Achievement & Ascription inEducational Attainment

Genetic & Environmental Influences on Adolescent Schooling

François Nielsen

In memory of Bruce Eckland 1932—1999

Blau & Duncan’s (1967) model of attainment

Classic Attainment Model

• Classic substantive interpretations:– there is low ascription as direct occupational

inheritance FsOcc -> RsOcc is only .115– education serves to reproduce inequality as

most of r(FsOcc, RsOcc) = .405 is indirect, thru RsEd

– there is much opportunity as the major part (.859 x .394) of r(RsEd, RsOcc) = .596 is driven by RsEd residual, thus independent of social origins

3 Problems

1. Model parameters are ambiguous measures of ascription versus opportunity for achievement in a system of stratification

2. Model is vulnerable to specification bias with respect to family background

3. Estimates of associations between explanatory variables and outcomes confound environmental and genetic influences

Each problem in more detail…

Problem 1: Interpretation

• Traditionally:– effects of background variables (e.g., FsOcc,

FsEd) associated with ascription or social reproduction

– effects of intermediate variables (e.g., RsIQ, RsEd) associated with opportunity for achievement

Problem 1 (cont’d)

• BUT classic interpretations are ambiguous:• Herrnstein & Murray (1994):

– strong effect of IQ on educational & occupational outcomes indicates high opportunity for achievement

• Fischer et al. (1996) counter: – IQ effect is not that strong– IQ score measures exposure to curricula & social

inheritance rather than native talent, so IQ effect measures ascription rather than achievement

• Same ambiguity with effect of RsEd!

Problem 2: Specification

• If family background is not completely specified:– opportunity for achievement overestimated – strength of ascription underestimated

• Herrnstein & Murray (1994):– use composite SES measure based on parental education &

income

• Critics (Korenman & Winship 2000; Fischer et al. 1996):– composite SES measure leaves out important aspects of

background causing specification bias which: – inflates effect of IQ, thus evidence for achievement opportunity– underestimates strength of social ascription

Problem 2 (cont’d)

• So Fischer et al. (1996):– re-estimate H&M’s (1994) model of being in poverty,

including IQ plus 28 control variables – find that the effect of IQ is reduced by half, but still

significant

• In general:– no way to guarantee that all relevant aspects of family

background have been explicitly measured and included in the model

– thus that (ascription / opportunity) has not been (under / over) -estimated

Problem 3: Confounding

2 remarkable papers in ASR:1. Eckland (1967):

– Occupational mobility tables assume null model in which sons from any origin category are equally likely to reach any destination category

– If ability to reach certain destinations is in part genetically determined and unequally distributed among sons from different origins, so that sons from certain origins are more likely to reach certain destinations, resulting asymmetry falsely attributed to a lack of perfect mobility

– Thus to estimate social mobility one must control for origin / destination association due to genetic inheritance of abilities

Problem 3 (cont’d)

2. Scarr & Weinberg (1978), study of adopted children:– Correlation of adoptive parents IQ with adopted

children IQ is low– Correlation of parents IQ with biological children IQ is

high– Correlation of adopted child IQ with education of

biological mother (proxy for cognitive ability) is high– Conclude: association between “family background”

and child achievement in biological families largely reflects genetic inheritance of abilities that enhance achievement, rather than environmental / social influences

Problem 3 (cont’d)

Conclusion :

• The classic attainment model confounds environmental & genetic influences on attainment

• Effect of FsEd or FsOcc on RsEd or RsOcc may include a genetic component, thus is potentially biased measure of social inheritance or ascription

A Solution?

• Using data on siblings with different degrees of biological relatedness (MZ twins, DZ twins, full sibs, half sibs, cousins, unrelated sibs)

• Estimate behavior genetic (BG) model that partitions variance in attainment into components due to– genes– common (shared) environment of siblings– specific (unshared) environment of siblings

Solution? (cont’d)

BG model alleviates problems of classical attainment model:

• BG model explicitly separates genetic and environmental influences– environmentality (= proportion of attainment variance

due to common environment of sibs) measures social ascription / inheritance

– heritability (= proportion of attainment variance due to genes) measures opportunity for achievement

• Specification problem eliminated as BG model estimates family environmental effects in “black box” fashion

Empirical Analysis

• I illustrate these ideas by estimating a BG model of adolescent school achievement (Verbal IQ, GPA & college plans)

• Using data on 6 types of sibling pairs from the AddHealth study (MZ twins, DZ twins, full sibs, half sibs, cousins, unrelated sibs)

VIQ1

GPA1

CPL1

A3A2A1E3

E2

E1

C2C1 C3

VIQ2

GPA2

CPL2

E3

E2E1

A3A2A1

C2C1 C3

k k k

1.01.01.0

Model Variables

• Measured variables:– VIQ = verbal IQ– GPA = grade point average– CPL = college plans

• Latent variables (Cholesky factorizations):– A1, A2, A3: genetic factors– C1, C2, C3: common environment– E1, E2, E3: specific environment (includes

measurement error)

Model Assumptions

• Genetic factors Aj (j=1…3) correlated across siblings by a quantity k:– k represents degree of relatedness of siblings– assuming (for the moment) no assortative

mating– MZ: k=1; DZ, FS: k=.5; HS: k=.25; CO:

k=.125; NR: k=0

Model Assumptions (cont’d)

• Each common environmental factor Cj (j=1…3) assumed perfectly correlated (r=1) across siblings

• Variances of all latent variables are set to 1.0

• Estimate by ML with Mx program (Mike Neale)

MZ twins (below diagonal, N=170) -- DZ twins (above diagonal, N=290) VIQ1 GPA1 CPL1 VIQ2 GPA2 CPL2 VIQ1 -- .239 .172 .356 .047 .035 GPA1 .277 -- .273 .132 .332 .062 CPL1 .290 .378 -- .136 .105 .264 VIQ2 .724 .308 .239 -- .245 .136 GPA2 .182 .660 .322 .308 -- .292 CPL2 .325 .362 .663 .374 .393 -- Full siblings (below diagonal, N=702) -- Half siblings (above diagonal, N=242) VIQ1 GPA1 CPL1 VIQ2 GPA2 CPL2 VIQ1 -- .183 .236 .310 -.103 .183 GPA1 .295 -- .434 .092 .278 .081 CPL1 .212 .380 -- .111 .102 .204 VIQ2 .411 .189 .148 -- .127 .203 GPA2 .163 .360 .245 .265 -- .295 CPL2 .133 .226 .332 .252 .406 -- Cousins (below diagonal, N=105) -- Non related siblings (above diagonal, N=174) VIQ1 GPA1 CPL1 VIQ2 GPA2 CPL2 VIQ1 -- .292 .182 .063 -.101 .013 GPA1 .171 -- .372 -.066 .080 -.007 CPL1 .061 .206 -- .099 .169 .190 VIQ2 .354 .127 .007 -- .253 .155 GPA2 .090 .104 -.013 .191 -- .180 CPL2 .238 .207 .121 .271 .224 --

Model comparisons Fit statistics Tests Model 2 df p AIC RMSEA Test 2 df P 1. BACE 153.930 105 .001 -56.070 .042 2. BAE 179.069 111 .000 -42.931 .047 2 vs. 1 24.35 6 .000 3. BCE 296.203 111 .000 74.203 .082 3 vs. 1 142.273 6 .000 4. ACE 153.930 108 .002 -62.070 .041 4 vs. 1 0.000 3 * 5. AE 179.069 114 .000 -48.931 .046 5 vs. 4 25.139 6 .000 6. CE 296.203 114 .000 68.203 .079 6 vs. 4 148.273 6 .000 7. ACEd 160.738 111 .001 -61.262 .045 7 vs. 4 6.808 3 .078 8. A1CE 221.945 111 .000 -.055 .064 8 vs. 4 68.014 3 .000 9. AdCE 188.139 111 .000 -33.861 .054 9 vs. 4 34.209 3 .000 10. ACdE 167.437 111 .000 -54.563 .043 10 vs. 4 13.507 3 .004 11. AC1E 158.807 111 .002 -63.193 .040 11 vs. 4 4.877 3 .181 12. AC1Eda 165.435 114 .001 -62.565 .044 12 vs. 4 11.505 6 .074 12 vs. 11 6.628 3 .085 Note: B = phenotypic paths; A = genetic paths; C = common environment paths; E = specific environment paths; Ad, Cd, Ed: off diagonal elements of A, C, or E fixed (specific factors model); A1, C1: lower triangular matrix A, C reduced to single column vector (common factor model). a favored model * probability incalculable Favored model is AC1Ed (although AC1E is also an attractive choice)

Estimated Model Parameters (Standardized)

Table 3 – Standardized path coefficients for genetic, common environmental, and specific environmental factors for favored AC1Ed model (maximum likelihood estimates)

Genetic factors Common environment

Specific environment

A1 A2 A3 C1 C2 C3 E1 E2 E3

VIQ .732 .371 .572

GPA .352 .738 -.041 0 0 .574

CPL .202 .376 .646 .172 0 0 0 0 .609

Note: VIQ = verbal IQ; GPA = grade point average; CPL = college plans. 0 denotes a coefficient fixed to zero

Squared standardized path coefficients and 95% maximum-likelihood confidence intervals for total genetic effects (heritabilities a2 = h2), total common environmental effects (environmentalities c2), and total specific environmental effects (specificities e2) for favored AC1Ed model 95% CI Squared genetic paths Total

(a2) Lower Upper

VIQ .536 .536 .408 .649 GPA .124 .545 .669 .585 .725 CPL .041 .142 .418 .600 .493 .677 Squared common environmental paths Total

(c2) Lower Upper

VIQ .137 .137 .060 .217 GPA .002 .002 .000 .043 CPL .030 .030 .001 .093 Squared specific environmental paths Total

(e2) Lower Upper

VIQ .327 .327 .269 .397 GPA .329 .329 .275 .394 CPL .370 .370 .310 .441 Note: VIQ = verbal IQ; GPA = grade point average; CPL = college plans. Entries are squared standardized path coefficients for the effects of latent factors on observed variables; the sums of squared paths for a set of latent factors estimate heritabilities (a2 or h2), environmentalities (c2), and specificities (e2) of the observed variables

Highlights

• “phenotypic” path coefficients (i.e., VIQ -> GPA; VIQ -> CPL; GPA -> CPL) become n.s. when BG structure of achievement process is controlled

• heritability (= a measure of opportunity) high for all three achievement measures (VIQ 54%, GPA 67%, CPL 60%), even though measurement error not corrected

• environmentality (= a measure of ascription) only substantial for VIQ (14%); it is hardly significant for GPA or CPL

• specificity (effect of specific environment of sibling; includes measurement error) substantial for all three outcomes (33% to 37%)

Highlights (cont’d)

• genetic influences cannot be reduced to a single latent factor representing academic ability; they are better represented as relatively independent factors specific to each educational outcome

• by contrast, common environmental effects can be represented as a single environmental factor

• specific environmental factors are largely independent across outcomes, suggesting they largely consist of measurement error

Discussion

BG parameters as macro-social variables?• heritability, environmentality, and specificity characterize

a population, not a trait• parameter values characterize stratification system with

respect to ascription versus opportunity for achievement:– high heritability = high opportunity, low ascription– high environmentality = high ascription, low opportunity

• thus, BG model parameters potential basis of new approach to:– comparative social stratification research– normative discussions of social inequality

Study Context and data

Measure of attainment

Comparison group

h2 c2 e2

♂ & ♀ b. bef. 1940 41 47 12 ♂ b. 1940 -49 74a 8 18 ♂ b. 1950 -60 67a 20 13 ♀ b. 1940 -49 45a 41 14

Heath et al. 1985

Norway; twins, parents

educational attainment

♀ b. 1950 -60 38a 50 12 occupation youngest 43b educ. attain. youngest 51b IQ youngest 66b occupation Oldest 16c 6 78 educ. attain. Oldest 10c 62 28

Tambs et al. 1989

Norway, twins b. 1944-60

IQ Oldest 37c 45 18 young ♂ 35 21 44 old ♂ 30 12 39d young ♀ 20 9 38d

Lichtenstein et al. 1992

Norway, twins & adopted

educational attainment

old ♀ 12 46 21d ♂ ♀ b. bef. 1950 57 24 19 Baker et al.

1996 Australia educational

attainment ♂ ♀ b. aft. 1950 82 18 - e IQ 64 23 13 educ. attain. 68 18 14

Rowe, Vesterdal and Rodgers 1999

US (NLSY); full & half sibs. hourly wages 42 8 49

verbal IQ unemployed parent

42 39 19

no unemployed parent

54 22 24

Black 58 19 23

Guo and Stearns 2002

US (AddHealth); MZ, DZ, FS, HS, CO, NR siblings

White 72 -1 29 verbal IQ 54 14 33 GPA 67 0 33

This study (Table 5)

Same

college plans 60 0 37 Note: a figure includes genetic dominance component; b average of 3 groups, average for c2 and e2 not given; c authors comment "this [oldest] sample is small and the estimates are unstable" (p. 209); d figures do not add up to 100 because of additional "correlated environmental variance" component; e estimate correcting for phenotypic assortative mating for educational level.