SCHOOL-LEVEL TRACKING AND THE BFLPE1
Supplemental Materials
Selective School Systems and Academic Self-Concept: How Explicit and Implicit School-Level Tracking Relate to the Big-Fish-Little-Pond-Effect Across Cultures
by S. Salchegger, 2015, Journal of Educational Psychology
Supplemental Materials
To be published on a separate webpage and linked to the published manuscript
Appendix A: Supplemental Methodological Details (Mplus Codes)
- Mplus input for computing the index of implicit school-level tracking
TITLE: ICC of PISA 2003 ESCS controlling for school selectivity
DATA: file is escs2Rev.dat;
VARIABLE:
NAMES ARE
COUNTRY
SCHOOLID
STIDSTD
ESCS
W_FSTUWT
SELECT!select has 4 categories; therefore it was recoded into 3 dummy variables
SELECT1!Dummy 0 = 0 vs. 1&2&3 = 1
SELECT2!Dummy 0&1 = 0 vs. 2&3 = 1
SELECT3!Dummy 0&1&2 = 0 vs. 3 = 1 (SELECT3 was not included into the
model for Iceland, because there were no schools in category 3)
t_fstwt;! student final weights, rescaled to sum up within each school to the school sample size
missing = ALL (-99);
usevar are escs SELECT1 SELECT2 SELECT3;
USEOBS COUNTRY EQ 40; !40 is Austria in the PISA 2003 files
BETWEEN = SELECT1 SELECT2 SELECT3;
cluster=SCHOOLID;
weight = w_fstuwt ;
wtscale = cluster ;
bweight = t_fstwt ;
bwtscale = sample ;
analysis: TYPE is twolevel;
model:
%within%
escs (sig2);
%between%
escs on SELECT1;
escs on SELECT2;
escs on SELECT3;
escs (tau2);
model constraint:
new (icc);
icc = tau2/(sig2+tau2);
output:
stand sampstat;
- Latent variable mediation model that controls for measurement error in the total sample
title: Latent variable mediation model controlling for measurement error in the total sample
data: file = bflpe.dat;
variable: names =
BFLPE
BFLPE_SE
BFLPE_V
sel16
ICCescs
ICCse
BSAV
BSAV_SE
country;
usevariables = BFLPE BSAV sel16;
define: sel16 = sel16/100; !divide by 100 to enhance numeric stability of results
analysis: bootstrap = 1000;
model: etaBFLPE by BFLPE@1;!fixing the factor loading to 1
etaBSAV by BSAV@1;
etaBFLPE on sel16 etaBSAV;
etaBSAV on sel16;
BFLPE@ .00247;!fixing the residual variance to the error variance
BSAV@ .00099;
model indirect: etaBFLPE ind sel16;
output: sampstat stdyx;
cinterval (bcbootstrap);
- Mplus Input for meta-analytic random-effects structural equation mediation model
title: meta-analytic random-effects structural equation mediation model
data: file = bflpe.dat;
variable: names =
BFLPE
BFLPE_SE
BFLPE_V
sel16
ICCescs
ICCse
BSAV
BSAV_SE
country;
usevariables = BFLPE BSAV sel16 inter;
define:w2 = SQRT (BFLPE_V**(-1)); !compute weight like Cheung (2008)
BFLPE = w2*BFLPE;
inter = w2*1;
BSAV = w2*BSAV;
sel16 = (w2*sel16)/100; !divide by 100 to enhance numeric stability of results
analysis: type=random;
estimator=ML;
MODEL:
f_BFLPE | BFLPE on inter;
[; ! Intercept is fixed at 0
; ! Error variance is fixed at 1
f_BFLPE*;!var (f_BFLPE): tau^2
[f_BFLPE*];!mean(f_BFLPE): intercept
f_BFLPE on sel16 (gamma_1);
BSAV on sel16 (gamma_2);
f_BFLPE on BSAV (beta_12);
model constraint:
new (ind, dir, total);
ind=gamma_2*beta_12;
dir=gamma_1;
total=ind+dir;
output: sampstat;
cinterval(symmetric);
- Mplus input for TIMSS 2007 BFLPE
TITLE: Doubly-latent MLM with latent constructs based on multiple indicators and latent aggregation;
DATA:FILE IS allFiles_imp.dat;
TYPE=IMPUTATION;!combines 5 files for each plausible value of mathematics achievement
VARIABLE: Names are
IDCNTRY IDSTUD schID
TOTWGT SCHWGT
ZMAT !Math achievement z-standardized for each country
ZSK1 ZSK2 ZSK3 ZSK4;!positively formulated self-concept items had been reverse coded already before; Items were z-standardized for each country
USEVAR ARE
ZSK1 ZSK2 ZSK3 ZSK4 ZMAT;
USEOBS IDCNTRY EQ 40 ; !40 is Austria
cluster=schID;
weight is TOTWGT ;
wtscale = cluster ;
BWEIGHT is SCHWGT ;
bwtscale = sample ;
missing are all (-99);
ANALYSIS: Type is twolevel ; algorithm=em; mconv=1000;
MODEL:
%within%
MSC_W by ZSK1 (1);
MSC_W by ZSK2 (2);
MSC_W by ZSK3 (3);
MSC_W by ZSK4 (4);
MSC_W on ZMAT (b_within);
%between%
MSC_B by ZSK1 (1);
MSC_B by ZSK2 (2);
MSC_B by ZSK3 (3);
MSC_B by ZSK4 (4);
MSC_B on ZMAT (b_betwn);
MODEL CONSTRAINT:
new(bflpe);
bflpe = b_betwn - b_within;
OUTPUT: sampstat stand tech1;
Appendix B: Results of Multilevel Models Testing Years of Explicit School-Level Tracking as Country-Level Moderator of the BFLPE
Table B1Three-Level Model Testing Years of Explicit School-Level Tracking as Country-Level Moderator of the BFLPE
Model 1 / Model 2 / Model 3
Effect / Estimate / SE / p / Estimate / SE / p / Estimate / SE / p
Main effects
Constant / -0.123 / 0.036 / .001 / -0.124 / 0.035 / .001 / -0.123 / 0.034 / .001
Linear ability / 0.511 / 0.019 / .001 / 0.511 / 0.019 / .001 / 0.510 / 0.019 / .001
Quadratic ability / 0.103 / 0.005 / .001 / 0.103 / 0.005 / .001 / 0.103 / 0.005 / .001
School-average ability / -0.312 / 0.022 / .001 / -0.310 / 0.018 / .001 / -0.308 / 0.019 / .001
Years of explicit school-level
tracking / 0.032 / 0.027 / .239 / 0.069 / 0.041 / .094
School-average X Years of
explicit school-level tracking / -0.075 / 0.018 / .001 / -0.059 / 0.023 / .010
Between-school achievement
variance / -0.065 / 0.040 / .105
School-average X Between
school achievement variance / -0.027 / 0.023 / .236
Random effects
Level 3 country intercept / 0.051 / 0.015 / .001 / 0.049 / 0.014 / .001 / 0.047 / 0.011 / .001
Level 3 linear ability / 0.015 / 0.003 / .001 / 0.015 / 0.003 / .001 / 0.015 / 0.003 / .001
Level 3 quadratic ability / 0.001 / 0.000 / .001 / 0.001 / 0.000 / .001 / 0.001 / 0.000 / .001
Level 3 school-average ability / 0.018 / 0.006 / .001 / 0.012 / 0.004 / .001 / 0.012 / 0.003 / .001
Level 2 school intercept / 0.031 / 0.002 / .001 / 0.031 / 0.002 / .001 / 0.031 / 0.001 / .001
Level 1 individual intercept / 0.780 / 0.036 / .001 / 0.780 / 0.036 / .001 / 0.780 / 0.002 / .001
–2*log-likelihood / 781885.075 / 781839.540a / 781868.026a
Note. BFLPE = big-fish–little-pond-effect. Estimates are standardized. The PISA 2003 index of mathematics self-concept is the dependent variable.
a The change in –2*log-likelihood from Model 1 is significant (p < .001).
Appendix C: Reliability (Cronbach's Alpha) for Self-Concept and Achievement Scales
Table C1Reliability (Cronbach's Alpha) for Self-Concept and Achievement Scales for Different Assessments, Academic Domains, and Age Groups in Participating Countries
Country / General Academic Self-Concept (PISA 2000) / Mathematics Self-Concept (PISA 2003) / Mathematics Achievement (PISA 2003) / Science Self-Concept (PISA 2006) / Science Achievement (PISA 2006) / Mathematics Self-Concept (TIMSS 2007, Fourth Grade) / Mathematics Achievement (TIMSS 2007, Fourth Grade)
Argentina / 0.89 / 0.90
Australia / 0.74 / 0.89 / 0.91 / 0.93 / 0.92 / 0.75 / 0.86
Austria / 0.76 / 0.89 / 0.92 / 0.90 / 0.94 / 0.78 / 0.82
Azerbaijan / 0.88 / 0.84
Belgium / 0.70 / 0.89 / 0.93 / 0.91 / 0.94
Brazil / 0.73 / 0.83 / 0.88 / 0.86 / 0.90
Bulgaria / 0.87 / 0.92
Canada / 0.91 / 0.89 / 0.94 / 0.91
Chile / 0.89 / 0.90
Chinese Taipei / 0.93 / 0.92 / 0.73 / 0.83
Colombia / 0.87 / 0.87 / 0.43 / 0.77
Croatia / 0.89 / 0.91
CzechRepublic / 0.76 / 0.89 / 0.91 / 0.88 / 0.92 / 0.75 / 0.83
Denmark / 0.80 / 0.90 / 0.90 / 0.94 / 0.92 / 0.78 / 0.84
Estonia / 0.86 / 0.91
Finland / 0.84 / 0.92 / 0.89 / 0.92 / 0.90
France / 0.89 / 0.90 / 0.91 / 0.93
Germany / 0.78 / 0.91 / 0.93 / 0.90 / 0.93 / 0.81 / 0.83
Greece / 0.86 / 0.89 / 0.90 / 0.91
Hong Kong / 0.89 / 0.92 / 0.93 / 0.92 / 0.72 / 0.81
Hungary / 0.73 / 0.81 / 0.9 / 0.88 / 0.91 / 0.78 / 0.88
Iceland / 0.81 / 0.93 / 0.9 / 0.94 / 0.92
Indonesia / 0.75 / 0.83 / 0.86 / 0.87
Ireland / 0.77 / 0.89 / 0.91 / 0.93 / 0.92
Israel / 0.92 / 0.91
Italy / 0.74 / 0.91 / 0.91 / 0.89 / 0.93 / 0.69 / 0.85
Japan / 0.88 / 0.91 / 0.93 / 0.91 / 0.76 / 0.85
Jordan / 0.83 / 0.90
Korea / 0.78 / 0.88 / 0.91 / 0.92 / 0.91
Kyrgyzstan / 0.82 / 0.85
Latvia / 0.66 / 0.85 / 0.89 / 0.82 / 0.90 / 0.72 / 0.83
Liechtenstein / 0.77 / 0.89 / 0.91 / 0.93 / 0.93
Lithuania / 0.86 / 0.92 / 0.71 / 0.85
Luxembourg / 0.74 / 0.89 / 0.90 / 0.91 / 0.93
Macao-China / 0.89 / 0.88 / 0.92 / 0.89
Mexico / 0.71 / 0.78 / 0.86 / 0.86 / 0.89
Montenegro / 0.87 / 0.89
Netherlands / 0.76 / 0.90 / 0.93 / 0.91 / 0.93 / 0.82 / 0.79
New Zealand / 0.79 / 0.87 / 0.92 / 0.92 / 0.93 / 0.69 / 0.87
Norway / 0.85 / 0.90 / 0.90 / 0.92 / 0.91 / 0.68 / 0.82
Poland / 0.87 / 0.90 / 0.88 / 0.91
Portugal / 0.73 / 0.89 / 0.90 / 0.91 / 0.92
Qatar / 0.88 / 0.88 / 0.41 / 0.58
Romania / 0.84 / 0.90
Russian Federation / 0.72 / 0.81 / 0.84 / 0.89 / 0.74 / 0.86
Serbia / 0.83 / 0.88 / 0.90 / 0.90
SlovakRepublic / 0.87 / 0.88 / 0.92 / 0.73 / 0.86
Slovenia / 0.90 / 0.93 / 0.66 / 0.84
Spain / 0.89 / 0.89 / 0.92 / 0.92
Sweden / 0.81 / 0.89 / 0.90 / 0.93 / 0.92 / 0.72 / 0.82
Switzerland / 0.74 / 0.90 / 0.91 / 0.92 / 0.93
Thailand / 0.78 / 0.86 / 0.87 / 0.88
Tunisia / 0.88 / 0.85 / 0.82 / 0.87 / 0.45 / 0.78
Turkey / 0.88 / 0.91 / 0.92 / 0.91
United Kingdom / 0.88 / 0.92 / 0.85 / 0.93
United States / 0.79 / 0.89 / 0.92 / 0.87 / 0.93 / 0.76 / 0.85
Uruguay / 0.88 / 0.89 / 0.90 / 0.90
Note. Empty cell = country did not participate in the study. No reliability estimates were available for the combined achievement scale used by Marsh and Hau (2003). Only those TIMSS 2007 countries that participated at least in one assessment of PISA 2000, 2003 or 2006 were included. Reliability estimates for self-concept scales for TIMSS 2007 are taken from Olson et al. (2008, p. 292) and are based on a trichotomized index; reliability estimates for self-concept scales for PISA 2000 are based on data fromAdams & Wu(2003, p. 240),estimates for PISA 2003 are based on data from OECD (2005b, p. 294); and estimates for PISA 2006 are based on data from OECD (2009, p. 324). Reliability estimates for achievement scales for TIMSS 2007 are based on Olson et al. (2008, p. 209),estimates for PISA 2003 are based on datafrom OECD (2005b, p. 410), and estimates for PISA 2006 are based on datafrom OECD (2009, p. 217).