Exploring the role of the family in multilevel models of school effectiveness and student achievement using Swedish registry data Rob French Longitudinal data analysis: Methods & Applications 6th ESRC Research Methods Festival 11:15 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)

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 relatedness 2.Mother ID & father ID We define the family as children with common mothers and fathers (+ other possible definitions…) Problems: 1.Family is constructed only for individuals in the 4 cohorts of data and ignores siblings from earlier / later cohorts 2.Family structure variables are also constructed only from the 4 cohorts of data.

Independent variables Family structure: 1.Birth order: categorical variable (1 st 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), months, 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 schools Twins: 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

SchoolNeighbourhood 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 studentsSwedish students Secondary school 14%22%7% Pupil86%78%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 studentsSwedish students Family60%72%70%49% Pupil40%28%30%51% Omitting prior attainment increases the family VPC Family VPC similar for Sweden and England Using 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 studentsSwedish students Secondary school10.3%21%6%5% Neighbourhood1.8%6%4% Family40.4%47%60%40% Pupil37.8%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 studentsSwedish students Intercept-0.039***(0.007)-0.103***(0.008)-0.263***(0.009)-0.297***(0.006) Prior attainmentYNNN Twin dummy0.154**(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) Female0.184***(0.002)0.229***(0.003)0.405***(0.006)0.406***(0.003) + individual variablesY N N Y + family variablesY N N Y Estimates for ‘Age within year’ similar for England and Sweden Greater gender differences in Sweden

Model D: Family structure Variance partition coefficient (VPC) Siblings approach All cohorts Swedish students Cohort: 2006 (reference category) Cohort: ***(0.004) Cohort: ***(0.005) Cohort: ***(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 family0.070***(0.013) Family size: 3 child family0.031(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 family 1st born in 2006 cohort 2nd born in 2007 cohort 2nd born in 2008 cohort 2nd born in 2009 cohort Zero spacing (twins)0.179 Close spacing Wide spacing Predicted achievement for children from a 2 child family, where both children are girls: 1 st born children have higher predicted achievement than 2 nd born Wider spacing reduces the gap between siblings

Family structure: 3 child family 3 child family 1st 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 Wide spacing Predicted achievement for children from a 3 child family, where all children are girls: 1 st born children have higher predicted achievement than 2 nd born 2 nd 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

Literature Belmont, L., Marolla, F.A.: Birth Order, Family Size, and Intelligence A study of a total population of 19-year-old men born in the Netherlands is presented. Science 182(4117), (1973) Blake, J.: Family Size and the Quality of Children. Demography 18(4), (1981) Bound, J., Griliches, Z., Hall, B.H.: Wages, Schooling, and IQ of Brothers and Sisters: Do the Family Factors Differ? National Bureau of Economic Research, (1986) Butcher, K.F., Case, A.: The effect of sibling sex composition on women's education and earnings. The Quarterly Journal of Economics 109(3), (1994) Conger, K.J., Rueter, M.A., Conger, R.D.: The role of economic pressure in the lives of parents and their adolescents: The Family Stress Model. (2000) Hanushek, E.A.: The Trade-Off between Child Quantity and Quality. The Journal of Political Economy 100(1), (1992) Hauser, R.M., Kuo, H.-H.D.: Does the gender composition of sibships affect women's educational attainment? Journal of Human Resources 33(3) (1998) Iacovou, M.: Family size, birth order, and educational attainment. Marriage & Family Review 42(3), (2008) Kuo, H.-H.D., Hauser, R.M.: How does size of sibship matter? Family configuration and family effects on educational attainment. Social Science Research 26(1), (1997) Powell, B., Steelman, L.C.: The liability of having brothers: Paying for college and the sex composition of the family. Sociology of Education, (1989) Rodgers, J.L., Cleveland, H.H., van den Oord, E., Rowe, D.C.: Resolving the debate over birth order, family size, and intelligence. American Psychologist 55(6), 599 (2000) van Eijsden, M., Smits, L.J., van der Wal, M.F., Bonsel, G.J.: Association between short inter-pregnancy intervals and term birth weight: the role of folate depletion. The American journal of clinical nutrition 88(1), (2008) Wichman, A.L., Rodgers, J.L., MacCallum, R.C.: A multilevel approach to the relationship between birth order and intelligence. Personality and social psychology bulletin 32(1), (2006) Zajonc, R.B.: Family configuration and intelligence: Variations in scholastic aptitude scores parallel trends in family size and the spacing of children. Science (1976)