Variable-based childhood gender atypicality and fertility: preliminary results

Missing data: score-specific and model-specific complete cases only; no imputation.

Executive summary

The NCDS can support a non-text, interpretable measure of childhood gendered expression. The strongest sex-diagnostic domains are the age-11 activity battery, the coded age-11 occupational aspiration (n958), and age-16 vocational orientation. Parent reports and teacher BSAG scores add a weaker but distinct behavioural-emotional axis. Cross-fitted elastic-net all-domain scores have excellent out-of-fold sex discrimination (AUC 0.981 through age 11 and 0.988 through age 16), while random forests give similar results (AUC 0.974 and 0.986).

For fertility, the integrated scores produce several statistically significant preliminary signals—especially an age-16 all-domain score associated with a no-child ideal, greater uncertainty at 23, a lower probability of respondent/partner sterilisation or reported medical fertility constraint at 42, a slightly larger age-23 target, and later entry into parenthood. The age-11 integrated score is associated with later entry into parenthood and two conditional realization/intention outcomes.

The domain-specific findings form three coherent candidate directions rather than a single preferred association: (1) age-11 activity/care atypicality and social parenthood at 55; (2) age-16 activity/vocational atypicality and entry into parenthood or childlessness; and (3) vocational atypicality and the development, revision and realization of fertility preferences. Smaller realization risk sets provide a fourth, secondary set of signals.

These measures are best described as gender diagnosticity / atypicality, not direct measures of gender identity. Recorded sex is classified only as a scaling device; the fertility models are associational and not causal.

1. Score construction

For each domain, a model predicts recorded sex (male=1) from childhood survey covariates. Every reported score is an out-of-fold prediction from five-fold stratified cross-fitting. Raw atypicality is the predicted probability of the other recorded-sex class; the analysis exposure is z-standardized within recorded sex. This makes one unit a one-SD shift toward less sex-typical expression within boys or within girls.

The estimator follows the measurement tradition most closely matched to the domain: shrinkage LDA for activities and the classic occupation diagnosticity score; logistic models for observer ratings; elastic-net logistic regression for high-dimensional academic/vocational/all-domain batteries; PCA followed by logistic regression for care orientation. Random forests are nonlinear benchmarks.

Construct-specific precedents and estimator choice

“Follow” means that the construct and modelling logic are anchored in the cited study; it does not mean that the NCDS implementation is an item-for-item replication. The available NCDS variables and their measurement levels determine the final estimator.

NCDS construct Main precedent Estimator Why this choice
Activities/leisure (11 and 16) Lippa & Connelly (1990); Lippa (1991) Shrinkage LDA Classic gender diagnosticity used activity/hobby profiles and discriminant functions to obtain continuous male–female diagnostic probabilities. Shrinkage stabilizes the covariance estimate in the NCDS battery.
Vocational orientation (11) Lippa & Connelly (1990); Lippa (1991) LDA on one-hot n958 categories Occupational preferences were the original gender-diagnosticity application. One-hot coding preserves the nominal occupation categories rather than imposing a false numerical order.
Academic orientation (16) Lippa (1991); Ilmarinen et al. (2023) Cross-fitted elastic-net logistic School subjects are a classic GD domain; Ilmarinen et al. extended GD to academic profiles with regularized logistic prediction and cross-validation. Penalization handles correlated, multi-category aptitude indicators.
Vocational orientation (16) Lippa & Connelly (1990); Ilmarinen et al. (2023) Cross-fitted elastic-net logistic The construct follows occupational GD, while elastic net is preferable for the larger set of overlapping broad/detailed job codes and job-value items.
Parent behaviour and teacher BSAG (7/11) Fleming, Harris & Halpern (2017) Cross-fitted logistic probability Fleming et al. used existing behavioural and emotional survey items in a logistic model to estimate the probability of behaving like same-sex peers. Parent and teacher batteries are kept separate to retain reporter-specific meaning.
Care/domestic orientation (11/16) Wandschneider et al. (2022), adapted PCA followed by logistic regression Their gender-score workflow considered household practices, evaluated PCA as a possible domain-reduction stage, and derived conditional probabilities with logistic regression. Here PCA summarizes overlapping care items; this is an adaptation, not an exact replication.
All-domain scores through 11/16 Fleming et al. (2017); Ilmarinen et al. (2023) Cross-fitted elastic-net logistic A single probability score combines multiple observed domains. Elastic net shrinks redundant predictors and cross-fitting supplies out-of-sample scores, limiting overfit in the downstream fertility associations.
Nonlinear all-domain benchmark Vedres & Vasarhelyi (2019) Cross-fitted random forest Random forest tests whether nonlinearities and interactions materially improve sex-diagnostic performance and provides held-out permutation importance. It is a benchmark, not the primary inferential score.
Score Construct Age Reporter Estimator Complete N OOF AUC OOF balanced accuracy
act11 activities/leisure 11 child lda 10,979 0.947 0.878
voc11 vocational orientation (n958) 11 child-generated/coded lda 13,664 0.886 0.806
care11 care/domestic orientation 11 child pca logit 12,810 0.865 0.792
parent_u11 behaviour/emotional presentation 7+11 parent (mostly mother) logit 10,567 0.693 0.641
bsag_u11 behaviour/emotional presentation 7+11 teacher (BSAG) logit 12,779 0.716 0.660
acad16 academic/subject orientation 16 cohort member elastic net 10,640 0.723 0.666
act16 activities/leisure 16 cohort member lda 10,223 0.768 0.699
voc16 vocational orientation 16 cohort member elastic net 10,366 0.935 0.854
care16 care orientation/information 16 cohort member pca logit 7,751 0.766 0.689
all_u11_en all domains through age 11 <=11 child + parent + teacher elastic net 7,375 0.981 0.934
all_u16_en all domains through age 16 <=16 child + parent + teacher elastic net 2,786 0.988 0.951
all_u11_rf all-domain nonlinear benchmark <=11 child + parent + teacher random forest 7,375 0.974 0.922
all_u16_rf all-domain nonlinear benchmark <=16 child + parent + teacher random forest 2,786 0.986 0.945

Face-valid direction and importance

The learned axes reproduce historically recognizable sex patterning in this cohort:

  • Age 11 activities: infrequent sewing/knitting and cooking, plus frequent model-making and sport, are male-classifying; the reverse is female-classifying. Because activity responses run from frequent to infrequent, coefficient signs must be read with the item coding.
  • n958 occupation at 25: skilled/manual work, forces, sport and foreman/manual categories are male-classifying; nursing, housewife, personal service, teaching, shop and clerical categories are female-classifying.
  • Age 16 academic orientation: higher reported aptitude in science/mathematics/practical subjects is male-classifying; English/music is female-classifying.
  • Age 16 occupation: building/engineering/manual categories are male-classifying; hairdressing, secretarial, nursing/welfare and clothing/textile categories are female-classifying.
  • Held-out RF permutation importance confirms that age-11 sewing/knitting, model-making and n958 dominate the integrated score; through age 16, occupational aspiration and outdoor sport also contribute.

Variable–domain mapping

  • Age-11 activities/leisure: meeting friends; reading outside schoolwork; listening to non-pop music; attending outside-school and school clubs; helping at home; sport; writing stories; drawing/painting; cooking; stamp collecting; sewing/knitting; model-making; and looking after animals.
  • Age-11 vocational orientation: the occupation the child expected or wanted to have at age 25 (n958), originally coded into occupational categories by the NCDS team.
  • Age-11 care/domestic orientation: helping at home, cooking, sewing/knitting, and looking after animals. These are a theoretically selected subset of the broader age-11 activity battery.
  • Age-7/11 parent-reported behaviour: activity level and peer contact; temper tantrums; difficulty concentrating or settling; preference for being alone; being bullied; destructiveness; misery/tearfulness; fidgetiness; worrying; irritability; distress in new situations; fighting; and disobedience.
  • Age-7/11 teacher-reported BSAG: unforthcomingness, withdrawal, depression, anxiety about acceptance by adults, hostility towards adults, writing off adult standards, anxiety about acceptance by children, hostility towards children, restlessness, inconsequential behaviour, miscellaneous symptoms, and miscellaneous nervous symptoms, measured at both ages.
  • Age-16 academic orientation: reported aptitude in mathematics, English, science, art, music, practical subjects, and sports/games.
  • Age-16 activities/leisure: frequency of reading, outdoor games/sport, swimming, indoor games/sport, television viewing, friends’ parties, dancing/discos, and voluntary work.
  • Age-16 vocational orientation: hoped-for and expected first job, each represented by a broad job area and a detailed occupational category, plus the first, second and third most important qualities sought in a job.
  • Age-16 care orientation/information: whether more information about baby care or child development was wanted; sources of information about baby care and child development (friends/siblings, television, films, books/magazines, church, parents, another person, youth clubs, or nowhere specific); and activities with younger children (babysitting at or away from home, helping a playgroup, helping younger children at school, or other activities).
  • All-domain scores through age 11: all age-11 activity and occupational variables, the age-7/11 parent reports, and the age-7/11 BSAG scores. The care items enter as part of the activity battery rather than being duplicated.
  • All-domain scores through age 16: all variables in the age-11 integrated score plus the age-16 academic, activity, vocational and care-information variables. The elastic-net and random-forest versions use the same domain inputs but different estimators.

2. Fertility outcomes and model mapping

Construct Variables Age/wave Source Model
Ideal size16; nochild_ideal16 Age 16 / sweep 3 childhood file (SN 5565) OLS; logit AME
Desire more23; uncertain23; target conditional sensitivity Age 23 / sweep 4 SN 5566 + parity from SN 9418 logit AME
Intention more33/42; uncertain33/42; constraint33/42 Ages 33 and 42 / sweeps 5-6 SN 5567/5578 + SN 9418 logit AME
Target target23, target33, target42; revision state Ages 23, 33, 42 intention items + SN 9418 parity OLS; multinomial AME
Parenthood childless50/55; age at first birth Ages 50 and 55 SN 9418; SN 7669 logit AME; Cox PH
Parity parity50/55; parent-only parity Ages 50 and 55 SN 9418; SN 7669 Poisson AME
Social parenthood broad/non-own counts and indicators Age 55 SN 7669 ND9TOTAC/ND9TOTOC logit/Poisson AME
Realization target-to-parity states; birth after positive intention; persistent childlessness 23/33/42 to age 50 SN 5566/5567/5578 + SN 9418 logit; multinomial AME

All pooled adjusted models include recorded sex and the pre-existing manuscript covariate set: childhood body-size measures, parental ages, birth order, age-11 reading/mathematics scores, father class, tenure, low birthweight, perinatal indicator, low mood at 11, and parental teen-birth indicators. Binary outcomes use logit average marginal effects (percentage points); size/target uses OLS; counts use Poisson average marginal effects; first-birth timing uses Cox proportional hazards; revision/realization categories use multinomial average marginal effects. Revision and realization models additionally condition on target and parity at the origin wave.

The age-33/42 constraint indicator is not a general social or relationship constraint. It equals one when the cohort member or partner was reported as sterilised, had been told by a doctor that they could not have children, or had been advised not to have children. In the intention-state construction it also identifies respondents routed around the intention question when that question is missing.

3. Main integrated-score results

The table lists adjusted pooled integrated-score results with p<0.05.

Score Construct Outcome Estimate Scale N p
All-domain elastic net, <=16 ideal ideal of no children at 16 0.88** percentage points 1,452 0.0036
All-domain elastic net, <=16 desire uncertain desire at 23 1.47** percentage points 1,331 0.0061
All-domain elastic net, <=16 intention respondent/partner sterilisation or medical fertility constraint at 42 -3.11* percentage points 1,259 0.0318
All-domain elastic net, <=11 realization remained childless 33-50 despite positive target -6.54* percentage points 255 0.0334
All-domain elastic net, <=11 intention positive intention at 33 (same-wave parity adjusted) -2.19* percentage points 1,857 0.0347
All-domain elastic net, <=16 target intended total family size at 23 0.07* children 1,228 0.0414
All-domain elastic net, <=16 realization 42_to_50: exact -0.84* percentage-point multinomial AME 677 0.0118
All-domain elastic net, <=16 realization 42_to_50: under 0.36* percentage-point multinomial AME 677 0.0398
All-domain elastic net, <=16 parenthood entry into biological parenthood by 50 0.918* hazard ratio 1,077 0.0129
All-domain elastic net, <=11 parenthood entry into biological parenthood by 50 0.952* hazard ratio 2,572 0.0302

Random-forest integrated-score results

The separate table below lists significant adjusted pooled results for the all-domain random-forest scores. As above, each estimate represents a one-within-sex-SD increase in gender atypicality.

Score Construct Outcome Estimate Scale N p
All-domain random forest, <=11 desire uncertain desire at 23 1.22** percentage points 3,355 0.0016
All-domain random forest, <=11 parity own-child count at 55, parents only 0.05** children 2,063 0.0097
All-domain random forest, <=11 intention positive intention at 33 (same-wave parity adjusted) -2.60* percentage points 1,857 0.0110
All-domain random forest, <=11 realization remained childless 33-50 despite positive target -7.42* percentage points 255 0.0123
All-domain random forest, <=11 desire desire for more children at 23 -1.37* percentage points 3,155 0.0133
All-domain random forest, <=11 social parenthood recognized non-own-child count at 55 0.04* children 2,555 0.0141
All-domain random forest, <=11 ideal ideal of no children at 16 0.64* percentage points 2,905 0.0245
All-domain random forest, <=11 parity biological parity at 50, parents only 0.04* children 2,085 0.0410
All-domain random forest, <=11 realization above age-33 target at age 50 2.00* percentage-point multinomial AME 1,414 0.0410
All-domain random forest, <=16 ideal ideal of no children at 16 1.16** percentage points 1,452 0.0095
All-domain random forest, <=16 desire uncertain desire at 23 1.39* percentage points 1,331 0.0233
All-domain random forest, <=16 intention respondent/partner sterilisation or medical fertility constraint at 42 -3.09* percentage points 1,259 0.0270
All-domain random forest, <=16 parenthood entry into biological parenthood by 50 0.929* hazard ratio 1,077 0.0290

Interpretation: the estimates are small on the population scale except for restricted realization risk sets. The Cox estimates imply slower transition to first biological parenthood for more atypical respondents (HR 0.952 through age 11; HR 0.918 through age 16).

4. Domain-specific decomposition

A. Childhood activities/care and social parenthood

Score Outcome Estimate Scale N p
Activities, 11 any recognized non-own child at 55 2.05*** percentage points 3,049 0.0005
Activities, 11 recognized non-own-child count at 55 0.04** children 3,065 0.0018
Care/domestic, 11 any recognized non-own child at 55 1.61** percentage points 3,512 0.0056
Care/domestic, 11 recognized non-own-child count at 55 0.04** children 3,528 0.0036

Age-11 activity and care/domestic atypicality both predict a greater probability and number of recognized non-own children at 55. The consistency across two related exposures and two operationalizations makes social parenthood a substantive candidate RQ.

B. Adolescent activities/vocation and entry into parenthood

Score Outcome Estimate Scale N p
Activities, 16 biologically childless at 50 2.43*** percentage points 2,752 0.0008
Activities, 16 no own child at 55 2.25** percentage points 2,741 0.0019
Activities, 16 no recognized child at 55 1.82** percentage points 2,741 0.0064
Vocational orientation, 16 biologically childless at 50 1.58* percentage points 2,740 0.0192
Vocational orientation, 16 no own child at 55 1.53* percentage points 2,731 0.0250
Activities, 16 entry into biological parenthood by 50 0.936** hazard ratio 2,749 0.0020
Vocational orientation, 16 entry into biological parenthood by 50 0.925*** hazard ratio 2,737 0.0002

Age-16 activity atypicality is associated with childlessness measured at both 50 and 55, while activity and vocational atypicality predict a slower transition to first biological parenthood. The repeated childlessness indicators are closely overlapping confirmations of one parenthood-entry pattern.

C. Vocational atypicality and preference–revision–realization

Score Outcome Estimate Scale N p
Vocational aspiration (n958), 11 revision, 33_to_42: upward 2.99*** percentage-point multinomial AME 1,646 0.000576
Vocational aspiration (n958), 11 realization, 33_to_50: over 3.28*** percentage-point multinomial AME 2,113 0.000025
Vocational orientation, 16 ideal family size at 16 -0.04** children 3,846 0.0053
Vocational orientation, 16 desire for more children at 23 -1.54** percentage points 3,296 0.0029
Vocational orientation, 16 desire for more children at 23 (same-wave parity adjusted) -1.57** percentage points 3,296 0.0016
Vocational orientation, 16 respondent/partner sterilisation or medical fertility constraint at 42 -2.53** percentage points 3,232 0.0041
Vocational orientation, 16 entry into biological parenthood by 50 0.925*** hazard ratio 2,737 0.0002

The age-11 occupational score is associated with upward revision from 33 to 42 and with ending above the age-33 target by 50. Age-16 vocational atypicality is associated with a slightly smaller ideal at 16, a lower probability of wanting more children at 23, a lower probability of respondent/partner sterilisation or reported medical fertility constraint at 42, and slower entry into parenthood. Together these results motivate a trajectory question rather than a single isolated target-realization coefficient.

D. Secondary realization signals in restricted risk sets

Score Outcome Estimate Scale N p
Care orientation, 16 birth 33-42 after positive intention 6.81** percentage points 452 0.0033
Academic orientation, 16 birth 33-42 after positive intention 5.08** percentage points 631 0.0076
Academic orientation, 16 birth 33-50 after positive intention 5.04** percentage points 556 0.0077

Care and academic atypicality are positively associated with births following a positive age-33 intention, but these risk sets are smaller and the intervals overlap. They are better retained as secondary results until a common-panel sensitivity and fuller event-history cleaning are completed.

6. Limitations

  • The measures capture cohort- and period-specific gendered expression, not latent gender identity. High sex classification accuracy partly reflects historically strongly segregated activities and occupations.
  • Complete-case samples differ by score. The all-domain age-16 score is available for 2,786 cohort members before fertility/covariate restrictions, versus 7,375 for the age-11 integrated score; comparisons across scores therefore mix construct and sample differences.
  • Parent ratings are mostly maternal and BSAG is teacher-reported; both may reflect observer expectations as well as child behaviour.
  • Target realization is not equivalent to preference fulfillment: targets may adapt, births may be constrained, and partnership/health conditions may intervene.
  • Exact parity-specific event sequences still require cleaning the raw child/pregnancy grids; the present SN 9418 outcomes support parity states and eldest/youngest birth timing but not a complete dated sequence for every birth.

Method references