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Competence Assessment as an Expert System for Human Resource Management: A Mathematical Approach
Mahdi Bohlouli, Nikolaos Mittas, George Kakarontzas, Theodosios Theodosiou, Lefteris Angelis, Madjid Fathi
TL;DR
Organizations need to identify competence gaps to match people with job requirements and guide training. The paper combines a configurable PIS competence tree with mathematical and statistical assessment and analysis. It reports that its approach can classify candidates by fit and support ranking and clustering for job positions.
Problem
Organizations need accurate acquired- and required-competence profiles to identify job-specific gaps and support employee selection and development.
Source: §1 · pp. 1–2Method
The approach uses a Professional, Innovative and Social competence tree to combine employee assessments, represent acquired and required competences, and analyze fit mathematically.
Source: §1 · p. 3Results
The Scott-Knott clustering algorithm groups job seekers as under-qualified, over-qualified, or best-fit relative to a specific job definition.
Source: §6 · p. 32Takeaways & Limitations
The approach supports finding suitable employees for job positions and identifying competence gaps relevant to career development.
Source: §5.3 · p. 31Further application in other contexts, including medical science, is needed to test the algorithms across domains and assess adaptation to varied sectors.
Source: §6 · p. 32
Abstract
from arXiv · showhide
Efficient human resource management needs accurate assessment and representation of available competences as well as effective mapping of required competences for specific jobs and positions. In this regard, appropriate definition and identification of competence gaps express differences between acquired and required competences. Using a detailed quantification scheme together with a mathematical approach is a way to support accurate competence analytics, which can be applied in a wide variety of sectors and fields. This article describes the combined use of software technologies and mathematical and statistical methods for assessing and analyzing competences in human resource information systems. Based on a standard competence model, which is called a Professional, Innovative and Social competence tree, the proposed framework offers flexible tools to experts in real enterprise environments, either for evaluation of employees towards an optimal job assignment and vocational training or for recruitment processes. The system has been tested with real human resource data sets in the frame of the European project called ComProFITS.
1. Introduction
The introduction frames competence-gap identification as a prerequisite for matching people to jobs and planning training. It proposes a mathematical, computer-supported framework that profiles acquired competences against job requirements.
1. Introduction
- The paper motivates expert systems as support for strategic decisions, identifying unused competences, anticipating future needs, and improving career development opportunities.The introduction also links efficient competence management to workforce planning and product and service quality.Source: §1 · p. 1
- Companies need to identify differences between a person’s competences and a target job’s requirements early to avoid costs from skill mismatch or misuse of human resources.The paper calls this difference a competence gap and frames person, performance, position, and period as the 4Ps of person-job fit.Source: §1 · p. 2
- The introduction positions the work within competence-management research and notes differing uses of “competence” and “competency” across definitions and perspectives.It describes competence as reflecting the performance perspective of the skills required for a specific job.Source: §1 · p. 2
- The research defines a reference competence tree and analyzes individual qualifications to support competence-gap visualization, candidate prioritization, clustering, and person-job fit.The authors describe the broader selection principle as choosing the best-fitting person or product against identified requirements or configuration gaps.Source: §1 · p. 3
- The framework combines 360-degree feedback and self-assessment into acquired competence data (ACD), then compares profiles with required competence data (RCD) for specific jobs.The comparison supports analysis of job qualification and recommendations for future improvement.Source: §1 · p. 3
2. Related Work
The related-work review spans competence models, assessment methods, and competence-management systems. It identifies limited cross-sector flexibility and generalized matching as gaps, motivating a mathematically represented reference tree and computerized assessment approach.
2. Related Work
- Prior work includes competence research across psychological, executive-planning, training, and domain-specific assessment perspectives.The review describes methods including multi-criteria evaluation of firms and studies of soft, business, and technical skills.Source: §2 · pp. 4–6
- Reviewed projects range from sector-focused competence systems to broad educational and vocational assessment initiatives.Examples include projects in production, SMEs, higher education, teacher training, and simulated work environments.Source: §2 · pp. 6–7
- 86% of the studied funded research projects focus on one career, with no insight into extension or flexibility for other careers and case studies.The review also says many projects rely on domain-specific ontologies or traditional paper- or interview-based assessment.Source: §2 · p. 8
- The review concludes that competence-management systems should identify required competences, assess acquired competences, match them, and recommend competence development.The proposed approach uses a general hierarchical reference tree for assessment across careers and applies mathematical methods to competence analysis.Source: §2 · p. 8
- A lack of efficient, generalized competence matching is a recurring challenge; the proposed mathematical representation is intended to make sector adaptation easier than customizing a domain ontology.The paper states that adapting an existing domain ontology to a new sector demands effort comparable to developing a new one.Source: §2 · p. 8
3. The Reference Competence Tree and Assessment
The PIS competence tree provides a configurable hierarchy for collecting and aggregating employee assessments. Multi-source feedback and self-assessment supply level-3 values, which are combined into higher-level competence profiles.
3. The Reference Competence Tree and Assessment
- The PIS tree has three tiers, with professional, innovative, and social categories at the top and level-3 competences assessed before higher levels are calculated.The tree supports configurable categories, statements, and weights; the authors default all nodes to equal weights for organizations to adjust.Source: §3 · pp. 8–9
- The assessment process combines multi-source assessment and self-assessment, with results summarized as acquired competence data for level-3 competences.Managers select job-relevant competences and plan the assessment, including its schedule, team, questionnaire, and assessment-type weights.Source: §3 · p. 9
- Level-1 competence values summarize lower-level measurements, while level-2 views provide more detailed information about organizational competence needs.The paper presents these aggregate levels as ways to examine general strengths, weaknesses, and competence gaps.Source: §3 · p. 10
3.1. Multi Source Assessment
- The 360-degree method collects feedback from colleagues and managers, and assessment values are stored as numerical competence data.The review describes a typical team as the assessee, three colleagues, and the immediate manager; weighted averages support higher-level competence values and job-specific weights.Source: §3.1 · p. 11
3.2. Self-Assessment
- Self-assessment uses expert-prepared multiple-choice statements to measure job knowledge that certificates or documents cannot assess.Question weights sum to one, and weighted mean answers provide level-3 competence values from which higher levels are calculated.Source: §3.2 · p. 12
4. A Mathematical Model of Competence Assessment
The model represents acquired and job-required competences in a shared hierarchy, weights job requirements, and compares the two profiles to assess suitability and qualification gaps.
4. A Mathematical Model of Competence Assessment
- The assessment model combines acquired competence data (ACD), requested competence data (RCD), and job-specific prioritization weights (PoC) to support suitability assessment.The combined data feed algorithmic steps for determining how available employees or applicants fit a specific job.Source: §4 · pp. 12, 14
- ACD scores are marked from 1 to 5 and aggregated bottom-up from level-3 competences to levels 2 and 1.The PIS tree contains 48 level-3, 12 level-2, and 3 level-1 competence categories; level-2 scores can use weighted aggregation, including equal weights of 1/4.Source: §4 · pp. 12–13
- PoC weights express the relative importance of competences for a position, using Hierarchical Cumulative Voting to allocate fixed totals from higher to lower levels.For ComProFITS, weights are assigned at levels 1 and 2.Source: §4 · p. 13
4.1. Gap function
- The gap function compares actual ACD scores with requested RCD scores to quantify competence deviations for the assignment problem.The paper names simple, absolute, and squared gap functions as examples.Source: §4.1 · p. 15
4.2. Qualification Space
- Qualification Space plots each candidate’s weighted over-qualification (SOQ) against under-qualification (SUQ), both calculated using the simple gap function.The axes provide a readable visual representation of qualification differences.Source: §4.2 · p. 15
- In Qualification Space, points above the diagonal indicate over-qualification, while points below indicate under-qualification.The example identifies the candidate farthest vertically from the reference line as having the least qualifications for the job.Source: §4.2 · p. 15
- Mean Simple Gap (MSG) averages SOQ and SUQ across level-2 competences, while Mean Absolute Gap (MAG) averages their absolute values.These measures quantify gap information represented in the Qualification Space plot.Source: §4.2 · p. 16
SUQ SOQ
The assessment phase compares candidate competence profiles with a position’s requirements, using designed comparisons and the Scott–Knott procedure to rank and cluster candidates. Gap indicators also give geometric summaries of competence differences.
SUQ SOQ
- The total single-gap numerator corresponds to distances from an assessee point to the diagonal, while the absolute-gap numerator is its Manhattan distance from the origin.Figure 3 labels the plots as Total Single Gap and Total Absolute Gap indicators.Source: SUQ SOQ · pp. 16–17, Figure 3 · p. 17
4.3. Assessment Phase through a Multiple-Comparisons Algorithm
- The assessment phase ranks and clusters candidates by comparing acquired competence data with the requirements of a specific position.The framework uses design-of-experiments principles and multiple-hypothesis testing.Source: §4.3 · p. 17
4.3.1. Design of Experiments
- The repeated-measures design treats level-2 competences as experimental units, candidates as treatments, and weighted single-gap scores as the response.It uses a randomized complete block design, with level-2 sub-competences as blocks to account for variation among them.Source: §4.3.1 · pp. 17–18
4.3.2. Ranking and Clustering Algorithm.
- The Scott–Knott algorithm forms non-overlapping homogeneous candidate groups, rather than identifying only one qualified candidate.Candidates first pass predefined eligibility criteria; those below minimum requirements are excluded from ranking.Source: §4.3.2 · pp. 18–19
- The Scott–Knott procedure tests whether candidate mean gap scores differ, then recursively splits groups when the test is significant.The resulting groups represent candidates with statistically differing competence profiles for the target position.Source: §4.3.2 · pp. 18–19
5. Discussion on Practical and Test Results
ComProFITS operationalizes competence assessment in a role-based web application, with a hierarchical competence data model and layered architecture; its TECNALIA validation applies the model to 11 candidates.
5. Discussion on Practical and Test Results
- Employees can be assessed through a five-person 360-degree process or direct supervisor assignment, with level-3 competence values feeding job-specific comparisons and PDF reports.Job importance terms map to values from 5 to 1, and weights for competences in the same category and level sum to 100.Source: §5 · pp. 19–20
5.1. Data Model used for the implementation
- The data model represents the competence hierarchy in a self-referencing table; level-3 assessments are recorded, while higher-level values are calculated from them.Calculated higher-level values are not stored, avoiding potential inconsistencies; job-specific competence requirements and their importance and weights are also recorded.Source: §5.1 · pp. 21–23
5.2. ComProFITS software architecture
- The Java Enterprise Edition application uses a layered architecture, with Java Server Faces, Enterprise Java Beans, and a database layer; it interfaces with R for statistical calculations.The architecture separates presentation, business logic, and data handling layers.Source: §5.2 · pp. 23–24
5.3. Empirical validation of the mathematical approach to competence assessment
- The validation used real, anonymized TECNALIA data from over 200 employees, then analyzed acquired and job-required competence profiles for 11 candidates.A department head set level-1 and level-2 job-profile weights using hierarchical cumulative voting.Source: §5.3 · pp. 24–25
- F(10, 110) = 43.144, p < 0.001 for candidate differences in mean gap scores; SK ranked candidates and clustered statistically similar mean gaps.The treatment effect had generally high effect size; Table 11 presents the ranking and clusters.Source: §5.3 · pp. 28–29, Table 11 · p. 30
- Candidates 4 and 10 were most overqualified, while candidates 1, 5, 9, 11, and 8 formed the cluster closest to equilibrium.The preferred group depends on company policy: favoring the most qualified points to candidates 4 and 10, while minimizing the gap points to the near-equilibrium cluster.Source: §5.3 · pp. 30–31
- The participating manager agreed with reported competence gaps in every case after one disagreement was traced to and corrected as a data-entry mistake.The manager reviewed the generated employee PDFs and then agreed with the corrected result.Source: §5.3 · p. 31
6. Conclusions and Outlook
On real HR data, the authors report that an industrial partner confirmed the test-phase accuracy of algorithms that classify job seekers by fit. They note that assessments can be reused across job applications and call for testing the algorithms in other contexts.
6. Conclusions and Outlook
- On real HR data, Scott-Knott clustering groups job seekers as under-qualified, over-qualified, or best-fit for a job; an industrial partner confirmed test-phase accuracy.Source: §6 · p. 32
- Assessments are performed once per person and reused across recruitments and job applications; jobs need not assess every category, and certificates can prove degrees or languages.Source: §6 · p. 32
- The authors call for testing algorithms in other domains, studying collective competence, and extending ComProFITS through social-media and big-data use and cloud deployment.Source: §6 · p. 32