Social Origin and Pupils Performance. How theory-sensitive models can solve methodological issues.

Abstract

Parental educational attainment and their economic resources, often jointly referred to as social origin, can be considered as a practically indispensable concept in educational research. Economic argumentation dominate the scientific debate about different students' performance with respect to parental socioeconomic status. For this reason, the Index of Socio-Economic Status (ISEI) is an important and frequently used empirical measurement tool in educational research. In addition to economic resources, cultural capital, often measured by parental educational qualification as representation of its institutionalized form, is another relevant factor in resource-orientated explanations of primary effects on pupils performance. However, when trying to account for socioeconomic and educational influences jointly in linear regression models, relevant theoretical and methodological issues arise.

During the analysis of social-origin-specific achievement differences between pupils in 4th grade using data from the National Educational Panel Study (NEPS-SC2), this contribution will discuss nonlinearity, collinearity and inconsistent variances as well as some distributional assumptions of OLS-Regression, which occur when regress ISEI and parental educational background on pupils mathematical competencies. Besides the fact that misspecification violates the requirements of linear ordinary least squares regression and lead to wrong interpretations, it also masks underlying mechanisms and structures. In contrast, the explicit consideration of theoretical premises and assumptions about the functional form of a correlation, as well as their methodological implication in the analysis can help to avoid statistical model violations and to develop statistically adequate, more informative models.

This empirical and methodological discussion of theory-sensitive modeling and interpretation strategies will illustrate how the use of non-linear, piecewise linear and non-parametric regression techniques can be used to implement empirical models which explicit respect the functional form of theoretical arguments. In addition to avoiding the demonstrated statistical issues, this approach improves the fit between theory, methods and data and consequently leads to more precise and meaningful empirical models as well as to deeper insights into the mechanisms behind the container of social origin. This is supposed to revitalize the discourse for a more theory-sensitive operationalization of Social Origin in educational research.

Full text

1
How theory-sensitive models can solve
methodological issues
Social Origin and Pupils
Performance
NEPS -C ONFERENCE 20 2 2 – B E N J A M I N G R Ö SCHL
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2
Social Origin and Pupils
Performance
PART 1 – Introduction
Social Origin – Theory & Mesurements
SES & Pupils Performance
Analysis-Model / Common Empirical Application
PART 2 – HISEI, Education & Performance: data issues and
theoryfunded solutions
Empirical Dependencies
Residual-Distributions and Correlation
Methodological Implications
Structures of Covariance and Correlations
Theoretical Mechanism
Non-Linearity
PART 3 – Summary & Conclusion
“Like all interpretative schemes,
functional analysis depends upon a
triple alliance between theory, method
and data.
Of the three allies, method is by all odds
the weakest.”
(Merton, 1968, p. 73)

3
PART 1 - Introduction
Analysis-Model
Theoretical foundations of Social Origin
Class & Habitus
Social Capital
Cultural capital
Economic Ressources
Pupils
Performance
Parental
Economic
Ressources
Educational
Investment
“A social mechanism, as defined here,
is a constellation of entities and activities
that are linked to one another in such a
way that they regularly bring about a
particular type of outcome.
We explain an observed phenomenon by
referring to the social mechanism by
which such a phenomenon is regularly
brought about.”
(Hedström, 2005, p. 11)

4
Analysis-Model
Data: NEPS – SC2 – 4. Grade (W6)
Economic Ressources & Performance
Parental SES reflects the potential for social and economic resources that
are available to invest in pupils education (Sirin, 2005)
Measurement
(H-)ISEI:
“is defined as the the intervening variable between education and income
that maximizes the indirect effect of education on income and minimizes
the direct effect” (Ganzeboom et al., 1992, p. 11)
dominance approach (Erikson, 1984; Thaning & Hällsten, 2020)
Missing by Design: carry forward
Pupils Performance:
WLE: Math competencies 4. Grade (mag4_sc1)
(Pohl & Carstensen, 2012)
Pupils
Performance
Parental
Economic
Ressources
Educational
Investment

5
OLS-Regression
(Math <- HISEI)
“perhaps one SES measure, if it is well
defined, carefully constructed, and
theoretically aligned with its outcome
variable, may be sufficient as a control
variable in educational research”
(Lee et al, 2019, p. 20)
OLS-Regression: (MAG4_sc1 = constant + b1(HISEI) + e *p<0.05 **p<0.01
R² = 0,12** Coef. N=6111
HISEI 0,02** Overall R²
constant -1,09** 0,12**

6
Part 2: HISEI & Pupils Performance
data issues and theory-funded solutions
Empirical Dependencies
Residual-Distributions and Correlation
Methodological Implications
Structures of Covarianz and Correlations
Theoretical Mechanism
Non-Linearity

7
Empirical dependencies
“parental education, is considered one of the
most stable aspects of SES because it is typically
established at an early age and tends to remain
the same over time” (Sirin, 2005, p. 419)
Parental education is also an indicator of parent’s
income because income and education level are
highly correlated (Sirin, 2005)
Educated Parents can substitut economic
resources
Statistical issue 1: E(e1i | x2i)≠0; Cov(ei,ej)≠0
Residual-Distributions (OLS)

8
ISEI & Education:
conditional means
Statistical issue 2: Cov(Xi,ei)≠0
* p<0.05 ** p<0.01
N=8.086 HISEI
R² : 0.49** Means t [ 95% CI ]
H/MS (+ Qual) 32,42** 0,54 60,22 31,36 33,47
Mittlere Reife 45,97** 0,29 159,96 45,4 46,53
HSR (All.+Fg.) 55,03** 0,31 176,96 54,42 55,64
FH 70,04** 0,5 138,99 69,06 71,03
HS / Prom. 75,66** 0,31 243,54 75,05 76,27
Std. Err.
(Δ)

9
ISEI & Education
There are many studies which describe
the ”tripartite nature of SES that
incorporates parental income, parental
education, and parental occupation as
the three main indicators of SES […]
but more important, these studies
showed that the components of SES are
unique and that each one measures a
substantially different aspect of SES that
should be considered to be separate
from the others.”
(Sirin, 2005, p. 418f)
Pupils
Performance
Parental
Education
Economic
Ressources
Occupation
Substitution
Educational Investment
Non-economic factors:
Class, Culture, habits etc.

10
ISEI & Education: joint OLS
Model
PART 2 - Empirical Dependencies
OLS: mag4_sc
Coef. Std. Err. [95% Conf. Interval]
R² = 0.145
hisei 0,022 ** 0,004 0,015 0,029
hiAB_cas1
Mittlere Reife 0,743 ** 0,148 0,452 1,033
HSR (All.+Fg.)
1,088 ** 0,158 0,779 1,397
(FH) 1,529 ** 0,289 0,963 2,095
HS / Prom. 1,219 ** 0,222 0,783 1,655
hiAB_cas1#c.hisei
Mittlere Reife -0,010 ** 0,004 -0,018 -0,003
HSR (All.+Fg.)
-0,013 ** 0,004 -0,020 -0,005
(FH) -0,017 ** 0,005 -0,027 -0,007
HS / Prom. -0,010 * 0,004 -0,019 -0,002
_cons -1,543 ** 0,125 -1,788 -1,298
*p<0.05 **p<0.01

11
ISEI & Education:
Methodological Implications
“From an explanatory point of view it is
not sufficient simply to postulate that one
social phenomenon causes another. Nor
is it sufficient just to point to a correlation
between a presumed cause and its
effect.
One must also open up the ‘black box’ to
reveal the social mechanisms that are
believed to be at work.”
(Hedström, 2005, p. 68)
Pupils
Performance
(WLE-Math)
Economic
Ressources
(HISEI)
Occupation
(ISCO-08)
Educational Investment
Non-economic factors:
Class, Culture, habits etc.
Parental
Education
(certificates)

12
OLS: MATH <- HISEI + EDU
Structures of Covarianz and Correlations
Education
r² = 0.49
ISCO
Education
(1. ISCO-Digit)
λb = 0.28
γ = -0.61
Job
title
Education
Math-Perf.
+
OLS: MATH Coef. VIF
R² = 0.145
HISEI (r² = 0.12) 0,0216 ** 26.20
Education (r² = 0.13)
Mittlere Reife 0,7428** 24.54
HSR (All.+Fg.) 1,0878** 25.90
HS-Abschluss (FH) 1,5287 ** 43.18
HS-Abschluss / Prom. 1,2189 ** 54.80
HISEI#Education
Mittlere Reife -0,0103 ** 42.51
HSR (All.+Fg.) -0,0128 ** 54.17
HS-Abschluss (FH) -0,0170 ** 67.61
HS-Abschluss / Prom. -0,0102 * 119.29
Mean VIF
_cons -1,5428 ** 50.91
OLS: HISEI Coef.
R² = 0.911
Education (r² = 0.493)
Mittlere Reife 1,447**
HSR (All.+Fg.) 3,017**
HS-Abschluss (FH) 4,662**
HS-Abschluss / Prom. 6,935**
ISCO (1. Digit)
2 8,984 **
3 -11,257 **
4 -21,165 **
5 -34,866 **
6 -46,566 **
7 -33,725 **
8 -38,488 **
9 -46,803 **
_cons 63,447 **
HISEI
*p<0.05 **p<0.01*p<0.05 **p<0.01
WLE-Math
HISEI
Education
certificates
ISCO-08

13
ISEI:
Multimodal Distribution Educational Cluster

14
Separate Mechanism -
Separate Models
Pupils
Performance
Parental
Education
(certificates)
Job-related
economic
ressources
Occupation
Substitution
Educational Investment
Non-economic factors
(class, Culture, habits etc.)
E(e1i | x2i) ≠ 0;
Cov(ei,ej) ≠ 0
Cov(Xi,ei) ≠ 0
high Variance-Influance-Faktors
Multimodal Distribution / Different “Subpopulations”
-> Separate Models by Education

15
Separate Models unbiased Residual-Distribution
Mittlere Reife H/MS (+Qual)
R² 0.014** 0,002 0.017** 0.02** 0.07**
hisei 0,011** 0,004 .008** .011** 0,021**
_cons -0,323 -0,014 -.454** -.799** -1,542**
HS-
Abschluss /
Prom.
HS-
Abschluss
(FH)
HSR
(Allg+Fg)

16
Economic mechanism HS / MS: MAG4<-HISEI
OLS vs. LOWESS
Law of diminishing marginal utility: marginal utilities
are diminishing across the ranges relevant to
decision-making (Gossen, 1854)
Law of diminishing returns (law of diminishing
marginal productivity): increasing a factor of
production by one unit, while holding all other
production factors constant, will at some point return
a lower unit of output per incremental unit of input
(Samuelson & Nordhaus, 2001)
PART 2 - Theoretical Mechanism Statistical issue 3: V(ei)≠0

17
Nonlinear Models
Asymtotic growth / exponential Model
Piecewise linear Model (restricted knots)
MAG 4=b
0
+b
1
(
b
2
HISEI
)
MAG 4=
{
b
0
+b
1
HISEI , HISEI <c
(
b
0
+b
1
c
)
+c
1
HISEI , c <HISEI <d
(
b
0
+b
1
c+c
1
(
d −c
)
)
+d
1
HISEI , HISEI >d
}
Theory-sensitive operationalsation
Empirical dependencies; methodological implications
-> Separate Models by Education
Ecomonic theory (educational investment):
Variing effects over the range of HISEI
-> Linear Modell is not appropiate for economic theory:
Asymtotic growth (Exponential)
Picewise linear
Nonparametric

18
Exponential: HS/MS
MAG4 Coef. Std. Err. [95% CI]
/b1 -2.394** 0.415 -3.211 -1.578
/b2 0.964** 0.007 0.952 0.978

19
Piecewise Linear: Mittlere
Reife

20
Separate Nonlinear Model EXP / Piecewise: “Hochschulreife”
Reduce Residual bias
Solve methodological Issues
Alligned with economic theory
Parametric interpretation is possible
Deepens the understanding of the relationship
Expotential and piecewise linear parametric
only show negligible differences in Modelfit and
Residual-Distribution

21
Piecewise linear Models
FH Overall R²
Joint OLS R² 0,145**
Separate OLS R² 0.014** 0.002 0.017** 0.02** 0.07** 0.145**
Picewise linear R² 0.015** 0.007* 0.025** 0.035** 0.087** 0.15**
Exponential 0.147**
HS /
Prom.
HSR
(Allg+Fg)
Mittler
e Reife
H/MS
(+Qual)

22
Statistical issue 3: V(ei)≠0
Residuals: Joint OLS Residuals: Separate OLS Residuals: (sep.) Piecewise Linear

23
Summary Conclusion
“Socioeconomic status (SES) is probably the most widely used contextual
variable in education research“ (Sirin, 2005, p. 417)
The same standards must be applied to control variables as to variables of
primary theoretical interest in order to cleanly separate the influence of
education from the effects of other variables (Schneider, 2016)
If SES is poorly conceptualised and measured as a control variable, it can
be assumed that the effects of other variables include the effects of
unmeasured differentiations of SES (Schneider, 2016)
„For the use of "method" involves not only logic but, unfortunately perhaps
for those who must struggle with the difficulties of research, also the
practical problems of aligning data with the requirements of theory“
(Merton, 1968: 73)
Empirical Dependencies:
E(e1i | x2i) ≠ 0; Cov(ei,ej) ≠ 0; Cov(Xi,ei) ≠ 0; Var(ei)
-> Biased Residuals = biased further analyses
-> include education
Methodological Implications
Open the Blackbox -> high VIF
Multimodal Distribution <> Different “Subpopulations”
-> Separate Models by Education
Theoretical Mechanism
economic law of dimishing returns
Substitution of economic investments
> Exponential and piecewise-linear models are both
appropiate for theoretical alignment

Dipl.-Soz. Benjamin Gröschl
Lehrstuhl für Allg. Pädagogik, Erziehungs- und Sozialisationsforschung
Ludwig-Maximilians-Universität München
Leopoldstraße 13, 80802 München
benjamin.groeschl@edu.lmu.de
Bukodi, E. and Goldthorpe ,J.H. (2013). Decomposing “Social Origins”: The Effects of Parents’ Class, Status, and Education on the Educational Attainment of Their Children.
European Sociological Review 29(5): 1024–1039. DOI: 10.1093/esr/jcs079.
Erikson, R. (1984). Social Class of Men, Women and Families. Sociology 18(4): 500–514.
Ganzeboom, H. B. G., De Graaf, P. M., & Treiman, D. J. (1992). A standard international socio-economic index of occupational status. Social Science Research, 21(1), 1–56.
Gossen,^H.^H.^(1854).^Entwickelung der Gesetze des menschlichen Verkehrs, und der daraus fließenden Regeln für menschliches Handeln.^Friedrich Vieweg und Sohn.
Hedstrom, P. (2005). Dissecting the Social: On the Principles of Analytical Sociology. Cambridge University Press. doi:10.1017/CBO9780511488801
Lee, J, Zhang, Y. and Stankov, L. (2019) Predictive Validity of SES Measures for Student Achievement. Educational Assessment 24(4). Routledge: 305–326. DOI:
10.1080/10627197.2019.1645590.
Merton, R. K. (1968). Social Theory and Social Structure. New York: The Free Press.
Pohl, S. and Carstensen, C. H. (2012). NEPS Technical Report – Scaling the Data of the Competence Tests (NEPS Working Paper No. 14). Bamberg: Otto-Friedrich-Universität,
Nationales Bildungspanel.
Samuelson, P.A. and Nordhaus, W.D. (2001). Economics. 17th Edition, McGraw-Hill.
Schneider, S. L. (2016). Die Konzeptualisierung, Erhebung und Kodierung von Bildung in nationalen und internationalen Umfragen. In GESIS Survey Guidelines.
https://doi.org/10.15465/10.15465/gesis-sg_020
Sirin, S.R. (2005). Socioeconomic status and academic achievement: A meta-analytic review of research. Review of Educational Research 75(3): 417–453. DOI:
10.3102/00346543075003417.
Thaning, M. and Hällsten, M. (2020). The End of Dominance? Evaluating Measures of Socio-Economic Background in Stratification Research. European Sociological Review 36(4):
533–547. DOI: 10.1093/esr/jcaa009.
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