Submitted:
09 March 2026
Posted:
13 March 2026
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Abstract
Keywords:
1. Introduction
2. Methods
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- centroid-based methods (k-means), assuming clusters with approximately spherical geometry,
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- hierarchical methods (Ward), modelling nested structures and minimising within-cluster variance,
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- graph-based methods (spectral clustering), identifying clusters based on neighbourhood structure in the data,
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- probabilistic mixture models (Gaussian Mixture Models [GMM]), allowing for soft assignment of observations to profiles.
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- - number of profiles,
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- - - profile weight (∑πₖ = 1),
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- - component distribution,
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- - component parameters.
- Data preparation – In the first step, items belonging to the shortened versions of the QQ and PQ scales and the UWES-9 scale were selected. Composite indicators (means) were then computed for QQ and PQ and – depending on the analytical variant – either the overall mean for UWES-9 or the means for its three subscales (VIG, DED, ABS). Only observations complete with respect to all profile variables were included in clustering (listwise deletion for missing data in QQ/PQ/UWES).
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Construction of the feature space – The pipeline was implemented in two variants of the feature space:
- a)
- 3D variant: (QQ, PQ, UWES),
- b)
- 5D variant: (QQ, PQ, VIG, DED, ABS).
- 3)
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Estimation of clustering models across a grid of K – For each feature space, a set of algorithms representing distinct geometric and probabilistic assumptions was estimated:
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- k-means (clusters with approximately spherical geometry),
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- hierarchical clustering using Ward’s method (AgglomerativeClustering, linkage = ward),
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- graph-based spectral clustering (SpectralClustering; affinity = nearest_neighbors, assign_labels = kmeans; number of neighbors ,
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- Gaussian Mixture Models (GMM) with four covariance structure variants: full, diag, tied, and spherical (n_init = 5).
- 4)
- Preparation for solution comparison – For each combination (algorithm × K × feature space), cluster labels were obtained (for GMM: maximum a posteriori assignment), along with a full set of segmentation quality metrics. These metrics constituted the basis for the multi-criteria selection of the final solution in Step 6 (separation measures and, for GMM, additionally AIC/BIC).
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- Silhouette index,
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- Davies–Bouldin index,
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- Calinski–Harabasz index.
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- ,
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- .
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- mean values of the indicators are computed within clusters,
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profiles are interpreted as configurations of three mechanisms:
- ○
- boundaries (QQ),
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- exhaustion (PQ),
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- energy (UWES).
3. Results
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- QQᵢ – mean of items from the shortened quiet quitting scale,
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- PQᵢ – mean of items from the shortened passive quitting scale,
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- UWESᵢ – mean of UWES-9,
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- additionally, subscales were calculated: vigour, dedication, and absorption.
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- 3-dimensional variant: (QQ, PQ, UWES),
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- extended 5-dimensional variant: (QQ, PQ, VIG, DED, ABS).
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- Profile 0 – Boundary Setters – This profile is characterised by elevated quiet quitting combined with moderate passive quitting and moderate engagement. It reflects a strategic limitation of work input while maintaining relatively stable occupational functioning, where withdrawal primarily serves as a boundary-regulation mechanism.
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- Profile 1 – Active Enthusiasts – This profile comprises employees with the lowest levels of withdrawal and the highest engagement. Low QQ and PQ values combined with very high UWES indicate a reference configuration of high energy, dedication, and active organisational functioning.
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- Profile 2 – Disengaged Withdrawn – A profile of extreme withdrawal, characterised simultaneously by very high quiet quitting and passive quitting and very low engagement. This configuration indicates the concurrent operation of boundary-regulation and exhaustion mechanisms, constituting the most organisationally risky profile.
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- Profile 3 – Passive Exhausted – This profile is characterised by high passive quitting combined with relatively low quiet quitting and reduced engagement. Withdrawal in this case is primarily energy-related and associated with exhaustion rather than deliberate limitation of work input.
4. Discussion of Results
5. Conclusion
Conflicts of Interest
References
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| Algorithm | K | Silhouette | Davies–Bouldin | Calinski–Harabasz | BIC | AIC |
|---|---|---|---|---|---|---|
| GMM (spherical) | 4 | 0.344 | 0.953 | 575.47 | 8171.84 | 8077.85 |
| GMM (tied) | 4 | 0.335 | 0.943 | 539.08 | 8149.44 | 8045.56 |
| KMeans | 4 | 0.333 | 0.960 | 593.67 | - | - |
| GMM (diag) | 4 | 0.328 | 0.985 | 535.91 | 8096.98 | 7963.41 |
| Spectral (NN) | 4 | 0.321 | 1.038 | 574.54 | - | - |
| GMM (spherical) | 5 | 0.314 | 0.954 | 508.86 | 8149.99 | 8031.27 |
| KMeans | 5 | 0.311 | 1.008 | 544.47 | - | - |
| GMM (diag) | 6 | 0.309 | 1.011 | 502.21 | 8086.92 | 7884.10 |
| GMM (spherical) | 7 | 0.308 | 1.000 | 517.89 | 8098.38 | 7930.18 |
| GMM (tied) | 6 | 0.305 | 0.938 | 464.28 | 8073.40 | 7929.94 |
| KMeans | 6 | 0.304 | 1.030 | 535.50 | - | - |
| GMM (spherical) | 6 | 0.304 | 0.977 | 501.23 | 8127.59 | 7984.13 |
| Algorithm | K | Silhouette | Davies–Bouldin | Calinski–Harabasz | BIC | AIC |
|---|---|---|---|---|---|---|
| GMM (tied) | 4 | 0.285 | 1.117 | 496.29 | 11196.55 | 11008.56 |
| Spectral (NN) | 4 | 0.283 | 1.142 | 556.48 | - | - |
| KMeans | 4 | 0.283 | 1.143 | 583.38 | - | - |
| GMM (tied) | 5 | 0.283 | 1.095 | 447.17 | 11160.26 | 10942.59 |
| GMM (spherical) | 4 | 0.276 | 1.138 | 562.39 | 12169.59 | 12036.02 |
| Agglomerative Ward | 4 | 0.272 | 1.136 | 491.80 | - | - |
| GMM (tied) | 6 | 0.264 | 1.141 | 408.26 | 11123.21 | 10875.86 |
| KMeans | 5 | 0.261 | 1.202 | 534.24 | - | - |
| KMeans | 6 | 0.259 | 1.198 | 496.89 | - | - |
| GMM (diag) | 4 | 0.257 | 1.222 | 546.65 | 11827.22 | 11614.50 |
| Spectral (NN) | 5 | 0.256 | 1.187 | 512.35 | - | - |
| Spectral (NN) | 6 | 0.256 | 1.198 | 479.49 | - | - |
| Profile | n | % |
|---|---|---|
| Profile 0 | 567 | 54.5 |
| Profile 1 | 134 | 12.9 |
| Profile 2 | 115 | 11.1 |
| Profile 3 | 224 | 21.5 |
| Profile | PQ | UWES | |
|---|---|---|---|
| Profile 0 | 3.67 | 2.68 | 3.15 |
| Profile 1 | 2.08 | 1.65 | 5.36 |
| Profile 2 | 4.23 | 3.82 | 1.06 |
| Profile 3 | 2.30 | 3.74 | 2.87 |
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