Summary

Key papers (10)

1. Development is in the details: Age differences in the Big Five domains, facets, and nuances. Mottus, R., & Rozgonjuk, D. - Journal of Personality and Social Psychology, 120(4), 1035-1048, 2021.
   The direct precedent. In ~24,000 internet respondents aged 18-50 with a 300-item inventory, age was predicted at r = .28 from domains, r = .44 from facets and r = .65 from items, and the unique variance of more than a third of 240 NEO-PI items correlated with age. Establishes the descriptive claim this study converts into a formal model test, and does so in a long inventory rather than a short form.
2. Age differences in the personality hierarchy: A multi-sample replication study across the life span. Hang, Y., Soto, C., Speyer, L. G., Haring, L., Lee, B., Ostendorf, F., & Mottus, R. - Journal of Research in Personality, 93, 104121, 2021.
   Replicates Mottus and Rozgonjuk across N = 51,524 in several samples, age ranges, cultures and instruments: lower hierarchy levels, especially nuances, carry substantially more age-sensitive information, and most of the UNIQUE age-sensitive information sits at the nuance level. Shows the phenomenon is robust but still leaves the underlying model untested.
3. Personality traits below facets: The consensual validity, longitudinal stability, heritability, and utility of personality nuances. Mottus, R., Kandler, C., Bleidorn, W., Riemann, R., & McCrae, R. R. - Journal of Personality and Social Psychology, 112(3), 474-490, 2017.
   Introduces the nuance construct and shows item-specific variance behaves like a trait (cross-rater agreement, rank-order stability, heritability, incremental utility) rather than like error. This is the theoretical warrant for treating within-domain item residuals as signal.
4. What personality scales measure: A new psychometrics and its implications for theory and assessment. McCrae, R. R., & Mottus, R. - Current Directions in Psychological Science, 28(4), 415-420, 2019.
   States the measurement model at issue: classical 'score = trait + random error' is wrong, and item variance decomposes into domain, facet, nuance and systematic bias. Also flags evaluative and acquiescent bias as item-level variance that can masquerade as nuance signal - a caution this study must carry.
5. Successful explanations start with accurate descriptions: Questionnaire items as personality markers for more accurate predictions. Seeboth, A., & Mottus, R. - European Journal of Personality, 32(3), 186-201, 2018.
   Shows the nuance-beats-domain pattern generalises beyond age to life outcomes, and reports the striking result that removing all Big Five variance from Big Five items barely changed their outcome prediction. Frames the general question of how much a domain score discards.
6. Structural and inter-individual differentiation in personality traits across the adult lifespan. Olaru, G., Jankowsky, K., & Allemand, M. - European Journal of Personality, 38(2), 306-325, 2024.
   Examines loadings, inter-domain correlations and variances across ages 16-90 in three samples of 3,000+ and finds age variation in inter-individual differences at the nuance level but not at the domain or facet level. Supplies the main alternative explanation to guard against: age-varying loadings could in principle mimic nuance-specific age effects.
7. Patterns of mean-level change in personality traits across the life course: A meta-analysis of longitudinal studies. Roberts, B. W., Walton, K. E., & Viechtbauer, W. - Psychological Bulletin, 132(1), 1-25, 2006.
   The canonical longitudinal evidence for the maturity principle from 92 samples, and the first clear signal of within-domain heterogeneity: the extraversion facets social dominance and social vitality change in opposite directions. Also the only non-cross-sectional anchor available, which matters for the age-differences-versus-change caveat.
8. Age differences in personality traits from 10 to 65: Big Five domains and facets in a large cross-sectional sample. Soto, C. J., John, O. P., Gosling, S. D., & Potter, J. - Journal of Personality and Social Psychology, 100(2), 330-348, 2011.
   Benchmark cross-sectional age curves from N = 1,267,218 web respondents aged 10-65, with domain-specific and non-monotonic trajectories and facets diverging within domains. Sets the expectation for the size and direction of domain-level age correlations in internet samples of this kind.
9. Constraints on Generality (COG): A proposed addition to all empirical papers. Simons, D. J., Shoda, Y., & Lindsay, D. S. - Perspectives on Psychological Science, 12(6), 1123-1128, 2017.
   The reporting standard for bounding inferences to the sampled population - essential here, because every study in this literature, including the present one, uses a self-selected internet convenience sample.
10. The new statistics: Why and how. Cumming, G. - Psychological Science, 25(1), 7-29, 2014.
    The target venue's estimation standard: effect sizes with confidence intervals and prespecification rather than bare significance testing. Dictates that the incremental-information claim be reported as an interval estimate, not a p value.

1. Idea 1Selected

   Are age differences in personality domain-general? A loading-conditioned test of the common-cause model in a 25-item Big Five short form

   Hypothesis. The domain-general (common-cause) model of age differences is false. If age is related to an item only through that item's domain factor, then within each Big Five domain the item-age correlations must be proportional to the items' factor loadings: r(item_i, age) = lambda_i x beta_domain. H1 predicts that this over-identifying restriction is rejected in at least one domain (minimum-distance chi-square with 4 df per five-item domain, alpha = .05), that the resulting item-specific ('nuance') age residuals form a profile that replicates across random split halves of the sample, and that the 25 items predict age out of sample better than the five domain scores do. The hypothesis is refuted if the restriction cannot be rejected in any domain, or if the split-half profile correlation is near zero, or if the cross-validated increment in explained variance from items over domain scores is not reliably greater than zero.

   Dataset. Big Five Inventory: 25 personality items, SAPA project bfi_personality_items

   Test plan, novelty and risk

   Test plan. Variables: the 25 IPIP items (A1-A5, C1-C5, E1-E5, N1-N5, O1-O5; six-point Likert, 1 = very inaccurate to 6 = very accurate), age in years, gender (1 = male, 2 = female) as a covariate in a robustness check. Preprocessing: reverse-score the seven negatively keyed items (A1, C4, C5, E1, E2, O2, O5) as 7 - x; z-standardise every item and age within the analysis sample. Sample filters, fixed before analysis: retain participants aged 14-70 (the range in which the SAPA sample has usable density; drops implausible or near-empty tails) with complete responses on all 25 items; report the exact number excluded by each filter and the analysed n. Estimation. (1) Loadings: for each domain separately, extract a one-factor solution from the 5x5 item correlation matrix by iterated principal-axis factoring (squared multiple correlations as initial communalities) to obtain standardised loadings lambda_i. (2) Item-age correlations r_i for all 25 items. (3) Sampling covariance: a seeded nonparametric bootstrap over participants (B = 2,000) recomputing r and lambda in every resample, giving the 25x25 covariance V of r and percentile 95% CIs. (4) Primary test: per domain, the minimum-distance statistic Q_d = min_beta (r_d - lambda_d beta)' W (r_d - lambda_d beta) with W = V_d^-1, distributed chi-square(4) under the domain-general null, plus a bootstrap-calibrated p value from recentred resamples so that sampling error in lambda is not ignored; a global statistic summing across domains on 20 df. Report beta_d (the implied domain-factor-age correlation), each item's nuance residual e_i = r_i - lambda_i beta_d with a bootstrap 95% CI, and the count of within-domain sign reversals in r_i, which no attenuation account can produce. (5) Profile reliability: 500 seeded random split halves; recompute e in each half; correlate the two 25-value profiles; report the mean split-half r with a 95% percentile interval and the Spearman-Brown-corrected value. (6) Practical magnitude: 10-fold cross-validation with a fixed seed, ordinary least squares, predicting standardised age from (a) the five unit-weighted domain scores, (b) five per-domain Thurstone factor scores with weights estimated in the training folds only, and (c) the 25 items; report out-of-fold R-squared for each, the increment of (c) over (a) and over (b), a percentile bootstrap 95% CI for the increment, a paired test on the out-of-fold squared errors, and the spread across 20 alternative fold seeds. (7) Robustness: repeat the item-age correlations as partial correlations controlling for gender and report the correlation between the adjusted and unadjusted nuance profiles. Power: with the analysed n, report the sensitivity analysis - the smallest |r| detectable at alpha = .05 two-tailed with 80% power, and the noncentrality needed for 80% power at 4 df. Refutation: non-significant Q in every domain, a split-half profile correlation whose CI includes zero, or a cross-validated increment whose 95% CI includes zero.

   Novelty. Mottus and Rozgonjuk (2021) and Hang et al. (2021) established descriptively that items predict age better than domains, but a prediction contrast cannot distinguish genuine item-specific age effects from optimal reweighting of items that merely differ in loading and reliability - a domain-general world produces exactly that ordering. No study in this literature appears to have tested the common-cause restriction itself, which is over-identified for a five-item scale and therefore falsifiable. Second, all existing evidence comes from 240- to 300-item inventories; the practically consequential case is the 20-30 item short form that most researchers actually administer, where there are five items per domain and no facet scores at all, and where the nuance signal has every reason to be weaker. Third, the split-half reliability of the whole nuance profile has not been estimated within a sample; prior work reports only 'at least moderate' cross-country replication of single-item correlations.

   Expected outcome. The domain-general restriction is expected to be rejected in most domains, because published facet-level work already shows components of a domain moving in opposite directions with age. The genuinely uncertain quantities are the size of the cross-validated increment - it could easily be near zero in a 25-item instrument, which would be an informative null about practical consequence - and whether the nuance profile is reliable rather than sampling noise. Domain-level age correlations should land near |r| = .07-.20, consistent with Soto et al. (2011).

   Main risk. Three. (i) Cross-sectional age differences confound development with cohort and with differential self-selection into an online study, so nothing here licenses a claim about change; the paper must say age differences throughout. (ii) Item-level acquiescent and evaluative response bias also lives in item-specific variance and could inflate apparent nuance signal; the gender-adjusted robustness check and the sign-reversal count mitigate but do not eliminate this. (iii) The minimum-distance test treats the estimated loadings as fixed, which would make it anticonservative; the bootstrap recalibration that recomputes loadings in every resample is included precisely to address that, and any gap between the asymptotic and bootstrap p values must be reported.

2. Idea 2

   Does the apparent five-factor structure of a short Big Five inventory depend on the respondent's age? A bootstrap test of age-varying congruence

   Hypothesis. Personality structure is age-differentiated: the five-factor solution recovered from younger respondents is not the same solution recovered from older respondents. Operationally, Tucker congruence coefficients between the five-factor loading matrices of a young subsample (age 14-24) and an older subsample (age 35-70) will fall below the conventional .95 'equivalence' threshold for at least one factor, and the mean absolute inter-factor correlation among the five domain scores will be reliably lower in the older group than in the younger group (differentiation). Refuted if all five congruence coefficients exceed .95 and the bootstrap 95% CI for the between-group difference in mean absolute inter-domain correlation contains zero.

   Dataset. Big Five Inventory: 25 personality items, SAPA project bfi_personality_items

   Test plan, novelty and risk

   Test plan. Variables: the 25 items, age. Reverse-score A1, C4, C5, E1, E2, O2, O5; complete cases on all 25 items; two age strata fixed in advance (14-24 and 35-70) so the groups are non-overlapping, with the exact n in each reported. In each stratum, extract five factors by principal-axis factoring with oblimin-style oblique rotation implemented via a target rotation to the a priori five-factor pattern, then compute Tucker's congruence coefficient factor by factor after Procrustes alignment. Separately compute unit-weighted domain scores, their 5x5 correlation matrix in each stratum, and the mean absolute off-diagonal correlation. Inference by seeded nonparametric bootstrap (B = 2,000) within strata: percentile 95% CIs on each congruence coefficient and on the between-stratum difference in mean absolute inter-domain correlation. Report Cronbach's alpha per domain per stratum, since a group difference in reliability is an alternative explanation for a difference in inter-domain correlation, and repeat the comparison on disattenuated correlations. Refutation: congruence above .95 for all five factors and a difference CI containing zero.

   Novelty. Olaru et al. (2024) examined structural differentiation across the adult lifespan in three large samples but found domain- and facet-level structure largely stable, with age variation confined to item-residual variance. Applying the same question to a 25-item public short form asks whether the very common practice of scoring a brief inventory identically across a wide age range is defensible, and whether the null result generalises to instruments with only five indicators per factor, where rotation is far less stable.

   Expected outcome. Congruence coefficients probably above .90 and plausibly above .95 for the better-defined factors (N, E) and lower for openness, whose alpha in this instrument is the weakest. A modest or null differentiation effect is the more likely outcome, which would be a useful constraint rather than a discovery.

   Main risk. Splitting into two strata roughly halves the effective n for each factor solution, and five-indicator factors rotate unstably, so congruence coefficients carry wide bootstrap intervals; the study could easily be underpowered to distinguish .93 from .96. The two strata also differ in composition (the young stratum is dominated by ages 17-22 in this sample), so any structural difference is confounded with education and with the recruitment channel.

3. Idea 3

   Does acquiescent responding masquerade as personality? Testing whether the individual acquiescence factor in a short Big Five inventory carries demographic signal

   Hypothesis. The individual tendency to agree with items regardless of content is not measurement noise: an acquiescence index built from the seven negatively keyed items and their positively keyed counterparts will (a) show non-trivial internal consistency, (b) correlate reliably with age and education, and (c) statistically account for part of the observed age-domain correlations, such that correcting the domain scores for acquiescence changes at least one domain-age correlation by more than .03 in absolute value. Refuted if the acquiescence index has near-zero internal consistency, or if its correlations with age and education have 95% CIs containing zero, or if acquiescence correction leaves every domain-age correlation essentially unchanged.

   Dataset. Big Five Inventory: 25 personality items, SAPA project bfi_personality_items

   Test plan, novelty and risk

   Test plan. Variables: the 25 items in raw (unreversed) form, age, education (1-5 ordinal band, missing for 223 participants - report the analysed n with and without education), gender. Construct the acquiescence index as the person mean across the seven negatively keyed items and seven loading-matched positively keyed items in raw scoring, so that content largely cancels and agreement remains; estimate its internal consistency by splitting the balanced pairs. Correlate the index with age, education and gender, with bootstrap 95% CIs (B = 2,000, seeded). Then recompute all five domain scores after within-person ipsatisation (subtracting the person's acquiescence index from every item before reverse-keying) and compare each domain-age correlation before and after, with a bootstrap CI on the change. Report Cronbach's alpha of each domain before and after correction. Refutation: the CIs for the acquiescence-age and acquiescence-education correlations both contain zero and no domain-age correlation shifts by more than .03.

   Novelty. McCrae and Mottus (2019) identify systematic response bias as a component of item variance alongside domain, facet and nuance variance, but the applied literature on this widely used public dataset almost never quantifies it, and the keying of this particular 25-item form is unbalanced (7 negative, 18 positive), which is precisely the condition under which acquiescence contaminates domain scores rather than cancelling out.

   Expected outcome. A small but non-zero acquiescence-age correlation and shifts in domain-age correlations of roughly .01-.05, i.e. real but not large enough to overturn the maturity principle.

   Main risk. With only seven negatively keyed items and unbalanced keying, the acquiescence index is confounded with agreeableness and conscientiousness content, so a 'response style' correlation may simply be a trait correlation under another name - a confound that this dataset cannot fully resolve, since it lacks a purpose-built balanced-keying subset.

Ranking rationale

Idea 1 is ranked first because it converts a descriptive regularity that the field already accepts into a falsifiable model test with a clear refutation criterion, it is the only one of the three whose primary result cannot be produced by an artefact of unequal item reliability (the loading-conditioned restriction is exactly what disposes of that alternative), and its second outcome - the cross-validated increment - is genuinely uncertain in a 25-item instrument, so the study is informative whichever way it lands. It also uses the full analysed sample for every estimate rather than splitting it. Idea 2 asks a question of comparable theoretical interest but must halve the sample and rotate five-indicator factors, so its confidence intervals would be too wide to separate the hypotheses it is meant to separate; with the available n it risks an uninterpretable null. Idea 3 is well-posed and cheap, but the instrument's unbalanced keying means the acquiescence index is structurally confounded with agreeableness and conscientiousness content, and no analysis of these 25 items can break that confound, so a positive result would be ambiguous by construction.

Data provenance

Result (RESULT_JSON)

{
  "n_total": 2800,
  "n_excluded_age_filter": 43,
  "n_excluded_incomplete_items": 364,
  "n_excluded_either": 399,
  "n_analysed": 2401,
  "age_min_raw": 3,
  "age_max_raw": 86,
  "age_min": 14,
  "age_max": 68,
  "age_mean": 28.762182423990005,
  "age_sd": 10.759089300139408,
  "age_median": 26,
  "n_female": 1608,
  "n_male": 793,
  "pct_female": 66.97209496043315,
  "alpha": {
    "A": 0.7233,
    "C": 0.7425,
    "E": 0.7693,
    "N": 0.8183,
    "O": 0.6128
  },
  "r_domain_age": {
    "A": 0.1761,
    "C": 0.1149,
    "E": 0.0768,
    "N": -0.1101,
    "O": 0.0676
  },
  "beta_domain_factor_age": {
    "A": 0.1732,
    "C": 0.142,
    "E": 0.1044,
    "N": -0.1289,
    "O": 0.0896
  },
  "Q": {
    "A": 65.064,
    "C": 26.447,
    "E": 51.971,
    "N": 21.469,
    "O": 10.503
  },
  "p_chi2": {
    "A": 2.4947583841952725e-13,
    "C": 0.00002570537913475557,
    "E": 1.3990470977691859e-10,
    "N": 0.0002555765533720819,
    "O": 0.03275825229482816
  },
  "p_bootstrap": {
    "A": 0.0004997501249375312,
    "C": 0.0004997501249375312,
    "E": 0.0004997501249375312,
    "N": 0.0004997501249375312,
    "O": 0.031984007996002
  },
  "Q_global": 175.454,
  "df_global": 20,
  "p_chi2_global": 7.50780489773615e-27,
  "p_bootstrap_global": 0.0004997501249375312,
  "n_nuance_ci_excludes_zero": 9,
  "n_sign_reversals": 0,
  "n_item_r_ci_excludes_zero": 19,
  "rms_r_age": 0.0893031520037177,
  "rms_nuance": 0.04158277731538501,
  "nuance_share_of_rms": 0.46563616605216707,
  "splithalf_profile_r_mean": 0.78798666779214,
  "splithalf_profile_r_ci": [
    0.664397873200389,
    0.886588582161129
  ],
  "splithalf_spearman_brown": 0.8801863284698088,
  "cv_r2_domain": 0.03693,
  "cv_r2_factor": 0.02855,
  "cv_r2_item": 0.08396,
  "cv_r_domain": 0.1928,
  "cv_r_factor": 0.1699,
  "cv_r_item": 0.292,
  "delta_r2_item_vs_domain": 0.04702517693240227,
  "delta_r2_item_vs_factor": 0.055412305223590086,
  "delta_r2_ci": [
    0.028125596746881372,
    0.06593706181389113
  ],
  "delta_r2_ratio": 2.273258603179837,
  "cohen_f2_increment": 0.05133518186556607,
  "paired_t_sqerr": 4.628517857748758,
  "paired_t_df": 2400,
  "paired_p_sqerr": 0.000003879084280752195,
  "seed_sweep_mean_r2": {
    "domain": 0.03796630106913018,
    "factor": 0.029550589040354076,
    "item": 0.08526946016320856
  },
  "seed_sweep_sd_delta_item_domain": 0.001391990561645162,
  "gender_adj_profile_r": 0.9977239824738464,
  "gender_adj_Q": {
    "A": 63.571,
    "C": 25.98,
    "E": 49.929,
    "N": 28.82,
    "O": 10.004
  },
  "gender_adj_p_chi2": {
    "A": 5.145342359636008e-13,
    "C": 0.000031932798444963485,
    "E": 3.7354888764862505e-10,
    "N": 0.000008502911682075744,
    "O": 0.040361844043608874
  },
  "sensitivity_min_detectable_r": 0.05714862432193938,
  "chi2_crit_4df": 9.487729036781154,
  "ncp_for_80pct_power_4df": 11.94,
  "n_bootstrap": 2000,
  "n_splits": 500,
  "n_folds": 10,
  "items": [
    {
      "item": "A1",
      "domain": "A",
      "loading": 0.38248310583221895,
      "r_age": 0.1521507363406825,
      "r_ci": [
        0.11489186191765846,
        0.19067826167404645
      ],
      "predicted_r": 0.06625753197357333,
      "nuance": 0.08589320436710916,
      "nuance_ci": [
        0.04833801891133457,
        0.12352252727460453
      ],
      "r_age_gender_adj": 0.1474058961327228
    },
    {
      "item": "A2",
      "domain": "A",
      "loading": 0.6851121359466298,
      "r_age": 0.11011085251046132,
      "r_ci": [
        0.07367554427794044,
        0.14755100403824498
      ],
      "predicted_r": 0.11868194584489576,
      "nuance": -0.008571093334434454,
      "nuance_ci": [
        -0.04452912468685696,
        0.028639887305887863
      ],
      "r_age_gender_adj": 0.1041364091594152
    },
    {
      "item": "A3",
      "domain": "A",
      "loading": 0.7640318047927989,
      "r_age": 0.0675681308172175,
      "r_ci": [
        0.027267191557908372,
        0.10640962998519632
      ],
      "predicted_r": 0.13235319668495937,
      "nuance": -0.06478506586774187,
      "nuance_ci": [
        -0.10472035709815994,
        -0.026902378239766853
      ],
      "r_age_gender_adj": 0.062327113032284394
    },
    {
      "item": "A4",
      "domain": "A",
      "loading": 0.4978585660017461,
      "r_age": 0.1496650572447036,
      "r_ci": [
        0.1110907659386506,
        0.1834176822142868
      ],
      "predicted_r": 0.08624401797670031,
      "nuance": 0.0634210392680033,
      "nuance_ci": [
        0.024969887953019115,
        0.0976002533029782
      ],
      "r_age_gender_adj": 0.1458359638839201
    },
    {
      "item": "A5",
      "domain": "A",
      "loading": 0.6217502149702241,
      "r_age": 0.12715688091092658,
      "r_ci": [
        0.08862251119052444,
        0.16419599813664917
      ],
      "predicted_r": 0.10770576299920734,
      "nuance": 0.01945111791171925,
      "nuance_ci": [
        -0.01934055258148516,
        0.05595119807776315
      ],
      "r_age_gender_adj": 0.12376430221506036
    },
    {
      "item": "C1",
      "domain": "C",
      "loading": 0.5648612206550991,
      "r_age": 0.09135733574894209,
      "r_ci": [
        0.05031460522357081,
        0.13418423328182086
      ],
      "predicted_r": 0.08022922369160528,
      "nuance": 0.011128112057336798,
      "nuance_ci": [
        -0.03066939882293591,
        0.05279102026750633
      ],
      "r_age_gender_adj": 0.09099534091500384
    },
    {
      "item": "C2",
      "domain": "C",
      "loading": 0.622589683569662,
      "r_age": 0.018728042896807528,
      "r_ci": [
        -0.02611603059946652,
        0.05930463121609643
      ],
      "predicted_r": 0.08842860009626198,
      "nuance": -0.06970055719945445,
      "nuance_ci": [
        -0.1136675504010747,
        -0.028562080231942857
      ],
      "r_age_gender_adj": 0.016257526713132565
    },
    {
      "item": "C3",
      "domain": "C",
      "loading": 0.5697129706192632,
      "r_age": 0.06843946460363183,
      "r_ci": [
        0.02614286808658052,
        0.10746533941004097
      ],
      "predicted_r": 0.080918334784626,
      "nuance": -0.012478870180994169,
      "nuance_ci": [
        -0.05467078888072688,
        0.02614407891495999
      ],
      "r_age_gender_adj": 0.06641511374206063
    },
    {
      "item": "C4",
      "domain": "C",
      "loading": 0.6861470898863191,
      "r_age": 0.1371763478407454,
      "r_ci": [
        0.09717744571368944,
        0.1765961533636754
      ],
      "predicted_r": 0.09745588181109374,
      "nuance": 0.03972046602965165,
      "nuance_ci": [
        -0.0011663604382641769,
        0.07962056204304417
      ],
      "r_age_gender_adj": 0.13454300740764058
    },
    {
      "item": "C5",
      "domain": "C",
      "loading": 0.5826186693334383,
      "r_age": 0.08737960891100213,
      "r_ci": [
        0.047673535876953166,
        0.12800099746744598
      ],
      "predicted_r": 0.08275137651447814,
      "nuance": 0.00462823239652399,
      "nuance_ci": [
        -0.03470853940656387,
        0.045252693984806386
      ],
      "r_age_gender_adj": 0.08437247106806509
    },
    {
      "item": "E1",
      "domain": "E",
      "loading": 0.6002559409091514,
      "r_age": 0.05443179658598209,
      "r_ci": [
        0.015581847092176996,
        0.09200461123106989
      ],
      "predicted_r": 0.06266194891268481,
      "nuance": -0.008230152326702725,
      "nuance_ci": [
        -0.04789242917703817,
        0.02935657597720163
      ],
      "r_age_gender_adj": 0.04936125926595092
    },
    {
      "item": "E2",
      "domain": "E",
      "loading": 0.7373915116695895,
      "r_age": 0.12181870340370474,
      "r_ci": [
        0.0814899206453671,
        0.1605509233389147
      ],
      "predicted_r": 0.07697781243597983,
      "nuance": 0.04484089096772491,
      "nuance_ci": [
        0.004698905542689069,
        0.08346491841812972
      ],
      "r_age_gender_adj": 0.11978717344522118
    },
    {
      "item": "E3",
      "domain": "E",
      "loading": 0.5952717365418456,
      "r_age": -0.006718107909780987,
      "r_ci": [
        -0.04693562909121147,
        0.03421819309795376
      ],
      "predicted_r": 0.06214163759521338,
      "nuance": -0.06885974550499437,
      "nuance_ci": [
        -0.10829397534703993,
        -0.02762634894628628
      ],
      "r_age_gender_adj": -0.00855050768281186
    },
    {
      "item": "E4",
      "domain": "E",
      "loading": 0.6932616638623387,
      "r_age": 0.0053002894649654365,
      "r_ci": [
        -0.03762496875381127,
        0.04486623464052839
      ],
      "predicted_r": 0.07237100710451701,
      "nuance": -0.06707071763955157,
      "nuance_ci": [
        -0.11008319170983692,
        -0.027775494154115607
      ],
      "r_age_gender_adj": 0.0017240741660574472
    },
    {
      "item": "E5",
      "domain": "E",
      "loading": 0.5408110877159297,
      "r_age": 0.10202925643210708,
      "r_ci": [
        0.06342679773805075,
        0.1417263928034564
      ],
      "predicted_r": 0.05645637875493859,
      "nuance": 0.04557287767716848,
      "nuance_ci": [
        0.005813952777821495,
        0.08522996583664258
      ],
      "r_age_gender_adj": 0.0992968104125413
    },
    {
      "item": "N1",
      "domain": "N",
      "loading": 0.7923916362856417,
      "r_age": -0.0829298624097287,
      "r_ci": [
        -0.12092024304079987,
        -0.04175525670424702
      ],
      "predicted_r": -0.10214896847474542,
      "nuance": 0.01921910606501671,
      "nuance_ci": [
        -0.018706942290312896,
        0.06034649175734547
      ],
      "r_age_gender_adj": -0.08496618203950569
    },
    {
      "item": "N2",
      "domain": "N",
      "loading": 0.7614477334414338,
      "r_age": -0.09974446445461949,
      "r_ci": [
        -0.1437102606714482,
        -0.056805692745060594
      ],
      "predicted_r": -0.09815992112571569,
      "nuance": -0.0015845433289038149,
      "nuance_ci": [
        -0.045507202635968205,
        0.04139245369700271
      ],
      "r_age_gender_adj": -0.10475862269890882
    },
    {
      "item": "N3",
      "domain": "N",
      "loading": 0.7645657279375294,
      "r_age": -0.10759786012753011,
      "r_ci": [
        -0.15041487392523298,
        -0.06568184272586668
      ],
      "predicted_r": -0.0985618687320522,
      "nuance": -0.00903599139547792,
      "nuance_ci": [
        -0.05114534636943804,
        0.032626132619463316
      ],
      "r_age_gender_adj": -0.1138252633673117
    },
    {
      "item": "N4",
      "domain": "N",
      "loading": 0.5975849277028593,
      "r_age": -0.025369008388681693,
      "r_ci": [
        -0.06556330151227326,
        0.02129852411964935
      ],
      "predicted_r": -0.07703600233218225,
      "nuance": 0.05166699394350055,
      "nuance_ci": [
        0.011424066221448962,
        0.09844024604973103
      ],
      "r_age_gender_adj": -0.025300062651486172
    },
    {
      "item": "N5",
      "domain": "N",
      "loading": 0.5333044329119532,
      "r_age": -0.10344303666219296,
      "r_ci": [
        -0.14274716863595727,
        -0.06520209404177432
      ],
      "predicted_r": -0.06874946075948658,
      "nuance": -0.03469357590270637,
      "nuance_ci": [
        -0.07347248957709987,
        0.003130707218330445
      ],
      "r_age_gender_adj": -0.11517456356353203
    },
    {
      "item": "O1",
      "domain": "O",
      "loading": 0.5382306268013634,
      "r_age": 0.04554958719378937,
      "r_ci": [
        0.006261158417874538,
        0.0846377313436954
      ],
      "predicted_r": 0.04823923923789037,
      "nuance": -0.0026896520441010013,
      "nuance_ci": [
        -0.041861441605594706,
        0.036794552687530215
      ],
      "r_age_gender_adj": 0.050627171733785725
    },
    {
      "item": "O2",
      "domain": "O",
      "loading": 0.4789056760229611,
      "r_age": 0.03197512950570044,
      "r_ci": [
        -0.007902514135078387,
        0.06985932951701758
      ],
      "predicted_r": 0.04292220532924292,
      "nuance": -0.010947075823542485,
      "nuance_ci": [
        -0.05069782387558767,
        0.0278467406759941
      ],
      "r_age_gender_adj": 0.03392264300066035
    },
    {
      "item": "O3",
      "domain": "O",
      "loading": 0.6369063090000574,
      "r_age": 0.04188855312672712,
      "r_ci": [
        0.0007406890237166756,
        0.08079167923427276
      ],
      "predicted_r": 0.05708310579530491,
      "nuance": -0.015194552668577783,
      "nuance_ci": [
        -0.057398596513546056,
        0.02478444559387904
      ],
      "r_age_gender_adj": 0.04390675962496845
    },
    {
      "item": "O4",
      "domain": "O",
      "loading": 0.27841835684151006,
      "r_age": 0.0014888375884181688,
      "r_ci": [
        -0.036520338682968646,
        0.04083549519143276
      ],
      "predicted_r": 0.024953410406454993,
      "nuance": -0.023464572818036825,
      "nuance_ci": [
        -0.06166527027362892,
        0.016610123385975558
      ],
      "r_age_gender_adj": 0.0026754178211335026
    },
    {
      "item": "O5",
      "domain": "O",
      "loading": 0.5383276217045065,
      "r_age": 0.09081405533153113,
      "r_ci": [
        0.04838660274415922,
        0.1289746863217161
      ],
      "predicted_r": 0.04824793246362779,
      "nuance": 0.04256612286790332,
      "nuance_ci": [
        -0.0006440117421527098,
        0.08031645467307706
      ],
      "r_age_gender_adj": 0.09261143248554828
    }
  ],
  "hypothesis_supported": true
}

"""Loading-conditioned test of the domain-general model of age differences in the Big Five.

Real data: 25 IPIP items + demographics from the SAPA project, loaded via `dataset.load()`.
Domain-general (common-cause) null: age relates to an item only through its domain factor, so
within a domain r(item_i, age) = lambda_i * beta_domain.  That is an over-identified restriction
(4 df per five-item domain) and is tested with a minimum-distance statistic.
"""
import json
import numpy as np
from scipy import stats as st
from dataset import load

DOMAINS = {"A": ["A1", "A2", "A3", "A4", "A5"], "C": ["C1", "C2", "C3", "C4", "C5"],
           "E": ["E1", "E2", "E3", "E4", "E5"], "N": ["N1", "N2", "N3", "N4", "N5"],
           "O": ["O1", "O2", "O3", "O4", "O5"]}
DOM_ORDER = ["A", "C", "E", "N", "O"]
ITEMS = [i for d in DOM_ORDER for i in DOMAINS[d]]
REVERSED = ["A1", "C4", "C5", "E1", "E2", "O2", "O5"]
AGE_LO, AGE_HI = 14, 70
B_BOOT, N_SPLITS, B_DELTA, K_FOLDS = 2000, 500, 4000, 10
SEED_BOOT, SEED_SPLIT, SEED_CV, SEED_DELTA = 20260908, 11, 7, 99

df = load()
print("loaded", df.shape, "columns ok:", all(c in df.columns for c in ITEMS + ["age", "gender"]))
n_total = int(len(df))
age_min_raw, age_max_raw = float(df["age"].min()), float(df["age"].max())
for c in REVERSED:                                    # 6-point Likert -> reverse as 7 - x
    df[c] = 7.0 - df[c].astype(float)

m_age = (df["age"] >= AGE_LO) & (df["age"] <= AGE_HI)
m_complete = df[ITEMS].notna().all(axis=1)
n_drop_age = int((~m_age).sum())
n_drop_incomplete = int((~m_complete).sum())
n_drop_either = int((~(m_age & m_complete)).sum())
d = df[m_age & m_complete].reset_index(drop=True)
N = int(len(d))
print("analysed n =", N, "| dropped by age filter", n_drop_age, "| dropped incomplete", n_drop_incomplete)

X = d[ITEMS].to_numpy(float)
age_raw = d["age"].to_numpy(float)
gender = d["gender"].to_numpy(float)
Z = (X - X.mean(0)) / X.std(0, ddof=1)
a = (age_raw - age_raw.mean()) / age_raw.std(ddof=1)

def paf(R, iters=60):
    """One-factor principal-axis loadings for a small correlation matrix."""
    smc = 1.0 - 1.0 / np.diag(np.linalg.pinv(R))
    h = np.clip(smc, 0.05, 0.99)
    lam = np.sqrt(h)
    for _ in range(iters):
        Rr = R.copy()
        np.fill_diagonal(Rr, h)
        w, v = np.linalg.eigh(Rr)
        lam = v[:, -1] * np.sqrt(max(w[-1], 1e-9))
        if lam.sum() < 0:
            lam = -lam
        hn = np.clip(lam ** 2, 0.01, 0.99)
        if np.max(np.abs(hn - h)) < 1e-9:
            h = hn
            break
        h = hn
    return lam

def item_stats(Zm, am):
    """Item-age correlations and per-domain one-factor loadings."""
    n = Zm.shape[0]
    zz = (Zm - Zm.mean(0)) / Zm.std(0, ddof=1)
    aa = (am - am.mean()) / am.std(ddof=1)
    r = (zz * aa[:, None]).sum(0) / (n - 1)
    R = np.corrcoef(zz, rowvar=False)
    lam = np.concatenate([paf(R[k * 5:k * 5 + 5, k * 5:k * 5 + 5]) for k in range(5)])
    return r, lam

def min_distance(r, lam, V):
    """Per-domain minimum-distance fit of r_d = lambda_d * beta_d."""
    Q, beta, e = {}, {}, np.zeros(25)
    for k, dm in enumerate(DOM_ORDER):
        sl = slice(k * 5, k * 5 + 5)
        rv, lv = r[sl], lam[sl]
        W = np.linalg.inv(V[sl, sl])
        b = float((lv @ W @ rv) / (lv @ W @ lv))
        res = rv - lv * b
        Q[dm] = float(res @ W @ res)
        beta[dm] = b
        e[sl] = res
    return Q, beta, e

def bootstrap(Zm, am, seed):
    rng = np.random.default_rng(seed)
    n = Zm.shape[0]
    rb = np.empty((B_BOOT, 25))
    lb = np.empty((B_BOOT, 25))
    for b in range(B_BOOT):
        idx = rng.integers(0, n, n)
        rb[b], lb[b] = item_stats(Zm[idx], am[idx])
    return rb, lb

# ---- primary: item-age correlations, loadings, minimum-distance test -----------------------
r_hat, lam_hat = item_stats(Z, a)
rb, lb = bootstrap(Z, a, SEED_BOOT)
V = np.cov(rb, rowvar=False)
Q_hat, beta_hat, e_hat = min_distance(r_hat, lam_hat, V)
Q_global = float(sum(Q_hat.values()))

# bootstrap calibration: recentre each resample on the fitted domain-general values
target = np.concatenate([lam_hat[k * 5:k * 5 + 5] * beta_hat[DOM_ORDER[k]] for k in range(5)])
Qb_dom = {dm: np.empty(B_BOOT) for dm in DOM_ORDER}
Qb_glob = np.empty(B_BOOT)
for b in range(B_BOOT):
    Qd, _, _ = min_distance(rb[b] - r_hat + target, lb[b], V)
    for dm in DOM_ORDER:
        Qb_dom[dm][b] = Qd[dm]
    Qb_glob[b] = sum(Qd.values())
p_boot = {dm: float((np.sum(Qb_dom[dm] >= Q_hat[dm]) + 1) / (B_BOOT + 1)) for dm in DOM_ORDER}
p_boot_global = float((np.sum(Qb_glob >= Q_global) + 1) / (B_BOOT + 1))

eb = rb - (lb * np.repeat([[beta_hat[dm] for dm in DOM_ORDER]], 5, axis=0).T.ravel())
ci_r = np.percentile(rb, [2.5, 97.5], axis=0)
ci_e = np.percentile(eb, [2.5, 97.5], axis=0)
print("global Q = %.2f on 20 df" % Q_global)

# ---- split-half reliability of the nuance profile -----------------------------------------
rs = np.random.default_rng(SEED_SPLIT)
prof_r = np.empty(N_SPLITS)
for s in range(N_SPLITS):
    perm = rs.permutation(N)
    h1, h2 = perm[:N // 2], perm[N // 2:]
    r1, l1 = item_stats(Z[h1], a[h1])
    r2, l2 = item_stats(Z[h2], a[h2])
    _, _, e1 = min_distance(r1, l1, V)
    _, _, e2 = min_distance(r2, l2, V)
    prof_r[s] = np.corrcoef(e1, e2)[0, 1]
sb = 2 * prof_r / (1 + prof_r)

# ---- cross-validated prediction of age ----------------------------------------------------
def thurstone(Ztr, Zte):
    Str, Ste = [], []
    for k in range(5):
        sl = slice(k * 5, k * 5 + 5)
        R = np.corrcoef(Ztr[:, sl], rowvar=False)
        w = np.linalg.solve(R, paf(R))
        Str.append(Ztr[:, sl] @ w)
        Ste.append(Zte[:, sl] @ w)
    return np.column_stack(Str), np.column_stack(Ste)

def cv_predictions(seed):
    rg = np.random.default_rng(seed)
    idx = rg.permutation(N)
    out = {k: np.zeros(N) for k in ("domain", "factor", "item")}
    for f in np.array_split(idx, K_FOLDS):
        tr = np.setdiff1d(idx, f)
        Dtr = np.column_stack([Z[tr][:, j * 5:j * 5 + 5].mean(1) for j in range(5)])
        Dte = np.column_stack([Z[f][:, j * 5:j * 5 + 5].mean(1) for j in range(5)])
        Ftr, Fte = thurstone(Z[tr], Z[f])
        for nm, (Xtr, Xte) in {"domain": (Dtr, Dte), "factor": (Ftr, Fte), "item": (Z[tr], Z[f])}.items():
            A = np.column_stack([np.ones(len(tr)), Xtr])
            coef, *_ = np.linalg.lstsq(A, a[tr], rcond=None)
            out[nm][f] = np.column_stack([np.ones(len(f)), Xte]) @ coef
    return out

pred = cv_predictions(SEED_CV)
sst = float(((a - a.mean()) ** 2).sum())
R2 = {k: float(1 - ((a - v) ** 2).sum() / sst) for k, v in pred.items()}
r_pred = {k: float(np.corrcoef(a, v)[0, 1]) for k, v in pred.items()}
d_item_dom = R2["item"] - R2["domain"]
d_item_fac = R2["item"] - R2["factor"]
sq_dom, sq_item = (a - pred["domain"]) ** 2, (a - pred["item"]) ** 2
tt = st.ttest_1samp(sq_dom - sq_item, 0.0)
rd = np.random.default_rng(SEED_DELTA)
dboot = np.empty(B_DELTA)
for b in range(B_DELTA):
    i = rd.integers(0, N, N)
    ss = float(((a[i] - a[i].mean()) ** 2).sum())
    dboot[b] = (1 - (sq_item[i]).sum() / ss) - (1 - (sq_dom[i]).sum() / ss)
seed_sweep = np.array([[1 - ((a - v) ** 2).sum() / sst for v in cv_predictions(100 + s).values()] for s in range(20)])

# ---- robustness: partial out gender -------------------------------------------------------
gz = (gender - gender.mean()) / gender.std(ddof=1)
Zg = Z - np.outer(gz, (gz @ Z) / (gz @ gz))
ag = a - gz * (gz @ a) / (gz @ gz)
r_g, lam_g = item_stats(Zg, ag)
rbg, _ = bootstrap(Zg, ag, SEED_BOOT + 1)
Vg = np.cov(rbg, rowvar=False)
Q_g, beta_g, e_g = min_distance(r_g, lam_g, Vg)

# ---- descriptives, power ------------------------------------------------------------------
alpha_rel, r_dom_age = {}, {}
for k, dm in enumerate(DOM_ORDER):
    Zi = Z[:, k * 5:k * 5 + 5]
    alpha_rel[dm] = float(5 / 4 * (1 - Zi.var(0, ddof=1).sum() / Zi.sum(1).var(ddof=1)))
    r_dom_age[dm] = float(np.corrcoef(Zi.mean(1), a)[0, 1])
z_crit = st.norm.ppf(0.975) + st.norm.ppf(0.80)
min_r = float(np.tanh(z_crit / np.sqrt(N - 3)))
crit4 = float(st.chi2.ppf(0.95, 4))
ncp80 = float(next(x for x in np.arange(0.0, 40.0, 0.01) if st.ncx2.sf(crit4, 4, x) >= 0.80))

n_sig_e = int(np.sum((ci_e[0] > 0) | (ci_e[1] < 0)))
reversals = 0
for k, dm in enumerate(DOM_ORDER):
    sl = slice(k * 5, k * 5 + 5)
    opp = np.sign(r_hat[sl]) == -np.sign(beta_hat[dm])
    excl0 = (ci_r[0][sl] > 0) | (ci_r[1][sl] < 0)
    reversals += int(np.sum(opp & excl0))

items_out = []
for j, name in enumerate(ITEMS):
    items_out.append({"item": name, "domain": name[0], "loading": float(lam_hat[j]),
                      "r_age": float(r_hat[j]), "r_ci": [float(ci_r[0][j]), float(ci_r[1][j])],
                      "predicted_r": float(lam_hat[j] * beta_hat[name[0]]),
                      "nuance": float(e_hat[j]), "nuance_ci": [float(ci_e[0][j]), float(ci_e[1][j])],
                      "r_age_gender_adj": float(r_g[j])})

hypothesis_supported = bool(
    min(p_boot.values()) < 0.05
    and np.percentile(prof_r, 2.5) > 0
    and np.percentile(dboot, 2.5) > 0)

result = {
    "n_total": n_total, "n_excluded_age_filter": n_drop_age,
    "n_excluded_incomplete_items": n_drop_incomplete, "n_excluded_either": n_drop_either,
    "n_analysed": N, "age_min_raw": age_min_raw, "age_max_raw": age_max_raw,
    "age_min": float(age_raw.min()), "age_max": float(age_raw.max()),
    "age_mean": float(age_raw.mean()), "age_sd": float(age_raw.std(ddof=1)),
    "age_median": float(np.median(age_raw)),
    "n_female": int((gender == 2).sum()), "n_male": int((gender == 1).sum()),
    "pct_female": float(100 * (gender == 2).mean()),
    "alpha": {k: round(v, 4) for k, v in alpha_rel.items()},
    "r_domain_age": {k: round(v, 4) for k, v in r_dom_age.items()},
    "beta_domain_factor_age": {k: round(v, 4) for k, v in beta_hat.items()},
    "Q": {k: round(v, 3) for k, v in Q_hat.items()},
    "p_chi2": {k: float(st.chi2.sf(v, 4)) for k, v in Q_hat.items()},
    "p_bootstrap": p_boot, "Q_global": round(Q_global, 3), "df_global": 20,
    "p_chi2_global": float(st.chi2.sf(Q_global, 20)), "p_bootstrap_global": p_boot_global,
    "n_nuance_ci_excludes_zero": n_sig_e, "n_sign_reversals": reversals,
    "n_item_r_ci_excludes_zero": int(np.sum((ci_r[0] > 0) | (ci_r[1] < 0))),
    "rms_r_age": float(np.sqrt(np.mean(r_hat ** 2))), "rms_nuance": float(np.sqrt(np.mean(e_hat ** 2))),
    "nuance_share_of_rms": float(np.sqrt(np.mean(e_hat ** 2)) / np.sqrt(np.mean(r_hat ** 2))),
    "splithalf_profile_r_mean": float(prof_r.mean()),
    "splithalf_profile_r_ci": [float(np.percentile(prof_r, 2.5)), float(np.percentile(prof_r, 97.5))],
    "splithalf_spearman_brown": float(sb.mean()),
    "cv_r2_domain": round(R2["domain"], 5), "cv_r2_factor": round(R2["factor"], 5),
    "cv_r2_item": round(R2["item"], 5),
    "cv_r_domain": round(r_pred["domain"], 4), "cv_r_factor": round(r_pred["factor"], 4),
    "cv_r_item": round(r_pred["item"], 4),
    "delta_r2_item_vs_domain": float(d_item_dom), "delta_r2_item_vs_factor": float(d_item_fac),
    "delta_r2_ci": [float(np.percentile(dboot, 2.5)), float(np.percentile(dboot, 97.5))],
    "delta_r2_ratio": float(R2["item"] / R2["domain"]),
    "cohen_f2_increment": float(d_item_dom / (1 - R2["item"])),
    "paired_t_sqerr": float(tt.statistic), "paired_t_df": int(N - 1), "paired_p_sqerr": float(tt.pvalue),
    "seed_sweep_mean_r2": {"domain": float(seed_sweep[:, 0].mean()), "factor": float(seed_sweep[:, 1].mean()),
                           "item": float(seed_sweep[:, 2].mean())},
    "seed_sweep_sd_delta_item_domain": float((seed_sweep[:, 2] - seed_sweep[:, 0]).std(ddof=1)),
    "gender_adj_profile_r": float(np.corrcoef(e_hat, e_g)[0, 1]),
    "gender_adj_Q": {k: round(v, 3) for k, v in Q_g.items()},
    "gender_adj_p_chi2": {k: float(st.chi2.sf(v, 4)) for k, v in Q_g.items()},
    "sensitivity_min_detectable_r": min_r, "chi2_crit_4df": crit4, "ncp_for_80pct_power_4df": ncp80,
    "n_bootstrap": B_BOOT, "n_splits": N_SPLITS, "n_folds": K_FOLDS,
    "items": items_out,
    "hypothesis_supported": hypothesis_supported,
}
print("RESULT_JSON: " + json.dumps(result))

Results and analysis

Key numbers

Caveats

• The design is cross-sectional. Every quantity here is an age DIFFERENCE, not a within-person change; birth cohort, differential attrition and age-varying self-selection into an online personality study are fully confounded with age and cannot be separated in these data.
• This is a single self-selected internet sample collected by the SAPA project in Spring 2010, 67% female, with a median age of 26 and very thin coverage above 55. It is not representative of any defined population, and no independent replication sample was analysed.
• Self-report only. Item-specific variance carries acquiescent and evaluative response bias as well as substantive nuance variance, and nothing in this design separates them; an item-level age effect could in part be an age difference in how people use a six-point scale rather than in what they are like. Informant reports would be needed to distinguish these.
• The openness result is the weakest link: alpha = .61, the smallest Q (10.50) and a bootstrap p of .032, below the noncentrality of 11.94 that 80% power at 4 df requires. It should be treated as suggestive.
• The minimum-distance statistic conditions on estimated loadings. The asymptotic chi-square treats them as known, which would be anticonservative; the bootstrap calibration recomputes loadings in every resample and gave materially the same p values, but with B = 2,000 the smallest reportable bootstrap p is .0005, so the four strong rejections are censored at that floor rather than precisely estimated.
• Complete-case analysis discarded 364 respondents with any missing item. Missingness was scattered across items (9 to 36 per item) and was not modelled; if item non-response is related to both age and item content, the analysed sample is mildly selected.
• Age was modelled as a linear correlate throughout. Published work finds non-monotonic age trajectories, so a curvilinear specification could change the size, though not the existence, of the heterogeneity; no non-linear specification was run.
• Absolute predictive accuracy is low: even all 25 items explain only 8.4% of the out-of-sample variance in age. The finding concerns the proportion of age information that domain scoring destroys, and should not be read as personality being a good predictor of age.
• The one-factor-per-domain measurement model is itself an approximation. Where a five-item domain actually contains two facets, the restriction will fail for that reason - which is a form of the substantive claim (structure below the domain matters), but it means the test cannot distinguish facet-level from item-level specificity in an instrument that measures no facets.

≈ 2800 words · AI-drafted manuscript · not peer-reviewed

This revision addresses every point raised previously and does so substantively rather than cosmetically. The manuscript is now within the venue's 2,000-2,800 word range with no executed result dropped; multiplicity is handled by naming the global chi-square(20) = 175.45 as the family-wise test and by setting the nine significant item-level intervals against the approximately 1.25 expected by chance; the four independent degrees of freedom per domain and the resulting 20-quantity profile are stated; the split halves are disclosed as sharing the full-sample weight matrix; bootstrap p values are reported as < .001 with the B = 2,000 resolution floor explained and their dependence on the same resamples as V made explicit; the priority claim is softened to a statement about what the cited literature does and does not test; the abstract now reports rejection in all five domains with openness marginal, chi-square(4) = 10.50, p = .033; and the linear-age limitation has been moved to its own early paragraph in the Discussion with a plain statement that curvature and slope heterogeneity cannot be separated by the analysis run. The science is unchanged and remains sound: the restriction is rejected globally, chi-square(20) = 175.45, p < .001, and in every domain; the nuance profile replicates across split halves, r = .788, 95% CI [.664, .887]; and the out-of-sample increment of items over their own domain scores is reliable if modest, Delta-R-squared = .047, 95% CI [.028, .066], with optimally weighted factor scores predicting worst of the three model classes. Every number, filter, seed and provenance detail matches the executed script and the archived file, and the respondents are correctly described as real people in a 2010 SAPA collection. What remains is presentational: an omnibus Table 1 that mixes sample descriptives with cross-validation results, two abbreviated item stems quoted as if verbatim, a dangling antecedent and an unexplained ratio introduced by the compression, and an assertion of low power in the Discussion that has lost its supporting statistic. None of these affect a single reported quantity. Minor revision.