Uncertainty-Certainty Matrix Logic Model and Algorithms

Richard Fiene PhD

Penn State Edna Bennett Pierce Prevention Research Center

May 2025

Recently the Uncertainty-Certainty Matrix (UCM) was introduced for licensing decision making and validating differential monitoring approaches (Fiene, 2025). A logic model was briefly introduced but not expanded upon in that paper. The purpose of this paper is to expand that thinking and to introduce the associated algorithms that specify the UCMLMA (Uncertainty-Certainty Matrix Logic Model and Algorithms).

The UCMLMA will build off the contingency table and confusion matrix logic modeling as was introduced in the Fiene (2025) paper in the following matrix (Table 1).

Table 1: UCMLMA: Uncertainty-Certainty Matrix Logic Model and Algorithms

From this matrix certain licensing decision making can be made and certain biases can be avoided with the following algorithms related to compliance and non compliance of rules/regulations.

TP + TN is the ideal situation in which all decisions are made correctly. Accuracy can be measured by ((TP x TN) - (FN x FP) / sqrt ((TP + FN) (FP + TN) (TP + FP) (FN + TN)) with a coefficient closer to +1.00.

TP + FP + FN + TN is a totally random situation where decisions are not reliable nor valid, there is no rhyme or reason to the decision making process by the individual inspector. Randomness can be measured by the following: (TP x TN) - (FN x FP) / sqrt ((TP + FN) (FP + TN) (TP + FP) (FN + TN)) with a coefficient closer to 0.00.

TP + FP introduces a positive bias in which the inspector has a tendency to always make a decision in which the program is in compliance with specific rules. They are overly lenient in their interpretation of the rules. Positive bias sensitivity can be measured by FP / (TP + FP). The higher the percent, the more bias is present.

FN + TN introduces a negative bias in which the inspector has a tendency to always make a decision in which the program is in non compliance with specific rules. They are overly stringent in their interpretation of the rules. Negative bias sensitivity can be measured by FN / (FN + TN). The higher the percent, the more bias is present.

Table 2: UCMLMA: Uncertainty-Certainty Matrix Logic Model and Algorithms Applied to Differential Monitoring

From this matrix (Table 2), certain decisions can be made regarding differential monitoring validation related to key indicators, risk assessment, regulatory compliance levels and individual rule performance with the following algorithms.

TP + TN is the ideal result when determining key indicators because the individual rule statistically predicts overall compliance with all rules. Accuracy can be measured with the following: ((TP x TN) - (FN x FP) / sqrt ((TP + FN) (FP + TN) (TP + FP) (FN + TN)) with the coefficient being closer to +1.00.

TP + FP is what happens with high risk rules in that they are always in compliance and one sees very little non compliance with these high risk rules generally. Sensitivity can be measured by FP / (TP + FP). Higher compliance rates would generally indicate higher risk rules.

TP is when 100% full compliance is always present. The greater the number or percent of total programs being 100% in full compliance, the greater the skewness in the data distribution.

TP + FN is present when substantial regulatory compliance is used as a criterion for licensing decision making. The higher the number, the greater the skewness in the data distribution.

FN + TN occurs when a rule is difficult to comply with. The following algorithm can be used FN / (FN + TN) to measure how difficult the rule is. The greater the percent, the more difficult the rule is.

FP + TN occurs when programs are performing poorly and there is a great deal of non compliance with the rules. The greater the number of programs indicates a poorly performing system of rules.

FP + FN is an example of a terrible rule that predicts the opposite of what we intended with overall regulatory compliance. The following algorithm ((TP x TN) - (FN x FP) / sqrt ((TP + FN) (FP + TN) (TP + FP) (FN + TN)) can be used with coefficients closer to -1.00 demonstrating this finding.

It is highly recommended for the interested reader to start with the Fiene (2025) paper first and then read this paper second. The Fiene (2025) paper provides the details of UCM which is needed to understand this additional extension UCMDMA.

The above two matrices and their corresponding algorithms give a structured approach to licensing decision making and differential monitoring validation. It should provide the licensing administrator with a data driven and empirical method based upon regulatory science principles.

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Fiene, R. (2025). The Uncertainty–Certainty Matrix for Licensing Decision Making, Validation, Reliability, and Differential Monitoring Studies. Knowledge, 5(2), 8. https://doi.org/10.3390/knowledge5020008

This entry is adapted from: DOI: 10.13140/RG.2.2.28963.98083 and DOI: 10.3390/knowledge5020008