allows you to access them in an S3 way, e.g. run1$final$popMean if run1 is a
PM_result object.
Public fields
dataA list with the following elements, which can also be extracted by name.
popPoints (NPAG only) Data frame of the final cycle joint population density of grid points with column names equal to the name of each random parameter plus prob for the associated probability of that point
popMean The final cycle mean for each random parameter distribution
popSD The final cycle standard deviation for each random parameter distribution
popCV The final cycle coefficient of variation (SD/Mean) for each random parameter distribution
popVar The final cycle variance for each random parameter distribution
popCov The final cycle random parameter covariance matrix
popCor The final cycle random parameter correlation matrix
popMed The final cycle median values for each random parameter, i.e. those that have unknown mean and unknown variance, both of which are fitted during the run
postPoints (NPAG only) Data frame of posterior population points for each of the first 100 subject, with columns id, point, parameters and probability. The first column is the subject, the second column has the population point number, followed by the values for the parameters in that point and the probability.
postMean A nsub x npar data frame containing the means of the posterior distributions for each parameter.
postSD A nsub x npar data frame containing the SDs of the posterior distributions for each parameter.
postVar A nsub x npar data frame containing the variances of the posterior distributions for each parameter.
postCov NPAG only: An list of length nsub, each element with an npar x npar data frame that contains the posterior parameter value covariances for that subject.
postCor NPAG only: An list of length nsub, each element with an npar x npar data frame that contains the posterior parameter value correlations for that subject.
postMed A nsub x npar data frame containing the medians of the posterior distributions for each parameter.
shrinkage A data frame with the shrinkage for each parameter.
gridpts (NPAG only) Initial number of support points
nsub Number of subjects
ab Tibble/data frame of boundaries for random parameter values with columns: name, lower, upper.
Active bindings
popPoints(NPAG only) Data frame of the final cycle joint population density of grid points with column names equal to the name of each random parameter plus prob for the associated probability of that point
popMeanThe final cycle mean for each random parameter distribution
popSDThe final cycle standard deviation for each random parameter distribution
popCVThe final cycle coefficient of variation (SD/Mean) for each random parameter distribution
popVarThe final cycle variance for each random parameter distribution
popCovThe final cycle random parameter covariance matrix
popCorThe final cycle random parameter correlation matrix
popMedThe final cycle median values for each random parameter, i.e. those that have unknown mean and unknown variance, both of which are fitted during the run
postPoints(NPAG only) Data frame of posterior population points for each of the first 100 subject, with columns id, point, parameters and probability. The first column is the subject, the second column has the population point number, followed by the values for the parameters in that point and the probability.
postMeanA nsub x npar data frame containing the means of the posterior distributions for each parameter.
postSDA nsub x npar data frame containing the SDs of the posterior distributions for each parameter.
postVarA nsub x npar data frame containing the variances of the posterior distributions for each parameter.
postCovNPAG only: An list of length nsub, each element with an npar x npar data frame that contains the posterior parameter value covariances for that subject.
postCorNPAG only: An list of length nsub, each element with an npar x npar data frame that contains the posterior parameter value correlations for that subject.
postMedA nsub x npar data frame containing the medians of the posterior distributions for each parameter.*
shrinkageA data frame with the shrinkage for each parameter. The total population variance for a parameter is comprised of variance(EBE) plus average variance(EBD), where each subject's EBE is the Empirical Bayes Estimate or mean posterior value for the parameter. EBD is the Empirical Bayes Distribution, or the full Bayesian posterior parameter value distribution for each subject.
The typical definition of \(\eta\) shrinkage is \([1 - \frac{SD(\eta)}{\omega}]\) or \([1 - \frac{var(\eta)}{\omega^2}]\), where \(\eta\) is the EBE and \(\omega^2\) is the population variance of \(\eta\).
In parametric modeling approaches \(\eta\) is the interindividual variability around the typical (mean) value of the parameter in the population, usually referred to as \(\theta\). In nonparametric approaches, there is no assumption of normality, so \(\eta\) simply becomes each subject's mean parameter value estimate.
Here is how Pmetrics derives and then calculates shrinkage for a given parameter. $$popVar = var(EBE) + mean(var(EBD))$$ $$1 = \frac{var(EBE)}{popVar} + \frac{mean(var(EBD)}{popVar}$$ $$1 - \frac{var(EBE)}{popVar} = \frac{mean(var(EBD))}{popVar}$$ $$shrinkage = \frac{mean(var(EBD))}{popVar}$$ Shrinkage is therefore a fraction between 0 and 1. If Bayesian posterior distributions are wide for a given parameter and \(mean(var(EBD))\) is high due to sparse or uninformative sampling, then most of the population variance is due to this variance and shrinkage is high, i.e., individual posterior estimates (EBE) shrink towards the population mean. Be aware, however, that a Bayesian posterior parameter value distribution for a given subject who is sparsely sampled may also be a single support point with no variance. Therefore EBD under nonparametric assumptions is not always large with uninformative sampling. This means that shrinkage is not as readily interpretable in nonparametric population modeling.
An alternative is to consider the number of support points relative to the number of subjects. Highly informed, distinct subjects will result in the maximum possible number of support points, N, which is the same as the number of subjects. In contrast, badly undersampled subjects can result in only one support point. There is no formal criterion for this statistic, but it can be used in combination with shrinkage to assess the information content of the data.
gridpts(NPAG only) Initial number of support points
nsubNumber of subjects
abMatrix of boundaries for random parameter values
Methods
Method new()
Create new object populated with final cycle information
Usage
PM_final$new(PMdata = NULL, path = ".", ...)Method plot()
Plot method
Arguments
...Arguments passed to plot.PM_final
Details
See plot.PM_final.
Method summary()
Summary method
Arguments
...Arguments passed to summary.PM_final
Details
See summary.PM_final.