Exploring the role of the family in multilevel models of school effectiveness and student

achievement using Swedish registry data

Rob FrenchLongitudinal data analysis: Methods & Applications

6th ESRC Research Methods Festival11:15 Wed 9th July 2014

School effectiveness

• Pupils in schools: (Raudenbush & Bryk, 1986); (Aitkin & Longford, 1986) (Goldstein et al., 1993)

Goldstein, 2011 ‘Multilevel Statistical Models’

Families & achievement

• Are families important for school effectiveness studies?

• Pupils in families: (Jenkins et al., 2005) (Georgiades et al., 2008)

• Pupils in schools & families: (Rasbash et al., 2010)

Rasbash et al. (2010)

Rasbash et al. (2010)

Family structure

• Birth order (Belmont & Marolla 1973), within family (Rodgers et al. 2000), (Wichman et al. 2006)

• Family size (Hanushek 1992), (Blake 1981), (Conger et al. 2000), (Kuo & Hauser 1997), (Iacovou 2008)

• Family Spacing (Zajonc 1976) (van Eijsden et al. 2008)• Family sibling sex composition (Bound et al. 1986),

(Butcher & Case 1994), (Hauser & Kuo 1998), (Powell & Steelman 1989)

Research Questions

1. How much of the within school variation in achievement in school effectiveness models should be attributed to the family?

2. Which family structure characteristics are important for explaining differences in achievement between students and families?

Data

• Swedish pupil registry datasets• 4 cohorts (students who finish compulsory

schooling in 2006, 2007, 2008 & 2009) • 339,897 pupils in analysis, 1,295 schools, 5,341

neighbourhoods and 288,974 families• Outcome measure = student achievement sum of

score (0,10,15 or 20) across 16 subjects - standardised for analysis

Defining family & family structure variables

We have 2 ways of identifying families:1. Genetic relatedness2. Mother ID & father IDWe define the family as children with common mothers and fathers (+ other possible definitions…)

Problems: 3. Family is constructed only for individuals in the 4 cohorts

of data and ignores siblings from earlier / later cohorts4. Family structure variables are also constructed only from

the 4 cohorts of data.

Independent variables

Family structure:1. Birth order: categorical variable (1st born is reference).2. Family size: categorical variable (1 child family is

reference).3. Family Spacing: age gap between oldest and youngest

recoded as categorical variable: 0 spacing (reference), 1-24 months, 25-48 months.

4. Family sibling sex composition: mixed sex sibships vs. single sex sibships.

Other variables: gender, immigration status, age within year

School

Pupil

Model A: Pupils in schoolsTwins:

All siblings:

,

,

• Model of student achievement of pupil i nested in school j

• Twins approach uses dummy variable for twin children• Siblings approach uses cohort dummies

Families

Pupil

Model B: Pupils in families

• Model of student achievement of pupil i nested in family j

• Twins approach uses the twin dummy variable to switch between twin families (1% of sample) and singletons

School Neighbourhood

Pupil

Model C & D: Schools + families

Family

• Model includes school AND family random effects• We also include neighbourhood effects

Model A: Pupils in schools

variance partition coefficient (VPC)

Twins approach (Rasbash) Siblings approach Rasbash et al.

(2010)Comparison model (single cohort,

common variables & clusters) All cohorts

English students Swedish students

Secondary school 14% 22% 7% 7%

Pupil 86% 78% 93% 93%

Omitting prior attainment increases the school effects / school variance partition coefficient (VPC)

School effects are much lower for Sweden than England

Using all 4 cohorts makes no difference to school effects for Sweden

Model B: Pupils in families

variance partition coefficient (VPC)

Twins approach (Rasbash) Siblings approach Rasbash et al.

(2010)Comparison model (single cohort,

common variables & clusters) All cohorts

English students Swedish students

Family 60% 72% 70% 49%

Pupil 40% 28% 30% 51%

Omitting prior attainment increases the family VPCFamily VPC similar for Sweden and EnglandUsing all 4 cohorts (families now include siblings

rather than just twins) reduces family VPC

Model C – Schools & families

variance partition coefficient (VPC)

Twins approach (Rasbash) Siblings approach Rasbash et al.

(2010)Comparison model (single cohort,

common variables & clusters) All cohorts

English students Swedish students

Secondary school 10.3% 21% 6% 5%

Neighbourhood 1.8% 6% 4% 4%

Family 40.4% 47% 60% 40%

Pupil 37.8% 26% 30% 52%

Impact of adding family 52% 64% 66% 44%

The proportion of variation identified as within school variation that should be attributed to families is 64% in England and 66% in Sweden (using the twins methodology with no prior attainment)This is reduced to 44% when we consider families of siblings rather than simply twins

Model D: Age & gender

Variance partition coefficient (VPC)

Twins approach (Rasbash) Siblings approach

Rasbash et al. (2010)

Comparison model (single cohort, common variables & clusters) All cohorts

English students Swedish studentsIntercept -0.039*** (0.007) -0.103*** (0.008) -0.263*** (0.009) -0.297*** (0.006)Prior attainment Y N N NTwin dummy 0.154** (0.007) 0.106*** (0.011) 0.035 (0.028) N Age within year -0.012*** (<0.001) 0.013*** (<0.001) 0.014*** (0.001) 0.012*** (<0.001)Female 0.184*** (0.002) 0.229*** (0.003) 0.405*** (0.006) 0.406*** (0.003)+ individual variables Y N N Y + family variables Y N N Y

Estimates for ‘Age within year’ similar for England and SwedenGreater gender differences in Sweden

Model D: Family structure

Variance partition coefficient (VPC) Siblings approach

All cohortsSwedish students

Cohort: 2006 (reference category)Cohort: 2007 0.041*** (0.004)Cohort: 2008 0.109*** (0.005)Cohort: 2009 0.137*** (0.005)Birth order: 1st born (ref.) Birth order: 2nd born -0.204*** (0.005)Birth order: 3rd born -0.357*** (0.022)Family size: 1 child family (ref.) Family size: 2 child family 0.070*** (0.013)Family size: 3 child family 0.031 (0.022)Birth spacing: none (ref. ) Birth spacing: close (1-24 months) 0.045** (0.014)Birth spacing: wide (2-48 months) 0.095*** (0.014)Mixed sibling sex composition -0.004 (0.006)

Family structure: 2 child family

2 child family1st born in

2006 cohort2nd born in2007 cohort

2nd born in2008 cohort

2nd born in2009 cohort

Zero spacing (twins) 0.179

Close spacing 0.222 0.060

Wide spacing 0.274 0.207

Predicted achievement for children from a 2 child family, where both children are girls:

• 1st born children have higher predicted achievement than 2nd born

• Wider spacing reduces the gap between siblings

Family structure: 3 child family

3 child family1st born in 2006 cohort

2nd born in

2007 cohort

2nd born in

2008 cohort

2nd born in

2009 cohort

3rd born in

2007 cohort

3rd born in

2008 cohort

3rd born in

2009 cohort

Zero spacing (triplets) 0.141

Close spacing 0.184 0.022 -0.129

Wide spacing 0.236 0.169 0.018

Predicted achievement for children from a 3 child family, where all children are girls:

• 1st born children have higher predicted achievement than 2nd born• 2nd born children have higher predicted achievement than 3rd born• Wider spacing reduces the gap between siblings

RQ1 - Conclusions

• How much of the “within school variation” in school effectiveness models is actually attributable to the family?

• We estimate 44% of the within school variation in our school effectiveness model is actually attributable to the family.

RQ2 - Conclusions

• Which family structure characteristics are important for explaining differences in achievement between students and families?

• Birth order has a large negative impact on achievement (interpreted alongside family size)

• Wider spacing is associated with higher achievement

• Sex composition has no significant association

Further work

• Additional waves of data to address the problem of family and family structure being defined by families over 4 waves

• Identify the genetic component of achievement

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