nonlinear trend in inequality of educational opportunity in the netherlands 1930 1989
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Nonlinear Trend in Inequality of Educational Opportunity in the Netherlands 1930-1989. Maarten L. Buis Harry B.G. Ganzeboom. Outline. Main results Model selection Continuous or discrete education and father’s status Importance mother’s education relative to father’s education

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nonlinear trend in inequality of educational opportunity in the netherlands 1930 1989

Nonlinear Trend in Inequality of Educational Opportunity in the Netherlands 1930-1989

Maarten L. Buis

Harry B.G. Ganzeboom

outline
Outline
  • Main results
  • Model selection
    • Continuous or discrete education and father’s status
    • Importance mother’s education relative to father’s education
    • Difference in effect between sons and daughters
  • Non-linearity in trend in effects: identify periods of negative, positive, and no trend.
main results
Main results
  • Model selection
    • distinction between highest and lowest educated parent is more important than distinction between father and mother, or same-sex-parent.
    • Effects of parental education and father’s occupational status is the same for sons and daughters
  • Non-linearity in trend
    • Effect of father’s status decreases non-linearly over time, slowing down significantly around 1970
    • parental education decreases most likely linearly.
slide5
Data
  • International Stratification and Mobility File (ISMF)
  • 49 surveys held between 1958 and 2003 with information on cohorts 1930-1989.
  • 80,000 observations, of which 66,000 have complete information on child\'s, father’s and mother’s education and father\'s status.
  • Number of cases are unequally distributed over cohorts.
model 1 linear regression
Model 1: linear regression
  • Dependent variable is years of education and treated as continuous.
  • Parental education is either entered as father’s and/or mother’s education, highest and/or lowest educated parent, or education of same sex parent
  • Father’s occupational status is measured in ISEI scores
  • Trend in effects are measured as third order orthogonal polynomials or lowess curves.
two objections against linear education
Two objections against linear education
  • Regression coefficient is effected by both ‘real’ effects of parental characteristics on probabilities of making transitions and educational expansion
    • True, if education is studied as a process
    • False, if education is studied as an outcome
  • education is discrete
    • this does not have to be a problem if there is no concentration in the lowest or highest category.
model 2 stereotype ordered regression sor
Model 2:Stereotype Ordered Regression (SOR)
  • SOR allows for ordered dependent variable
  • SOR will estimate (sequentially) an optimal scaling of education and the effect of independent variables on this scaled education.
model 3 row collumn model ii rc2
Model 3: Row Collumn Model II (RC2)
  • Objection against use of ISEI:
    • Effect of father’s occupation is better represented by small number of discrete classes, rather than on continuous scale.
  • Classes used are EGP classification.
  • RC2 is extension of SOR that also estimates an optimal scaling for EGP
father s and mother s education
Father’s and mother’s education
  • Conventional model: Only father matters
  • Individual model: Both mother and father matter
  • Joint model: Effect of father and mother are equal
  • Dominance model: Highest educated parent matter
  • Modified Dominance model: Highest and lowest educated parent matter
  • Sex Role model: Same sex parent matters
identifying periods with significant trend
Identifying periods with significant trend
  • A negative slope means a negative trend.
  • A positive slope mean a positive trend.
  • A zero slope means no trend.
identifying periods with significant change in trend
Identifying periods with significant change in trend
  • An accelerating trend means that a negative trend becomes more negative, so a negative change in slope.
  • A decelerating trend means that a negative trend becomes less negative, so a positive change in slope.
  • A constant trend means no change in slope.
slide19
Data
  • The ISMF dataset is converted into a new dataset, containing estimated IEO for 60 annual cohorts.
  • The precision of the estimates (the standard error) is used to weigh the cohorts.
lowess
Lowess
  • We have a dataset consisting of estimates of IEO for each annual cohort which used only information from that cohort
  • If we think that IEO develops like a smooth curve over time, than nearby estimates also contain relevant information.
  • The lowess curve creates an improved estimate of the IEO for each cohort using information from nearby cohorts.
  • It results in a smooth line by connecting the lowess estimates.
  • Estimates of the trend and change in trend at each cohort can also be obtained from this curve.
lowess curve in 1949
Lowess curve in 1949
  • Point on lowess curve in 1949
  • Select closest 60% of the points.
  • Give larger weights to nearby points.
  • Adjust weights for precision of estimated IEO.
  • Normal regression of IEO on time, time squared and time cubed on weighted points.
  • Predicted value in 1949, is smoothed value of 1949.
  • First derivative in 1949 is trend in 1949.
  • Second derivative in 1949 is change in trend in 1949.
  • Repeat for all cohorts and connect the dots.
selecting spans
Selecting spans
  • Percentage closest points (span) determines the smoothness of the lowess curve.
  • Trade-off between smoothness and goodness of fit.
  • Can be judged visually by comparing lowess curves with different spans.
  • Numerical representations of this trade-off are Generalize Cross Validation, and Akaike Information Criterion.
  • Lower values mean a better trade-off.
bootstrap confidence intervals
Bootstrap confidence intervals
  • Confidence interval gives the range of results that could plausibly occur just through sampling error.
  • Make many `datasets\' that could have occurred just by sampling error.
  • Fit lowess curves through each `dataset\'.
  • The area containing 90% of the curves is the 90% confidence interval.
  • The estimates of IEO are regression coefficient with standard errors.
  • The standard error gives information about what values of IEO could plausibly occur in `new\' dataset.
slide28

OLS

SOR

RC2

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