calcAliasingScoresFromMatrix.RdCalculate the normalized sensitivities and aliasing scores for a given variational matrix. This matrix may be parameter- and/or output-normalized. Parameter-normalization will not change the outcome (as the sensitivities are normalized anyway), but output-normalization may do so.
calcAliasingScoresFromMatrix(df, vars = NULL)Data frame of variations in tall format (normalized or not), that is, with columns 't', 'i', 'y' and 'dy_d(varsj)', where variables varsj are replaced by names.
Vector of names of parameters to be included in aliasing analysis. If NULL or missing, all parameters in df are used.
A list with two elements, named "normSens" and "aliasingScore".The first contains a matrix with as named columns the time "t", output indicator index "i",
and normalized sensitivities of the parameters selected by vars.
The second contains a matrix with the aliasing scores, one for each pair of parameters
from the selection in vars.
Each score is a percentage between 0 and 100, where 100 indicates similarity between the parameters
and unidentifiability, and 0 means the parameters are not similar, indicating identifiability.
The matrix is symmetric and the diagonal elements are 100.
In case of errors, the return value is NULL.
Aliasing scores are calculated as follows. The sensitivity of the model to parameter p_j is s_j(t,i) = dy_i/d_p_j(t), where y_i is the i-th output variable and t is time. The normalized sensitivity is sn_j(t,i) = s_j(t,i) / max_t,i|s_j(t,i)|, and takes values between -1 and 1. The aliasing score of of parameters p_j and p_k is defined as a(j,k) = 100% * (1-max_t,i(| |sn_j(t,i)| - |sn_k(t,i)| |)), i.e. it measures the similarity between the profiles of their normalized sensitivities. In particular a(j,j) = 100%. For more details see Augustin et al (2019) and Braakman (2019).
Augustin, Braakman, Paxson - A workflow to detect non-identifiability in parameter estimation using SimBiology, Github (2019). Sietse Braakman - A general workflow for parameter estimation to help establish confidence in model predictions, Rosa Webinar 2019-12-01, slides 39-42.
Other calculation functions:
calcAliasingScoresFromModel(),
calcFimFromMatrix(),
calcFimFromModel(),
calcFirstVariations(),
calcSensitivityFromMatrix(),
calcSensitivityFromModel(),
calcVariationsFim(),
calcVariations(),
fimIdent()