Estimating the Importance of Families in Modeling Educational Achievement Using Linked Swedish Administrative Data

Figures & data

Table 1. Descriptive statistics for child and family characteristics.

	Student (n = 357,459)
Child-level continuous variables	Mean	SD
Student achievement (standardized)^a	0.293	0.979
Age within year in months (centered on July)	0.759	3.344
Child-level categorical variables	Count	Percent
Female	174,240	48.7
Immigrant status: Swedish (no recent immigration history)	340,156	95.2
Immigrant status: 1st generation (child born outside Nordic countries)	12,639	3.6
Immigrant status: 2nd generation (at least 1 parent born outside Nordic countries)	4,610	1.3
Cohort: finish compulsory schooling in 2006	92,880	26.0
Cohort: finish compulsory schooling in 2007	91,182	25.5
Cohort: finish compulsory schooling in 2008	89,072	24.9
Cohort: finish compulsory schooling in 2009	84,325	23.6
Family structure variables (N = child)	Count	Percent
Birth order: 1st born child	150,693	42.2
Birth order: 2nd born child	127,618	35.7
Birth order: 3rd born child	55,468	15.5
Birth order: 4th born child	16,569	4.6
Birth order: 5th born child	4,650	1.3
Birth order: 6th (or more) born child	2,461	0.7
Family size: Children from a 1-child family	22,531	6.3
Family size: Children from a 2-child family	157,876	44.2
Family size: Children from a 3-child family	114,471	32.0
Family size: Children from a 4-child family	41,161	11.5
Family size: Children from a 5-child family	13,261	3.7
Family size: Children from a 6 (or more) child family	8,159	2.3
Birth spacing: Child from family with zero spacing	25,006	7.0
Birth spacing: Child from close-spaced family (1–24 months)	46,002	12.9
Birth spacing: Child from wide-spaced family (>24 months)	286,451	80.1
Child from mixed-gender sibships	222,132	62.1
	Family (n = 301,980)
Family structure variables (N = families)	Count	Percent
Family size: Number of 1 child families	22,531	7.5
Family size: Number of 2 child families	135,846	45.0
Family size: Number of 3 child families	94,488	31.3
Family size: Number of 4 child families	32,754	10.8
Family size: Number of 5 child families	10,312	3.4
Family size: Number of 6 (or more) child families	6,049	3.4
Birth spacing: Number of families with zero spacing	23,780	7.9
Birth spacing: Number of families with close spacing (1–24 months)	33,117	11.0
Birth spacing: Number of families with wide spacing (>24 months)	245,083	81.1
Number of families with mixed-gender sibships	184,116	61.0

Note. ^aStudent achievement is standardized to have zero mean and variance of one.

Table 2. Single-cohort twins approach models fitted to the Sweden 2007 data.

Parameter	Model 1.1		Model 1.2		Model 1.3		Model 1.4
	Est.	SE	Est.	SE	Est.	SE	Est.	SE
Regression coefficients
Intercept	−0.002	(0.009)	0.006*	(0.003)	−0.003	(0.009)	−0.190***	(0.010)
Twin-family	0.071***	(0.021)	0.069*	(0.027)	0.062*	(0.025)	0.055*	(0.025)
Age within year (months)							0.012***	(0.001)
Female							0.369***	(0.006)
Variance components
School	0.083***	(0.004)			0.070***	(0.004)	0.069***	(0.004)
Neighborhood					0.038***	(0.002)	0.039***	(0.002)
Family (twins only)			0.575***	(0.033)	0.477***	(0.030)	0.476***	(0.029)
Student (twins only)			0.290***	(0.013)	0.289***	(0.013)	0.268***	(0.012)
Family + Student (non-twins only)			0.917***	(0.004)	0.812***	(0.004)	0.777***	(0.004)
Student	0.839***	(0.004)
Total	0.922		0.865		0.874		0.852
Variance partition coefficients (VPCs)^a
School	9%				8%		8%
Neighborhood					4%	5%
Family			67%		55%		56%
Student	91%		33%		33%		31%
Model summary
Number of schools	1,152				1,152		1,152
Number of neighborhoods					4,747		4,747
Number of non-singleton families^b			970		970		970
Number of students	91,182		91,182		91,182		91,182
Bayesian deviance information criterion	243,703		249,416		241,026		236,951

Note. All models are fitted by MCMC. The estimates and standard errors are the means and SDs of the parameter chains.

^aIn models 1.2, 1.3, and 1.4, VPCs are derived from twin-family estimates of the family and student variance components.

^bThere are a total of 90,160 sibships represented in the analysis cohort. These include 970 twin pairs and 89,164 families where just one sibling is represented. In addition, there are 26 triplet families; however, we do not use these cases to estimate the twin family effect.

*p < 0.05, **p < 0.01, and ***p < 0.001.

Table 3. Multiple-cohort siblings approach models fitted to the Sweden 2006–2009 data.

	Model 2.1		Model 2.2		Model 2.3		Model 2.4
Parameter	Est.	SE	Est.	SE	Est.	SE	Est.	SE
Regression coefficients
Intercept	−0.010	(0.009)	0.006	(0.003)	−0.002	(0.008)	−0.198***	(0.003)
Cohort: 2006 (ref. category)
Cohort: 2007	0.011*	(0.004)	0.008	(0.004)	0.005	(0.004)	0.011**	(0.004)
Cohort: 2008	0.047***	(0.004)	0.033***	(0.004)	0.024***	(0.004)	0.040***	(0.004)
Cohort: 2009	0.057***	(0.005)	0.040***	(0.004)	0.028***	(0.004)	0.049***	(0.004)
Age within year (months)							0.012***	(<0.001)
Female							0.372***	(0.003)
Immigrant: Swedish (ref. category)
Immigrant: second generation							−0.061***	(0.012)
Immigrant: first generation							−0.066***	(0.012)
Family size: 1 child (ref. category)
Family size: 2 child							0.172***	(0.009)
Family size: 3 child							0.131***	(0.009)
Family size: 4 child							−0.013	(0.012)
Family size: 5 child							−0.146***	(0.015)
						−0.281***	(0.019)
Birth order: 1st born (ref. category)
Birth order: 2nd born							−0.136***	(0.003)
Birth order: 3rd born							−0.156***	(0.005)
Birth order: 4th born							−0.130***	(0.003)
Birth order: 5th born							−0.118***	(0.015)
Birth order: 6th (or more) born							−0.068**	(0.023)
Birth spacing: none (ref. category)
Birth spacing: close (1–24 months)							−0.013**	(0.005)
Birth spacing: wide (>24 months)							−0.029***	(0.005)
Mixed sibling sex composition							−0.017***	(0.004)
Variance components
School	0.087***	(0.004)			0.064***	(0.003)	0.058***	(0.003)
Neighborhood					0.040***	(0.001)	0.034***	(0.001)
Family			0.485***	(0.003)	0.380***	(0.003)	0.370***	(0.003)
Student	0.880***	(0.002)	0.474***	(0.003)	0.473***	(0.003)	0.432***	(0.003)
Total	0.967		0.959		0.957		0.894
Variance partition coefficients (VPCs)
Secondary school	9%				7%		6%
Neighborhood					4%	4%
Families		50%		40%		41%
Student	91%		50%		49%		48%
Model summary
Number of schools	1,298				1298		1298
Number of neighborhoods					5998		5998
Number of families with >1 sibling in model			53,754		53,754		53,754
Number of students	357,459		357,459		357,459		357,459
Deviance information criterion	969,813		909,487		892,977		865,088

Note. All models are fitted by MCMC. The estimates and standard errors are the means and SDs of the parameter chains.

Birth spacing is categorized using the time between the first and last birth within the family.

Sibling sex composition is estimated for mixed-gender siblings versus a reference category of single-sex families.

Estimation of the family effects is primarily driven by families with more than one sibling in the analysis sample. In this table, we report the number of families with more than one sibling in the analysis sample (53,754). Of these, there are 52,030 families with two siblings in the analysis sample (of these, 22,030 are from 2 child families, 18,419 from 3 child families, 7,464 from 4 child families, 2,473 from 5 child families, and 1,644 from 6+ child families), 1,723 families with three siblings in the analysis (of these 782 are from 3 child families, 470 from 4 child families, 238 from 5 child families, and 233 from 6+ child families), and just one family with four siblings in the analysis sample (also a four child family). There are many more family units (248,226) where only one of the siblings is represented in the analysis sample (of these, 22,531 are from 1 child families, 113,816 from 2 child families, 75,287 from 3 child families, 24,819 from 4 child families, 7,601 from 5 child families, and 4,172 from 6+ child families).

*p < 0.05, **p < 0.01, and ***p < 0.001.

Figure 1. Variance partition coefficients for the three series of student achievement models using the (1) Sweden 2007 data and the twin definition of families (Table 2, models 1.1, 1.2 and 1.3); and (2) Sweden 2006–2009 data and the fuller definition of families (Table 3, models 2.1, 2.2 and 2.3).

Figure 2. Predicted differences in achievement (SD units) relative to a one-child family by birth order for each family size using the Sweden 2006–2009 data and the fuller definition of families (Table 3, model 2.4).

Table 4. Unconditional (Model 2.3) and conditional (Model 2.4) intraclass correlation coefficients for student achievement among siblings, neighbors, and schools.

Family	School	Neighborhood	Unconditional intraclass correlations (Model 2.3)	Conditional intraclass correlations (Model 2.4)
Different family	Different school	Different neighborhood	0.000	0.000
Different family	Different school	Same neighborhood	0.042	0.038
Different family	Same school	Different neighborhood	0.067	0.065
Different family	Same school	Same neighborhood	0.109	0.103
Same family	Different school	Different neighborhood	0.397	0.414
Same family	Different school	Same neighborhood	0.439	0.452
Same family	Same school	Different neighborhood	0.464	0.479
Same family	Same school	Same neighborhood	0.506	0.517

Note. The correlation between children from different families, different neighborhoods, and different schools is zero by assumption.