1 SUPPLEMENTARY MATERIALS Project Code All R code files for this study can be found in a publicly accessible repository at https://github.com/amyonkman/LPA-Paper-Code.

SUPPLEMENTARY MATERIALS Project Code

All R code files for this study can be found in a publicly accessible repository at https://github.com/amyonkman/LPA-Paper-Code.

Tables and Figures

Supplementary Table 1: Covariate-adjusted linear regression coefficients showing the relationship between participant demographic characteristics and mean WPPSI-III scores, adjusted for child sex, maternal age, race, and education, marital status, household income, parity, prenatal smoking and alcohol, HOME score, and test city, with 95% confidence intervals (n = 517).

VIQ (95% CI) PIQ (95% CI) FSIQ (95% CI) Intercept 101.8 (95.6, 107.9) 88.3 (81.0, 95.7) 94.3 (87.8, 100.7) Child Sex

Male 0.0 (0.0, 0.0) 0.0 (0.0, 0.0) 0.0 (0.0, 0.0)

Female 4.4 (2.4, 6.4) 3.4 (1.0, 5.9) 4.5 (2.4, 6.6)

Maternal Age

19-29 0.0 (0.0, 0.0) 0.0 (0.0, 0.0) 0.0 (0.0, 0.0)

30-34 -0.6 (-3.6, 2.3) -2.4 (-5.9, 1.2) -1.8 (-4.9, 1.3)

35+ 0.4 (-2.9, 3.7) -3.1 (-7.1, 0.8) -1.6 (-5.0, 1.8)

Maternal Race

White 0.0 (0.0, 0.0) 0.0 (0.0, 0.0) 0.0 (0.0, 0.0)

Other -2.6 (-5.7, 0.6) -1.8 (-5.6, 1.9) -2.4 (-5.7, 0.8)

Maternal Education

Highschool 0.0 (0.0, 0.0) 0.0 (0.0, 0.0) 0.0 (0.0, 0.0)

College 1.4 (-3.6, 6.4) 7.2 (1.3, 13.2) 4.6 (-0.6, 9.8)

Undergraduate 4.8 (-0.2, 9.8) 9.3 (3.4, 15.2) 7.9 (2.7, 13.1)

Graduate 6.9 (1.7, 12.1) 9.6 (3.5, 15.8) 9.3 (3.9, 14.6)

Marital Status

Married 0.0 (0.0, 0.0) 0.0 (0.0, 0.0) 0.0 (0.0, 0.0)

Unmarried -0.2 (-2.8, 2.5) 1.3 (-1.8, 4.5) 0.6 (-2.1, 3.3) Household Income (CAD)

<40 000 0.0 (0.0, 0.0) 0.0 (0.0, 0.0) 0.0 (0.0, 0.0)

40 000 - 80 000 -2.1 (-6.2, 1.9) -4.9 (-9.7, -0.1) -3.9 (-8.1, 0.3) 80 000 - 100 000 -0.9 (-5.2, 3.3) -3.9 (-9.0, 1.2) -2.5 (-7.0, 1.9) >100 000 -1.2 (-5.4, 3.0) -3.8 (-8.7, 1.2) -2.6 (-7.0, 1.7) Parity

0 0.0 (0.0, 0.0) 0.0 (0.0, 0.0) 0.0 (0.0, 0.0)

1 -2.0 (-4.3, 0.3) -1.3 (-4.0, 1.5) -1.8 (-4.2, 0.6)

2 -3.8 (-7.3, -0.3) -2.0 (-6.1, 2.1) -3.3 (-6.9, 0.3)

3+ -6.6 (-12.6, -0.7) -1.0 (-8.1, 6.1) -4.5 (-10.7, 1.7)

Prenatal Smoking

No 0.0 (0.0, 0.0) 0.0 (0.0, 0.0) 0.0 (0.0, 0.0)

Yes -1.4 (-5.2, 2.4) -3.5 (-8.0, 1.0) -2.5 (-6.4, 1.4)

Prenatal Alcohol

No 0.0 (0.0, 0.0) 0.0 (0.0, 0.0) 0.0 (0.0, 0.0)

Yesht 1.5 (-1.2, 4.3) 3.4 (0.1, 6.8) 2.6 (-0.3, 5.5)

HOME Score Quartile

1^st 0.0 (0.0, 0.0) 0.0 (0.0, 0.0) 0.0 (0.0, 0.0)

2^nd 6.0 (3.2, 8.8) 6.1 (2.7, 9.4) 6.9 (4.0, 9.8)

3^rd 6.5 (3.4, 9.6) 5.8 (2.1, 9.5) 7.3 (4.1, 10.6)

4^th 7.6 (4.6, 10.7) 7.6 (3.9, 11.2) 8.9 (5.7, 12.1)

Test Site

Montreal 0.0 (0.0, 0.0) 0.0 (0.0, 0.0) 0.0 (0.0, 0.0)

Vancouver 4.6 (0.5, 8.6) 11.7 (6.9, 16.6) 9.4 (5.2, 13.6)

Toronto 2.8 (-1.2, 6.9) 4.5 (-0.3, 9.3) 4.3 (0.1, 8.5)

Hamilton 2.3 (-1.5, 6.0) 8.1 (3.6, 12.6) 6.0 (2.1, 9.9)

Kingston -2.4 (-5.6, 0.8) 4.2 (0.3, 8.0) 0.7 (-2.6, 4.1)

Halifax -3.9 (-7.2, -0.6) 10.6 (6.7, 14.5) 3.7 (0.3, 7.1)

Supplementary Table 2: Covariate-adjusted linear regression coefficients showing the

associations between the log2-concentrations of individual chemical biomarkers and WPPSI-III scores in MIREC participants, adjusted for maternal age, race, education, and marital status, household income, parity, prenatal smoking and alcohol, HOME score, and test city, and stratified by child sex, with 95% confidence intervals (n = 517).

VIQ (95% CI) PIQ (95% CI) FSIQ (95% CI) Metals

Arsenic

All Children -0.5 (-1.7, 0.7) -0.8 (-2.2, 0.6) -0.8 (-2, 0.4) Male Children -0.8 (-2.5, 0.9) -0.2 (-2.2, 1.8) -0.7 (-2.4, 1.1) Female Children 0 (-1.6, 1.7) -1.6 (1.7, -0.8) 1.7 (-0.8, -2.8) Cadmium

All Children -1.1 (-2.2, 0.1) -0.9 (-2.2, 0.4) -1.2 (-2.3, 0) Male Children -1.9 (-3.7, -0.2) -1.6 (-3.7, 0.5) -2.1 (-3.9, -0.2) Female Children -0.1 (-1.5, 1.3) -1.5 (1.3, -0.3) 1.3 (-0.3, -2.1) Lead

All Children -1.4 (-3, 0.3) -1 (-3, 0.9) -1.3 (-3.1, 0.4) Male Children -0.8 (-3.3, 1.6) -0.5 (-3.4, 2.4) -0.7 (-3.3, 1.9) Female Children -2.4 (-4.7, -0.1) -4.7 (-0.1, -1.2) -0.1 (-1.2, -4) Manganese

All Children -0.5 (-2.9, 2) 0 (-2.8, 2.9) -0.3 (-2.9, 2.2) Male Children -0.4 (-3.9, 3) -0.5 (-4.6, 3.6) -0.6 (-4.2, 3.1) Female Children -0.9 (-4.3, 2.4) -4.3 (2.4, 0) 2.4 (0, -4.2) Mercury

All Children -0.1 (-0.9, 0.6) 0.2 (-0.7, 1.1) 0 (-0.8, 0.8)

Male Children -0.1 (-1.3, 1.2) 0.3 (-1.1, 1.8) 0.1 (-1.2, 1.4) Female Children -0.1 (-1.1, 0.9) -1.1 (0.9, 0.6) 0.9 (0.6, -0.7) OCPs

β-HCH

All Children -0.3 (-1.1, 0.5) 0.1 (-0.9, 1) -0.1 (-1, 0.7) Male Children -0.3 (-1.5, 0.9) 0.4 (-1.1, 1.8) 0 (-1.3, 1.3) Female Children -0.4 (-1.5, 0.7) -1.5 (0.7, -0.1) 0.7 (-0.1, -1.5) DDE

All Children -0.7 (-1.8, 0.4) -0.7 (-2, 0.6) -0.8 (-1.9, 0.3) Male Children -1.4 (-3, 0.2) -0.6 (-2.5, 1.3) -1.2 (-2.9, 0.5) Female Children -0.1 (-1.6, 1.4) -1.6 (1.4, -1) 1.4 (-1, -2.9) Oxychlor

All Children -0.4 (-1.8, 1) 0.5 (-1.1, 2.2) 0 (-1.5, 1.5) Male Children -0.8 (-3.1, 1.6) 1.7 (-1.1, 4.4) 0.5 (-2, 2.9) Female Children 0.1 (-1.7, 1.9) -1.7 (1.9, 0.4) 1.9 (0.4, -1.9) Transnona

All Children -0.6 (-2, 0.8) 0.2 (-1.4, 1.8) -0.4 (-1.8, 1.1) Male Children -1.4 (-3.5, 0.8) 0.2 (-2.3, 2.8) -0.8 (-3, 1.5) Female Children -0.3 (-2.1, 1.6) -2.1 (1.6, 0.7) 1.6 (0.7, -1.6) OPPs

DEP

All Children -0.3 (-1.1, 0.6) -0.7 (-1.6, 0.3) -0.5 (-1.4, 0.4) Male Children -1.3 (-2.6, 0.1) -1 (-2.6, 0.6) -1.3 (-2.7, 0.2) Female Children 0.4 (-0.6, 1.4) -0.6 (1.4, -0.5) 1.4 (-0.5, -1.8) DETP

All Children 0.4 (-0.4, 1.1) 0.3 (-0.6, 1.2) 0.4 (-0.4, 1.2) Male Children -0.4 (-1.5, 0.7) -0.6 (-1.9, 0.7) -0.5 (-1.7, 0.7) Female Children 1 (-0.1, 2.1) -0.1 (2.1, 1.4) 2.1 (1.4, 0) DMDTP

All Children 0.6 (0, 1.1) 0 (-0.7, 0.6) 0.3 (-0.2, 0.9)

Male Children 0.7 (-0.2, 1.6) -0.2 (-1.2, 0.9) 0.4 (-0.6, 1.3)

Female Children 0.3 (-0.4, 1) -0.4 (1, 0) 1 (0, -0.9)

DMP

All Children 0.2 (-0.6, 0.9) -0.4 (-1.2, 0.5) -0.1 (-0.8, 0.7) Male Children -0.2 (-1.3, 0.9) -0.4 (-1.7, 0.9) -0.3 (-1.5, 0.9) Female Children 0.3 (-0.7, 1.3) -0.7 (1.3, -0.4) 1.3 (-0.4, -1.7) DMTP

All Children 0.3 (-0.2, 0.8) -0.1 (-0.7, 0.5) 0.1 (-0.4, 0.7) Male Children 0.4 (-0.4, 1.2) -0.1 (-1.1, 0.9) 0.2 (-0.7, 1.1) Female Children 0.2 (-0.4, 0.9) -0.4 (0.9, -0.1) 0.9 (-0.1, -1) Phthalates

MnBP

All Children -0.5 (-1.3, 0.4) -0.8 (-1.9, 0.2) -0.8 (-1.7, 0.2) Male Children -1.1 (-2.4, 0.2) -1.7 (-3.2, -0.2) -1.6 (-3, -0.3) Female Children 0.4 (-0.8, 1.6) -0.8 (1.6, 0) 1.6 (0, -1.5) MBzP

All Children -0.1 (-0.9, 0.7) 0.2 (-0.8, 1.1) 0 (-0.8, 0.9) Male Children -0.1 (-1.3, 1.1) 0.2 (-1.2, 1.7) 0.1 (-1.2, 1.4)

Female Children 0 (-1.1, 1) -1.1 (1, 0) 1 (0, -1.3)

MCPP

All Children -0.4 (-1, 0.2) -1.1 (-1.8, -0.4) -0.9 (-1.5, -0.2)

Male Children -0.3 (-1.1, 0.6) -0.9 (-1.9, 0.1) -0.6 (-1.5, 0.2) Female Children -0.1 (-1, 0.7) -1 (0.7, -1.1) 0.7 (-1.1, -2.2) MEP

All Children 0 (-0.6, 0.5) 0 (-0.6, 0.6) 0 (-0.6, 0.5)

Male Children 0.7 (-0.1, 1.6) 0.3 (-0.7, 1.3) 0.6 (-0.3, 1.5) Female Children -0.7 (-1.4, 0) -1.4 (0, -0.5) 0 (-0.5, -1.3) Sum of DEHP

All Children -0.3 (-1.3, 0.7) -1.4 (-2.6, -0.2) -0.9 (-2, 0.1) Male Children 0 (-1.5, 1.5) -1.6 (-3.3, 0.2) -0.8 (-2.4, 0.8) Female Children 0.2 (-1.2, 1.6) -1.2 (1.6, -0.9) 1.6 (-0.9, -2.6) PCBs

PCB118

All Children -1.1 (-2.3, 0.2) 0.2 (-1.3, 1.7) -0.6 (-1.9, 0.7) Male Children -1.5 (-3.3, 0.3) 0.4 (-1.8, 2.5) -0.7 (-2.6, 1.2) Female Children -0.5 (-2.2, 1.2) -2.2 (1.2, 0.2) 1.2 (0.2, -1.9) PCB138

All Children -0.8 (-1.9, 0.4) -0.6 (-2, 0.7) -0.8 (-2, 0.4) Male Children -1 (-2.8, 0.9) -0.3 (-2.5, 1.8) -0.8 (-2.7, 1.2) Female Children -0.7 (-2.2, 0.7) -2.2 (0.7, -1) 0.7 (-1, -2.8) PCB153

All Children -0.7 (-1.9, 0.5) -0.2 (-1.6, 1.2) -0.5 (-1.8, 0.7) Male Children -0.7 (-2.5, 1.1) -0.1 (-2.2, 2.1) -0.5 (-2.4, 1.4) Female Children -1 (-2.6, 0.6) -2.6 (0.6, -0.4) 0.6 (-0.4, -2.4) PCB170

All Children -0.4 (-1.5, 0.6) 0.4 (-0.8, 1.6) -0.1 (-1.1, 1) Male Children -0.7 (-2.2, 0.9) 0.2 (-1.6, 2) -0.3 (-1.9, 1.3)

Female Children -0.6 (-2, 0.8) -2 (0.8, 0.3) 0.8 (0.3, -1.5) PCB180

All Children -0.3 (-1.3, 0.8) 0.1 (-1.2, 1.3) -0.2 (-1.2, 0.9) Male Children -0.4 (-2.1, 1.2) 0.2 (-1.7, 2.1) -0.2 (-1.9, 1.5) Female Children -0.6 (-2, 0.8) -2 (0.8, -0.2) 0.8 (-0.2, -1.9) PCB187

All Children 0 (-1.1, 1.1) 0.2 (-1.2, 1.5) 0.1 (-1.1, 1.2) Male Children 0.2 (-1.5, 1.9) 0.2 (-1.9, 2.2) 0.2 (-1.7, 2) Female Children -0.3 (-1.7, 1.2) -1.7 (1.2, 0.3) 1.2 (0.3, -1.6) PBDE

BDE47

All Children -0.4 (-1.1, 0.3) -0.4 (-1.2, 0.5) -0.4 (-1.2, 0.4) Male Children -0.7 (-1.8, 0.5) -0.1 (-1.5, 1.2) -0.4 (-1.6, 0.8) Female Children 0.3 (-0.7, 1.2) -0.7 (1.2, -0.2) 1.2 (-0.2, -1.4) Smoking Metabolites

Cotinine

All Children -0.1 (-0.4, 0.3) -0.2 (-0.6, 0.2) -0.2 (-0.5, 0.2) Male Children -0.1 (-0.6, 0.4) 0 (-0.6, 0.6) -0.1 (-0.6, 0.4) Female Children 0 (-0.5, 0.5) -0.5 (0.5, -0.3) 0.5 (-0.3, -0.9)

Supplementary Table 3: Comparison of three quality measures for each of the proposed models: the Bayesian Information Criterion, Akaike Information Criterion, and Entropy. Each model has a different combination of number of profiles and assumptions about model variance and covariance.

Number of Profiles BIC AIC Entropy

Equal variance; covariance = 0

1 45457 45227 1.000

2 43409 43061 0.900

3 42422 41954 0.942

4 42149 41562 0.919

5 42125 41418 0.928

6 41695 40869 0.948

7 41712 40767 0.927

8 41709 40644 0.933

9 41701 40517 0.911

10 41653 40350 0.924

11 41674 40252 0.917

12 41739 40197 0.912

1 45457 45227 1.000

2 43347 42883 0.905

3 42228 41530 0.948

4 41900 40968 0.934

5 42025 40858 0.944

6 41714 40313 0.956

7 41788 40153 0.953

8 41774 39905 0.957

9 41893 39790 0.959

10 42041 39704 0.961

11 42098 39526 0.962

12 42140 39335 0.965

Equal variance and equal covariance

1 39777 38053 1.000

2 39719 37875 0.978

3 39847 37884 0.797

4 39666 37584 0.973

5 39625 37424 0.885

6 39834 37514 0.869

7 39656 37216 0.906

8 39566 37008 0.899

9 39670 36992 0.877

10 39784 36986 0.884

11 39857 36941 0.893

12 39974 36938 0.893

Supplementary Table 4: Covariate-adjusted linear regression coefficients showing the associations between latent profile membership and WPPSI-III scores, adjusted for maternal age, race, education, and marital status, household income, parity, prenatal alcohol, HOME score, and testing city compared to the Reference Profile, with 95% confidence intervals.

Results are shown for all children, and then stratified by sex. We found no significant interactions between latent profiles and child sex (all p-values > 0.05; n = 517).

VIQ (95% CI) PIQ (95% CI) FSIQ (95% CI) All Children

Intercept 98.5 (92.0, 105.0) 98.6 (90.9, 106.2) 98.3 (91.5, 105.0) High MEP -0.9 (-3.9, 2.0) -2.0 (-5.5, 1.5) -1.7 (-4.8, 1.4) High POP -1.8 (-6.3, 2.8) 0.0 (-5.4, 5.4) -0.9 (-5.7, 3.8) Low POP -2.0 (-7.9, 3.9) 4.5 (-2.5, 11.5) 1.2 (-5.0, 7.4) Smoking Chemicals -1.1 (-7.1, 4.9) -3.5 (-10.5, 3.5) -2.6 (-8.8, 3.7) Boys

Intercept 99.5 (89.7, 109.3) 100.3 (88.8, 111.8) 100.0 (89.8, 110.3) High MEP 0.4 (-4.0, 4.8) -1.1 (-6.3, 4.1) -0.3 (-4.9, 4.3) High POP -0.5 (-7.3, 6.2) -1.5 (-9.4, 6.4) -1.0 (-8.1, 6.0) Low POP -1.8 (-14.2, 10.5) 12.1 (-2.4, 26.5) 5.0 (-8.0, 17.9) Smoking Chemicals 0.5 (-8.4, 9.4) -0.3 (-10.7, 10.1) 0.2 (-9.1, 9.6) Girls

Intercept 102.6 (92.7, 112.6) 102.3 (90.1, 114.5) 102.5 (92.1, 112.9) High MEP -0.9 (-5.0, 3.2) -3.5 (-8.5, 1.5) -2.5 (-6.8, 1.8) High POP -2.3 (-8.6, 4.0) 0.3 (-7.5, 8.0) -1.1 (-7.7, 5.5) Low POP -1.9 (-8.7, 5.0) 2.3 (-6.1, 10.7) 0.1 (-7.0, 7.3) Smoking Chemicals -3.2 (-11.4, 4.9) -6.7 (-16.6, 3.3) -5.6 (-14.1, 2.9)

Supplementary Table 5: Demographic characteristics of participants in each k-means cluster compared to the total study population.

Total (%) Reference

Cluster (%) Phthalate

Cluster (%) High POP

Cluster (%) OPP

Cluster (%) Smoking Chemicals Cluster (%)

N = 517 N =115 N =133 N = 111 N = 140 N =18

Child Sex

Male 49 47 55 47 46 50

Female 51 53 45 53 54 50

Maternal Age

19-30 21 13 29 7 27 39

30-35 39 39 37 32 47 28

35+ 41 48 35 61 26 33

Maternal Race

White 86 93 85 78 86 89

Other 14 7 15 22 14 11

Maternal Education

Highschool 5 3 10 2 4 22

College 27 19 35 23 29 39

Undergraduate 38 45 32 35 42 39

Graduate 29 33 23 41 24 0

Marital Status

Married 72 84 71 71 67 50

Unmarried 28 16 29 29 33 50

Household Income

< 40 000 9 4 14 9 6 39

40 000 - 80 000 29 23 34 27 31 17

80 000 - 100 000 21 26 20 16 23 11

> 100 000 41 46 33 48 41 33

Parity

Zero 44 33 38 56 47 50

One 41 48 45 37 37 33

Two 12 15 13 6 12 17

Three or More 3 4 5 1 4 0

Prenatal Smoking

No 91 98 93 92 94 11

Yes 9 2 7 8 6 89

Prenatal Alcohol

No 83 83 89 78 84 56

Yes 17 17 11 22 16 44

HOME Score

1st 26 20 29 21 31 39

2nd 28 27 32 32 22 17

3rd 22 25 21 19 22 22

4th 24 28 18 28 25 22

Test City

Vancouver 9 14 7 15 4 6

Toronto 10 6 11 14 8 6

Hamilton 13 10 19 9 14 0

Kingston 24 32 23 13 24 44

Montreal 25 15 23 31 30 22

Halifax 20 23 17 18 20 22

Supplementary Table 6: Covariate-adjusted linear regression coefficients showing associations between k-means cluster membership and WPPSI-III scores, adjusted for maternal age, race, education, marital status, household income, parity, prenatal alcohol, HOME scores, and test city compared to medium-level Reference class membership. Results shown for all children, and then stratified by sex, with 95% confidence intervals (n = 517).

VIQ (95% CI) PIQ (95% CI) FSIQ (95% CI) All Children

Intercept 97.3 (90.7, 103.8) 100.4 (92.7, 108.1) 98.6 (91.8, 105.4) Phthalates 0.4 (-2.7, 3.5) -2.2 (-5.9, 1.4) -1.0 (-4.2, 2.2)

High POP -1.0 (-4.2, 2.3) -1.4 (-5.3, 2.4) -1.4 (-4.8, 2.0)

High OPPs 1.3 (-1.8, 4.3) -1.5 (-5.0, 2.1) 0.1 (-3.1, 3.2)

Smoking Chemicals -1.8 (-8.0, 4.4) -5.4 (-12.7, 1.8) -4.1 (-10.5, 2.3) Male Children

Intercept 95.1 (86.0, 104.2) 100 (89.3, 110.7) 97.1 (87.6, 106.6) Phthalates 0.8 (-3.8, 5.3) -1.6 (-6.9, 3.8) -0.3 (-5.1, 4.5)

High POP -1.4 (-6.4, 3.5) -0.1 (-6.0, 5.8) -0.8 (-6.1, 4.4)

High OPPs -0.4 (-5.1, 4.4) -2.5 (-8.1, 3.1) -1.4 (-6.5, 3.6) Smoking Chemicals -2.5 (-11.8, 6.7) -3.7 (-14.6, 7.2) -3.5 (-13.2, 6.3) Female Children

Intercept 101.1 (91.4, 110.8) 103.0 (91.0, 115.0) 98.6 (92.0, 112.3) Phthalates -0.1 (-4.3, 4.2) -3.5 (-8.8, 1.8) -1.0 (-6.7, 2.3)

High POP -1.0 (-5.3, 3.4) -3.1 (-8.5, 2.3) -1.4 (-7.1, 2.0)

High OPPs 2.2 (-1.8, 6.2) -1.4 (-6.4, 3.5) 0.1 (-3.6, 4.7)

Smoking Chemicals -2.1 (-10.4, 6.1) -7.5 (-17.7, 2.7) -4.1 (-14.2, 3.2)

Supplementary Figure 1: Study sample flow chart.

Supplementary Figure 2: Directed acyclic graph (DAG) showing confounders and mediators of the effects of gestational chemical mixtures on child WPPSI-III scores.

Supplementary Figure 3: Covariate-adjusted linear regression coefficients showing the

associations between k-means cluster membership and WPPSI-III scores, adjusted for maternal age, race, education, and marital status, household income, parity, prenatal alcohol, HOME score, and testing city compared to the Reference Cluster, with 95% confidence intervals.

Results are shown for all children, and then stratified by sex (n=517).