2.1.1. Total sample (Study 1 and Study 2).

The total sample comprised participants, with ages ranging from 15 to 45 years (M = 21.2, SD = 5.6 years). The sample consisted of 535 males (57.8%), aged 15–45 years (M = 20.9, SD = 5.8), and 390 females (42.2%), aged 15–43 years (M = 21.1, SD = 4.8). Sports experience among the participants ranged from one year in specific sport to 35 years (M = 7.2 years, SD = 4.8 years), and training intensity ranged from 1 to 25 hours per week (M = 7.8 hours/week, SD = 4.8 hours/week); 490 (53.0%) participants represented Team sports (356 males, 134 females) and 435 (47.0%) participants represented Individual sports (179 males, 256 females). Sport Achievement Level initially was classified in three categories: elite (n = 46, 5.0%), pre-elite (n = 433, 46.8%), or non-elite (n = 446, 48.2%). Together, athletes represented 84 different sports, including basketball (n = 107), hockey (n = 96), football (n = 94), volleyball (n = 65), athletics (n = 56), fitness (n = 47), handball (n = 42), floorball (n = 41), luge sport (n = 31), swimming (n = 28), orienteering (n = 27), judo (n = 15), sports dances (n = 15), table tennis (n = 13), rugby (n = 13), weightlifting (n = 12), boxing (n = 10), artistic gymnastics (n = 10), cross-country skiing (n = 9), tennis (n = 9), karate (n = 9), cycling (n = 8), beach volleyball (n = 8), equestrian sport (n = 8), alpine skiing (n = 7), gymnastics (n = 6), kayaking (n = 6), taekwondo (n = 6), figure skating (n = 6), climbing sport (n = 5), running (n = 5), shooting (n = 5), biathlon (n = 4), bodybuilding (n = 4), curling (n = 4), triathlon (n = 4), road cycling (n = 4), disc golf (n = 4) and, other (n = 82).

Athletes’ competitive status was categorized based on training intensity and performance criteria. Elite athletes were defined as those who trained at least 8 sessions per week (or > 12 hours weekly) and had achieved at least one high-level competitive result, such as a podium at a national championship, a top placement in a regional league or participation in a major international competition (European Championships at junior or senior level, World Cup, World Championships, or Olympic Games). All athletes in the elite category also had a minimum of five years of sport-specific experience. pre-elite athletes trained at least 5 times per week (≈7.5 hours weekly) and had competitive experience at the national championship level (in any age category), in regional leagues, or at university-level events such as Universiade. Non-elite athletes engaged in a minimum of 2 training sessions per week (≈3 hours weekly), and their competition experience was limited to lower- or mid-tier competitions.

Missing data per participant did not exceed 5% and deletion was applied to maintain data integrity. Although the sample was broad and diverse, it represents a convenience sample of active athletes rather than a random selection from the national athlete population. The inclusion of participants aged 15 years and older reflects the study’s aim to examine personality measurement across key developmental stages in sport. Age-related differences were explicitly examined and addressed through stratified analyses and normative procedures rather than assumed equivalence across age groups.

2.1.2. Normative sample (Study 1).

Participants from the total sample (N = 925) were stratified based on three criteria: gender (male/female), age (15–17, 18–20, 21–29, 30–45), and sport type (individual/team). The respondent distribution across these strata in the Analysis Sample was highly uneven. Since no official population data on the distribution of athletes by these specific characteristics was available, and because the primary aim of norm development was comparability rather than population representativeness, equal number of respondents per stratum were selected to ensure maximum structural uniformity and direct comparability across groups. This approach reflects a deliberate methodological trade-off between statistical balance and population representativeness. The equal-cell strategy was selected to ensure stable and comparable normative estimates across demographic strata, while recognizing that the resulting norms should be interpreted as balanced reference standards rather than direct representations of the natural distribution of athlete characteristics in the broader population.

Following the principle of the smallest available cell size, the final sample size for most strata was determined by the number of participants in the smallest available group, which was the female 15–17 age group in team sports (n = 32). To ensure a uniform representation across all other strata, a total of 32 participants were randomly selected from each of the remaining strata that had more than 32 available respondents. The randomization was performed using an online random number generator (e.g., randomizer.org), ensuring that each participant within a stratum had an equal chance of being selected for the final sample.

An exception was made for the 30–45 age group, which had a significantly smaller number of participants. To ensure sufficient power for the gender-specific norms, it was decided to use the highest number of available respondents for each gender within this age group. This meant including all 21 available male respondents in each of their respective sport type strata. For female respondents, due to the low number of participants in team sports (n = 5), a proportional number of participants (n = 5) were randomly selected from the female individual sports group to maintain proportional representation within the female 30–45 age group. This decision prioritized obtaining the largest possible sample size for each gender while preserving the sport type balance within the older female group. This approach prioritized the largest feasible sample size within older age strata while maintaining internal consistency of stratification criteria.

Therefore, to ensure minimally sufficient representation (or adequate sample sizes) within age strata for the development of both gender- and age-specific norms where required, a decision was made to consolidate the initial four age groups into two broader categories: adolescents/young adults (15–20 years) (combining 15–17 and 18–20 age groups) and Adults (21–45 years) (combining 21–29 and 30–45 age groups). This approach allowed for the standardization of LPI-v3s scores for males and females, with the flexibility to implement age-based norms for specific scales identified as being significantly influenced by age (as detailed in Section 2.2.3). The final composition of the normative sample is detailed in Appendix A Table S1 in S1 Appendix, which illustrates the initial and final counts for each stratum. The data from this normative sample (n = 436) were utilized to develop and offer a reliable measure of the abbreviated version of the LPI-v3s and establish the necessary normative scores for the athlete population (see Appendix A Table S2 in S1 Appendix).

2.1.3. Final analytical sample and data quality control (Study 2).

The total sample (N = 925) was subsequently subjected to a final data quality control procedure to form the Final Analytical Sample used for the main predictive analyses. Crucially, scores on the Lie Scale (M) from the shortened version of the LPI-v3s (as detailed in Section 2.2.2.) were utilized as a criterion for data exclusion to ensure the validity of the personality profile analysis and minimize the impact of socially desirable responding within the final analytical sample. Participants who scored above the established cutoff on the Lie Scale (the T score > 60), commonly interpreted as indicating potentially distorted self-presentation, were identified as providing potentially invalid data. This threshold corresponds to scores exceeding one standard deviation above the normative mean and is widely used as a conservative criterion for data quality control. To evaluate the robustness of this decision rule, sensitivity checks were conducted using slightly alternative cutoff thresholds. These analyses indicated that the overall pattern of predictive results and model estimates remained substantively unchanged, suggesting that the exclusion criterion did not materially influence the main findings. Consequently, a total of 160 participants (≈17.3% of the sample) were excluded.

The final Analytical sample used for all subsequent statistical analyses (prediction of sport achievement) consisted of 753 participants (437 males and 316 females). Detailed distributions by sport type, performance level, and gender are presented in Appendix A Table S3 in S1 Appendix.

2.2.1. The original version of the Latvian Personality Inventory (LPI-v3).

The Latvian Personality Inventory (LPI-v3) is a 100-item self-report questionnaire used to assess six personality factors: Neuroticism, Extraversion, Openness to Experience, Agreeableness, Conscientiousness, and Honesty-Humility [29]. The instrument is hierarchically structured, also measuring four narrower personality traits (facets) within each of the six factors. Each of the six factors is measured by 16 items, while each facet (subscale) is measured by 4 items. An additional 4 items form a Lie scale, which assesses the tendency toward socially desirable responding. Participants respond using a 5-point Likert scale ranging from 1 (“Does not correspond to me”) to 5 (“Corresponds to me”). Scale scores for both the personality factors and the facets were derived by summing the scores of the respective items, dividing the sum by the number of items (to yield the mean score), and finally multiplying this mean score by 10. The resulting scaled scores range from 10 to 50. Higher scores indicate a greater expression of the trait as defined by the scale name.

Previous research in general population samples has reported satisfactory internal consistency and an interpretable factor structure for the LPI-v3 in the general Latvian population sample. Internal consistency (Cronbach’s alpha, N = 1294) for the factor scales range from 0.81 to 0.88, and for the facet scales, from 0.61 to 0.86. The inventory also shows high test-retest reliability [29]. Retest coefficients (n = 166; mean interval of 19 weeks) ranges from 0.85 to 0.90 at the factor level and from 0.68 to 0.85 at the subscale level [28]. The complete LPI-v3 questionnaire (Latvian) and scoring key are provided in Appendix B.

2.2.2. Shortened version of the LPI-v3 (LPI-v3s).

The data from the normative sample (n = 436) was utilized to develop an abbreviated version of the LPI-v3 empirically derived and evaluated for use in the athlete population represented in this study. The primary objective of developing this shortened version was to ensure it achieved measurement invariance across gender groups, which is a prerequisite for correctly comparing mean scores between male and female athletes. Furthermore, the short version was designed to be robust enough to allow for the development of gender-specific and, where necessary, age-specific norms tailored to this athletic population (Study 1). The subsequent analyses for predicting sports achievement status were based on the T-scores derived from the empirically evaluated short version of LPI-v3s (Study 2).

To ensure accurate interpretation of personality traits, the necessity for developing separate age-based norms (adolescents/young adults [14–19] vs. adults [21–45]) was examined. This decision was informed by a preliminary analysis of the normative sample (n = 436), with the goal of detecting systematic variation of traits across the lifespan. The analysis was conducted separately for males and females.

A scale was deemed to require age-specific norms if: (1) Age correlated statistically significantly with the scale score (p < 0.05); and (2) The Independent Samples t-test or Mann-Whitney U test revealed a statistically significant mean difference (p < 0.05) between the 15–20 age group and the 21–45 age group, with a corresponding effect size of at least a small to moderate magnitude (e.g., Cohen’s d or r ≥ 0.20). Scales meeting both criteria were subsequently normed separately by age group, resulting in four distinct normative tables: (1) male adolescents/young adults, (2) male adults, (3) female adolescents/young adults, and (4) female adults. Fig 1 provides a visual summary of the sequential steps and methodological structure for the two-study research design, including sample flow, psychometric analyses, and predictive modeling. Raw-to-T conversions and continuous norm tables are available in Appendix C (Excel).

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Fig 1. Overview of the research process (independent sample flow, psychometric evaluation, and predictive validity analysis).

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2.4.1. Study 1: Psychometric evaluation and norm development.

Factorial structure was evaluated iteratively. Initially, the model fit was tested on the full normative sample (n = 436) using hierarchical confirmatory factor analysis (HCFA). This was based on a polychoric correlation matrix and the diagonally weighted least squares (DWLS) estimator, which is robust for ordinal data. To identify a parsimonious structure, exploratory factor analysis (EFA) was subsequently conducted, employing principal axis factoring with Promax rotation at the item level and Varimax rotation at the scale level. The final configuration was then validated using the same HCFA procedure. To reduce the risk of sample-dependent optimization, item removal and model re-specification were guided by a combination of statistical criteria and theoretical interpretability, rather than solely by modification indices. All model refinement decisions were evaluated for conceptual consistency with the underlying personality framework, and the final structure was retained only when improvements in model fit were accompanied by stable factor interpretation and internal consistency. The sequential analytical steps and decision logic underlying the factorial structure evaluation and model refinement process are summarized in Fig. 2.

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Fig 2. Analytical decision flow for factorial structure evaluation and model refinement in Study 1.

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Model fit was evaluated using the Comparative Fit Index (CFI), Tucker–Lewis Index (TLI), Root Mean Square Error of Approximation (RMSEA, 90% CI), and Standardized Root Mean Square Residual (SRMR). Thresholds for acceptable fit were CFI and TLI ≥ 0.90, RMSEA ≤0.08, and SRMR ≤0.08. Given the complexity of hierarchical personality models and the number of observed indicators, slightly lower CFI/TLI values were interpreted cautiously and in conjunction with other fit indices and substantive interpretability, consistent with recommendations by previous research [30].

Measurement invariance across gender groups (male vs. female athletes) was examined using multigroup CFA. Configural, metric, and scalar invariance were tested sequentially. Invariance was supported when ΔCFI < 0.01 and ΔRMSEA < 0.015.

To determine the need for age-specific norms, Pearson’s correlations were calculated between age and personality-scale scores separately for males and females. Scales showing significant correlations (p < 0.05) were further compared between age groups (15–20 vs. 21–45 years) using independent-samples t-tests or Mann–Whitney U tests. Effect sizes were expressed as Cohen’s d (parametric) and rank-biserial r (non-parametric), with values ≥ 0.20 interpreted as practically meaningful.

Continuous norming was performed using the cNORMj package in Jamovi [31], supplemented by conventional T-score transformations (M = 50, SD = 10) to facilitate comparability across methods. The quality of norm models was verified by coefficients of determination (R² ≥ 0.996), indicating empirical equivalence between continuous and conventional norms. To minimize the risk of overfitting during model refinement, item removal decisions were guided by predefined statistical thresholds (factor loading < 0.35, internal consistency) and theoretical interpretability rather than post-hoc model fit optimization. Measurement invariance testing across athlete groups further supported the structural stability of the model. However, because no independent validation sample or split-sample cross-validation was available, the final measurement structure should be interpreted as provisional rather than definitively confirmed. The use of the same stratified normative sample for exploratory model refinement and subsequent confirmatory testing may have introduced some degree of sample-specific optimization; therefore, replication in independent athlete samples is required before stronger claims about the generalizability of the factorial structure can be made.

2.4.2. Study 2: Predictive validity (trait and factorial level analysis).

Predictive validity of the LPI-v3s was evaluated using hierarchical binary logistic regression. Analyses were performed at two hierarchical levels: (1) Trait-level model: Step 1 included all trait-scale T-scores and sport type (Team = reference). Step 2 added interaction terms (Sport Type × Personality Trait) to test for moderating effects; (2) Factor-level model: A parallel analysis was conducted at the broader personality factor level.

Model performance was evaluated via Nagelkerke R², overall classification accuracy, and Receiver Operating Characteristic (ROC) curves. Discrimination was interpreted using the Area Under the Curve (AUC), with thresholds of 0.60 = fair, 0.70 = good, ≥ 0.80 = very good. Sensitivity and specificity were calculated using a 0.50 cut-off. All predictive analyses were interpreted as exploratory and descriptive, given the measurement-development focus of Study 1.

3.1.1. Initial model fit analysis.

Considering that the LPI-v3 was developed and standardized on a general population sample aged 18 and older, and this study’s data were collected from an athlete sample aged 15 and older, it was first necessary to confirm that the inventory’s theoretical model was appropriate for this dataset before calculating standardized scores. The model fit was initially tested on the full normative sample (n = 436) using hierarchical confirmatory factor analysis (HCFA).

The initial hierarchical model showed a poor fit to the data. The chi-square statistic was significant, χ² (4424) = 7484, p < .001, which is common in large samples. The Comparative Fit Index (CFI = 0.728) and Tucker–Lewis Index (TLI = 0.719) were below the acceptable threshold (> .90), indicating insufficient model fit. The Standardized Root Mean Square Residual (SRMR = 0.087) also exceeded the recommended limit (< 0.08), whereas the Root Mean Square Error of Approximation (RMSEA = 0.040; 90% CI [0.038, 0.041]) met the acceptable standard, suggesting a reasonable approximation of the population covariance matrix. Taking together, these indices indicated that the initial measurement model did not adequately represent the relationships among the observed variables in the normative sample. Therefore, further modifications were required to improve overall fit.

3.1.2. Development and evaluation of modified models (Models 1–4).

To improve model fit, several modified models were sequentially tested, aiming to enhance the fit indices while retaining the original theoretical model as much as possible. This sequential process was guided primarily by the analysis of standard estimates of factor loadings and finally by modification indices.

In the first modified model, the O2 (Tolerance) scale was excluded from O (Openness) factor, as its standard estimate on the O factor was 0.153, which is too low. Additionally, eight other items were removed (J41 from the E2 (Joyfulness) scale, J3 from the H1 (Sincerity) scale, J59 from the H3 (Modesty) scale, J78 and J91 from the H4 (Fairness) scale, J64 from the N3 (Depressivity) scale and J37 because their standard estimates representing factor loadings were below 0.35. The fit indices improved slightly but as seen in Appendix A Table S4 in S1 Appendix, all indices except for RMSEA remained inadequate.

In the next step, using the same procedure, one more item was identified and removed: J15 from the H1 (Sincerity) scale. The fit indices for this second modified model also improved slightly but were still inadequate. Therefore, the model modification process continued.

Analyzing the second model, all items showed appropriate factor loadings, but four scales (A1: Flexibility, H3: Modesty, H4: Fairness and O2: Tolerance) showed unsatisfactory internal consistency metrics (Coefficient α and ω in the range of 0.381 to 0.591), indicating low reliability. Consequently, it was decided to exclude these scales from further analysis completely. This resulted in Modified Model 3. Although all fit indices for this model improved slightly (see Appendix A Table S4 in S1 Appendix), they still indicated inadequate model fit, with the exception of the RMSEA.

Analysis of the third modified model’s results showed that the H2 (Greed-Avoidance) scale’s factor loading in the H factor was inappropriate (λ = 0.287), leading to its removal from the H factor. However, since only one scale was left in this factor, it was also removed from the higher-order factors. But two separate scales (H1 and H2) were left in the model, which did not fit into any of the higher-order factors. Additionally, it was found that the J34 item had a reduced factor loading (λ = 0.366), and it was also excluded. Furthermore, at this stage, the proposed modification indices were carefully analyzed, and the model was supplemented with several relaxations, allowing four subscales to correlate with the N factor, one with the A factor, three with the C factor, and four with the O factor. Four correlations between the subscales were also permitted. All permitted correlations are theoretically justified and reflect complex relationships between personality factors and their constituent traits. As a result, the fourth modified model was obtained.

Despite slight improvements, this fourth modified model still revealed an unsatisfactory fit for the proposed model (CFI = 0.830) on the overall normative sample. This inadequate model fit was more pronounced in the male athlete subsample, where the CFI was below the 0.80 threshold, but a little better in the female subsample (CFI = 0.832) (see Appendix A Table S4 in S1 Appendix). A more detailed analysis revealed that in the male subsample, three items (J100 from O4: Creativity, J52 from N3: Depressivity, and J28 from H2: Greed-Avoidance) showed excessively low factor loadings, and some scales dropped from their factors (the E3 scale and O1: Aesthetic Interests scale). However, subsequent modifications to the model, including those based on modification indices, did not lead to significant improvements. The results remained illogical, at least with respect to some items and scales in the male subsample. Models 1–4 were tested sequentially to improve fit while retaining the original structure as far as possible. Respecifications were guided by standardized loadings (removing indicators < 0.35), internal consistency of facet scales, and only then modification indices. Across Models 1–4, fit improved but remained suboptimal, particularly in the male subsample (Table S4 in S1 Appendix). Therefore, we proceeded with an EFA-guided re-specification.

3.1.3. EFA-guided model and final HCFA (Model 5a).

To better understand the underlying factor structure of the LPI-v3s and address the poor fit of the initial a priori models, an exploratory factor analysis (EFA) was performed on the overall normative sample (N = 436). The EFA utilized a polychoric correlation matrix and the Principal Axis Factoring method. The number of factors was determined using Kaiser’s criterion (eigenvalues > 1), which yielded a 14-factor solution for the personality traits, plus an additional 15th factor representing the Social Desirability (Lie – coded as M scale) scale (see Appendix A Table S5 in S1 Appendix). Promax rotation was applied to allow for correlations between factors, as facet-level personality scales are theoretically expected to overlap.

The EFA results revealed a more parsimonious structure, explaining 53.7% of the total variance, yet demonstrating significant deviations from the original 24-facet model. Seven scales were entirely eliminated due to poor psychometric performance, theoretical inconsistency, or problematic mergers: H1 (Sincerity), H3 (Modesty), H4 (Fairness), A1 (Flexibility), E4 (Social Boldness), O2 (Social Tolerance), and C3 (Perfectionism). Specifically, E4 was removed due to cross-loadings with O4 (Creativity), while C3 merged unacceptably with O3 (Inquisitiveness). In the Honesty-Humility domain, only the H2 (Greed-Avoidance) scale remained viable.

A significant structural shift occurred within the Neuroticism domain. While the original LPI-v3 designates four distinct facets (Anxiety, Vulnerability, Depression, and Diffidence), the EFA indicated that these traits merged into a single, unified factor—the Anxious-Insecurity scale (N1_new). This newly formed composite scale represents the broader Neuroticism domain and consists of nine items: all four items from the original Vulnerability (N2) facet, two items from Depression (N3), two items from Diffidence (N4), and one item from Anxiety (N1).

Regarding the final scale lengths, the Anxious-Insecurity scale consists of nine items, while five other personality facets and the Lie (M) scale retained all four of their original items. The remaining eight facets were reduced to three items each.

The internal consistency, measured by Cronbach’s alpha, was evaluated in light of these reductions. While scales with only three items exhibited slightly lower alpha coefficients, this decrease is mathematically consistent with the reduced item count, as internal consistency is inherently sensitive to scale length. Given the multidimensional nature of the LPI-v3s and its intended use for group-level comparisons and norming in athletic populations, these reliability levels were considered acceptable. This refined 15-factor measurement model served as the basis for the final Model 5a, subsequently subjected to confirmatory factor analysis and measurement invariance testing.

3.1.4. Second-order factor analysis and domain structure.

To explore the higher-order structure of the LPI-v3s and determine how the identified facets group into broader personality domains, a second-order EFA was conducted. Given that the facet scores represent interval-level data, the analysis was based on a correlation matrix. The Principal Axis Factoring extraction method was employed, followed by a Varimax rotation to achieve a simple, independent factor structure. The optimal number of factors was determined using Parallel Analysis, which suggested a six-factor solution.

While the analysis generally supported the expected multi-factor structure, explaining 43.7% of the total variance, several deviations from the original taxonomies were observed (see Appendix A Table S6 in S1 Appendix). A notable finding concerned the E3 (Sensation-seeking) scale, which failed to load significantly on the general Extraversion (E) factor, suggesting that for this specific athletic population, physical risk-taking and excitement-seeking may function independently from social extraversion. Furthermore, the Honesty-Humility domain was significantly weakened; as H2 (Greed-Avoidance) was the only remaining facet of this factor, it lacked the necessary saturation to form an independent, stable H-domain. Consequently, the sixth factor identified by the Parallel Analysis was deemed uninterpretable and psychometrically unstable, leading to its exclusion from the final domain-level model.

The analysis also highlighted the complex nature of the A4 (Composure) scale. In line with the Five-Factor Model (FFM), this scale demonstrated a higher factor loading on the Neuroticism (N) factor when reversed, alongside the newly unified Anxious-Insecurity scale (N1_new). However, it also maintained a substantial loading on the Agreeableness (A) factor, as originally intended in the HEXACO framework. To preserve the psychological richness of this trait and ensure internal consistency within both domains, a dual-loading scoring decision was implemented. Specifically, the scale is scored in its reversed form as a new Neuroticism facet, N2_new (Irritability), reflecting emotional volatility, while concurrently being scored in its original form within the Agreeableness domain to reflect interpersonal composure. This refined 15-factor measurement model (including the Lie scale) served as the basis for the final Model 5a, which was subsequently subjected to confirmatory factor analysis and measurement invariance testing.

3.1.5. Confirmatory factor analysis and model fit of the refined LPI-v3s.

Based on the EFA findings, a revised, shortened model was developed, comprising 53 items, 14 facets, and 5 higher-order factors and additional 4 items of validity scale (Lie scale) (not included in the CFA). This model was subsequently subjected to a hierarchical confirmatory factor analysis (CFA), designated as Model 5. To establish a baseline, the fit indices for this initial structural model were gathered. Following an evaluation of the modification indices and theoretical justifications, several correlations between specific scale residuals and factors were permitted (e.g., based on covariances > 0.35). This refined version, referred to as Model 5a, demonstrated a significantly improved fit to the data.

Although the CFI for Model 5a was 0.885 (see Table 1), it remained below the conventional threshold of 0.90. However, as Model 5a is significantly more parsimonious than the original version, it still retains considerable structural complexity. As noted by Marsh et al. [32,33] and McNeish and Wolf [34], psychometric instruments with a large number of scales and items often face difficulty in achieving the stringent benchmarks (CFI and TLI > 0.95) proposed by Hu and Bentler [30]. These authors argue that for complex personality constructs, fit indices around 0.80 or 0.85 can be considered acceptable. Given that the model was nearing the 0.90 threshold and provided a theoretically sound representation of the data, it was deemed suitable for further analysis.

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Table 1. Goodness-of-fit indices of the HCFA modified Model 5a.

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The primary objective of this CFA was to identify a measurement model suitable for measurement invariance testing a critical prerequisite for valid gender-based norming and comparisons of personality traits in athletic performance. Model 5a’s fit indices for the overall normative sample and the separate male and female subsamples are presented in Table 1. The indices were higher in the female subsample compared to the male subsample (CFI = 0.878 and 0.849, respectively), though both were lower than in the combined normative sample. Nevertheless, these values represented a significant improvement over previous iterations and satisfied the minimum criterion of > 0.80, which is acceptable for such complex survey structures.

The decision to utilize the same stratified normative sample for both the EFA and the subsequent CFA was driven by the need to maintain the psychometric integrity of the gender- and age-balanced group required for norming. The full stratified sample provided the necessary statistical power to identify a stable structure and immediately verify its suitability for invariance testing. This approach ensured that the resulting measurement model provided a robust foundation for the planned gender-based comparisons. Fit indices for the initial refined model (Model 5), the final retained model (Model 5a), and its performance across the overall, male, and female subsamples are presented in Table 1. For readability, the key result in Table 1 is the final retained Model 5a in the total normative sample, which showed improved but still moderate fit (CFI = 0.885, TLI = 0.876, RMSEA = 0.041, SRMR = 0.068). The male and female subgroup results are presented to demonstrate the stability of the retained model across gender groups, rather than as separate alternative models.

Due to its enhanced parsimony and improved, although not optimal, fit indices, Model 5a was adopted as a provisional measurement model for the LPI-v3s. This structure was deemed sufficiently robust to serve as the basis for subsequent measurement invariance testing and the development of normative data (Study 1), as well as for the predictive validity analyses conducted in Study 2.

3.1.6. Measurement invariance.

Factorial invariance was tested using multigroup confirmatory factor analysis (MG-CFA) to determine if the measurement model for the modified shortened version (Model 5a) of LPI-v3s was equivalent across male and female athlete samples. The analysis followed a hierarchical approach, starting with the least restrictive model and progressing to more restrictive models. The goodness-of-fit was evaluated using the chi-square statistic (χ²), degrees of freedom (df), comparative fit index (CFI), Tucker-Lewis Index (TLI), and the root mean square error of approximation (RMSEA) with its 95% confidence interval. A significant drop in fit for the more restricted models was assessed using the change in CFI (ΔCFI), with a value less than 0.01 considered acceptable [35,36].

The first step was to test for configural invariance, which assesses whether the factor structure is the same across both groups without imposing equality constraints on the model parameters. The results of the configural model indicated an acceptable, but not excellent, fit to the data (χ²(2552) = 3516; p < 0.001). The fit indices were CFI = 0.863, TLI = 0.852, and RMSEA = 0.042 [0.038; 0.045]. These results support the notion that the same number of factors and the same pattern of factor loadings were present in both male and female samples.

Following the establishment of configural invariance, metric invariance was tested by constraining the factor loadings to be equal across both groups. This model showed a slight deterioration in fit compared to the configural model (χ²(2603) = 3553; p < 0.001). The change in fit was minimal (Δχ²(51) = 37; ΔCFI = 0.002), which is below the recommended threshold of 0.01. This suggests that the factor loadings are equivalent across both male and female samples, supporting the comparability of the factor-item relationships between the two groups.

The final step was to test for scalar invariance by adding the constraint that the item interceptions are equal across both groups. This model provides the strongest test of measurement equivalence. The results showed a significant drop in model fit compared to the metric invariance model based on the chi square test (χ²(2741) = 3746; p < 0.001), nevertheless, the change in CFI was 0.008 (ΔCFI = 0.008), which is below the recommended threshold of 0.01. This suggests that the item interceptions are equivalent, allowing for direct comparison of latent mean scores between the groups. Based on the ΔCFI criterion, scalar invariance was supported (see Table 2), indicating that gender-based score comparisons are permissible within the present sample. However, this result should be interpreted in the context of the provisional measurement model and requires replication in independent athlete samples.

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Table 2. Sequential tests of measurement invariance across gender groups for the LPI-v3s.

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3.1.7. Gender differences and decision for gender norms.

To determine which scales require gender-specific norms, mean differences between male and female athletes were examined using the Mann-Whitney U test due to non-normality across most scales.

The analysis identified statistically significant differences (p < 0.05) in the central tendency (median) for six scales. However, only five scales demonstrated a meaningful effect size (r > 0.20): N1_new (Anxious Insecurity), N2_new (Irritability), N (Neuroticism), A4 (Composure), and O1 (Aesthetic Interests). The largest effect sizes were observed for N (r = 0.32) and N1_new (r = 0.29).

Based on the combined criteria of statistical significance and meaningful effect size, gender-specific norms were deemed necessary for the five identified scales. All remaining scales (including those that reached statistical significance but had r < 0.20) showed negligible differences between male and female athletes, suggesting that unified norms can be applied for these traits (see Table 3).

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Table 3. Mean differences and effect sizes between gender groups in the LPI-v3s normative sample.

https://doi.org/10.1371/journal.pone.0352794.t003

3.1.8. Age effect and decision for age norms.

Correlations with age (Criterion 1). To empirically determine the necessity of establishing age-based norms, Pearson correlational analyses were conducted between respondent age and all shortened version of the LPI-v3s scales’ scores within the normative sample, with analyses performed separately for the female and male subsamples. The results are detailed in (see Appendix A Table S7 in S1 Appendix).

Findings in the female subsample. Age was statistically associated with two factor-level scales and four facet scales in the female subsample. Consistent with general population trends, a negative, weak but statistically significant correlation was between age and Neuroticism (r = −0.18, p = 0.012). This relationship was reflected in the facet Anxious-Insecurity (r = −0.18, p = 0.009), suggesting that women tend to report lower levels of emotional instability or worry with increasing age. Similarly, Sensation-Seeking showed a small, significant decline with age (r = −0.19, p = 0.006). Conversely, a positive, weak but statistically significant correlation was found between age and Conscientiousness (r = 0.20, p = 0.005), which was primarily driven by the facet Orderliness (r = 0.19, p = 0.008), and weakly by Prudence (r = 0.14, p = 0.046).

Findings in the male subsample The male subsample displayed more numerous and often stronger correlations between age and personality traits, suggesting a greater influence of age on self-reported scores in this group. Positive, statistically significant correlations were found with the following factors:

1. Openness to Experience (r = 0.23, p < 0.001), which was largely accounted for by the facet Inquisitiveness (O3) (r = 0.28, p < 0.001).
2. Conscientiousness (r = 0.15, p = 0.022), which was largely accounted for by the facet Prudence (C4) (r = 0.22, p < 0.001), indicating increased cautiousness in decision-making with age.
3. The facet Greed-Avoidance (r = 0.31, p < 0.001) under the Honesty-Humility factor, which was the strongest correlation observed across all scales, indicating that male athletes report becoming substantially less status-conscious and more modest as they age.

Only two negative correlations in the male group were observed for the Agreeableness factor (r = −0.17, p = 0.08), which was largely accounted for by the facet Obedience (A3) (r = −0.18, p < 0.001), suggesting that older male athletes may be less inclined to defer to others or compromise compared to their younger counterparts.

Mean differences between age groups Following the correlational analysis which served as the first filtering criterion for age-specific norms, the second criterion for requiring age-specific norms was tested. Independent Samples t-tests (or the Mann-Whitney U test, based on normality assumptions) were performed only on those scales that had shown a statistically significant correlation with age in the respective gender subsamples. This step was necessary to confirm that the observed relationship translated into a meaningful mean difference (criterion) between the newly defined age groups: adolescents/young adults (15–20) and adults (21–45).

Prior to conducting mean difference analyses, assumptions of normality (Shapiro-Wilk test) and homogeneity of variances (Levene’s test) were examined for all scales demonstrating a significant correlation with age in their respective gender subsamples.

In the female subsample, Levene’s test indicated that the assumption of homogeneity of variances was met for all scales (p > 0.05). However, the normality assumption was violated for the Sensation-Seeking (E3) and Orderliness (C1) scales (p_Shapiro < 0.05). Consequently, mean differences for these two non-normally distributed scales were analyzed using the non-parametric Mann-Whitney U test, while the remaining scales were analyzed using the Independent Samples t-test (assuming equal variances).

A similar pattern was observed in the male subsample: Levene’s test confirmed the homogeneity of variances assumption for all correlating scales (p > 0.05). However, the Shapiro-Wilk test revealed a violation of the normality assumption (p_Shapiro < 0.05) for four facets: Prudence (C4), Obedience (A3), Inquisitiveness (O3), and Greed-Avoidance (H2). Therefore, the Mann-Whitney U test was applied to these four non-normally distributed scales, and the remaining scales were tested using the Independent Samples t-test (assuming equal variances).

Female subsamples mean differences. For the female subsample, five scales met the initial correlation criterion (p < 0.05). Subsequent mean comparison tests (Independent Samples -test or Mann-Whitney test, based on normality) confirmed that four out of five scales met the dual criteria for requiring age-specific norms (i.e., < 0.05 AND d or r ≥ 0.20) (see Appendix A Table S8 in S1 Appendix):

1. Neuroticism (t (200) = 3.35, p < 0.001, d = 0.49) and its facet Anxious-Insecurity (N1_new) (t (200) = 2.79, p < 0.006, d = 0.41) showed higher scores among younger women, indicating greater emotional stability with age.
2. Conscientiousness (t (200) = −2.97, p < 0.001, d = −0.43) and its facet Orderliness (C1) (U = 3775, p = 0.013, r = −0.20) showed higher scores among adult women, suggesting increased organization and diligence with age.

The Sensation-Seeking facet (E3) failed to meet the effect size criterion (r = − 0.08), despite the statistically significant value (p = .033), and thus did not warrant age-specific norms.

Male Subsample Mean Differences. In the male subsample, seven scales met the initial correlation criterion. Mean comparison tests confirmed that six out of the seven scales met the criteria for requiring age-specific norms (see Appendix A Table S9 in S1 Appendix):

1. Conscientiousness (t (232) = −2.60, p = 0.01, d = −0.34) and its facet Prudence (C4) (U = 5167, p < 0.001, r = 0.24) showed higher scores among adult men, indicating increased responsibility and long-term planning with age.
2. Obedience (A3) (U = 4920, p < 0.001, r = −0.27) showed lower scores among adult men, confirming the finding from the correlation analysis that older male athletes report being less yielding.
3. Openness (t (232) = −2.14, p = 0.034, d = −0.28) and the facet Greed-Avoidance (H2) (U = 4348, p < 0.001, r = 0.32) also met the criteria.

The Inquisitiveness facet (O3) failed to meet the effect size criterion (r = 0.19) with the established cut-off of r > 0.20, despite the statistically significant p-value (p = 0.014). Similarly, the Agreeableness factor (A) failed to meet the statistical significance criterion (p = 0.103), despite meeting the effect size criterion (d = 0.21). Therefore, these two scales did not warrant age-specific norms.

Based on the sequential analyses, age-specific norms were established for four scales in the female subsample and six scales in the male subsample. For all other scales, a single, gender-specific norm was retained, as these traits did not show a simultaneous statistically significant and practically meaningful change across the two age groups.

3.1.9. Development of norm construction.

Normative scores for the LPI-v3s scales were calculated using a dual approach to ensure both high-quality norm tables and simplified scoring for subsequent analysis.

For the creation of the final norm tables, a regression-based continuous norming approach was employed, utilizing the cNORMj for single group module within the JAMOVI statistical software. This method offers significant advantages over conventional approaches, as it models the relationship between raw scores and normative scores using polynomial regression, thereby smoothing the percentile curve and eliminating gaps or abrupt changes that often occur with traditional percentile calculations [37]. Although the continuous function for age-normed scores was constrained to predefined groups (due to the single-group approach), this method effectively optimized the endpoints and filled any sparsity in the data.

For the purposes of the subsequent analytical steps (e.g., regression analysis) involving the Total Analytic Sample, T-scores were calculated using the conventional approach (using a linear transformation where the mean is set to M = 50 and the standard deviation to SD = 10).

Based on the preliminary statistical analysis of the athlete sample, it was determined that gender- and/or age-specific norms were necessary only for a subset of the scales. Specifically, gender-specific norms were developed for the following scales: N1_new, N2_new, N, C1, C4, C, A3, A4, O1, O and H2. Furthermore, a detailed review of the data indicated the need for age-specific norms within genders for several key traits:

1. For female athletes, separate norms for two age groups were created for N1_new, N, and C1.
2. For male athletes, separate norms for two age groups were created for A3, O, and H2.

For the remaining scales (E, E1, E2, E3, C2, A2, O3, O4, A, and M), a unified set of norms was developed, without subdivision by age or gender, as no statistically significant differences were observed across these demographic variables.

The cNORMj package allows for a direct comparison between conventional norms and the regression-based continuous norms. The quality of the continuous norming model was excellent, with the final model’s being no lower than 0.996 for all individual norm tables. This high degree of fit indicates that the two methods are empirically equivalent, and that no systematic error exists between the linear transformation and the regression model. Therefore, the T-scores calculated using the conventional approach are considered equivalent to those that would be assigned based on the newly created continuous norm tables, justifying their use in the primary data analysis.