educational option choice in secondary school. a multinomial multilevel approach maarten pinxten,...

Educational Option Choice in Secondary School. A Multinomial Multilevel Approach

Maarten Pinxten, Bieke De Fraine & Jan Van Damme

Presentation Earli Sig Interest Group 18 (Leuven) 2010

They say the definition of madness is doing the same thing and expecting a different result

T.H.E.H.I.V.E.S.

Presentation Earli Sig Interest Group 18 (Leuven)2010

1. Introduction

• Structure of Flemish educational system

► Different tracks - Academic track

- Technical track- Vocational track

► Different cycles- Cycle 1: Grade 7 + Grade 8 (orienting scope)- Cycle 2: Grade 9 + Grade 10 (specialization)- Cycle 3: Grade 11 + Grade 12 (further specialization)


1. Introduction

• Educational option choice: A Flemish perspective

- The term ‘option choice’: In contrast with other countries no subject choice but choice of a fixed package of subjects

For example: ‘Latin/Mathematics’ in Grade 9: core curriculum + 4hours/week of Latin + 2hours/week supplementary math

- Number of option choices fans out progressively due to further specialization

- Two important decisional thresholds: transition from Cycle 1 to Cycle 2 (end of Grade 8) and transition from Cycle 2 to Cycle 3 (end of Grade 10)


2. Determinants of Subject Choice

1. Student level determinants

► Gender- Uptake math & science courses in favour boys- Weaking gender gap of gender-stereotypical choice? * ICT & math: typical male * Humanities and expressive arts: typical female

► Socio-Economical Status (SES)- In general: higher social background > more Math &

Science- Interesting interaction effects with gender * For example: High SES girls tend to make more gender atypical

choices compared to low SES girls (Smyth & Hannan, 2006)



►Absolute achievement- Absolute performance in a subject is indicative for

choosing that subject (e.g., high grades in math, choosing more math subjects)

►Relative achievement (Jonsson, 1999)- Different comparative profiles for boys and girls * Girls: comparative advantage in social sciences * Boys: comparative advantage in math

- This comparative profile reduced the gender effect with 10 to 30%



►Individual psychological constructs1. Interest (e.g., Elsworth et al., 1999)

“intrapersonal influences predominate in school subject choice and show a particularly clear and persuasive pattern of direct relations between

interests and subject choices” (p.313)

2. Economic utility and future relevance (e.g.,Stokking, 2000)

3. Academic self concept, self-efficacy beliefs (e.g., Dickhauser et al., 2005)

4. Subject enjoyment and subject appreciation (e.g., van Langen, 2006a, 2006b)



2. School level determinants► In general: school level effects are rather small in comparison with individual level effects (e.g. Daly & Ainley, 1999)

► Some examples

- Dryler (1999) found that in schools with a high proportion of students with parents working in humanities that the odds for boys choosing engineering reduced significantly

- Ayalon and Yogev (1997)observed that the link between ability and choice of math/science subjects is intensified in more able environments

- A liberal school policy with regard to curriculum access seems to narrowthe gender gap in the uptake of mathematics subjects (Lamb, 1996).


3. Purpose

1. What is the effect of student level (e.g., achievement, gender, SES) and school level (e.g., gender-composition, SES-composition) determinants on option choice and is it possible to identify major (and minor) determinants of option choice? What is the relative impact of academic interest on option choice?

2. Are there differences between schools with respect to the option choices of their students? Are the log odds of choosing option A in contrast with choosing option B different between schools?


4. Data

► Data of LOSO project (Dutch acronym for Longitudinal Study of Secondary Education)

► LOSO-project followed the educational career of 6411 students in 90 schools

► We only considered option choice in academic track1. Homogeneity in the offer of option choices over schools2. Inclusion of all tracks: number of categories to large

► Students that repeated a grade were included in our sample


4. Data

► Grade 9: (N = 2518 – 22 schools)- Economical/Languages (N = 559)- Economical/Sciences (N = 722) >>> Reference Category- Classical/Languages (N= 250)- Classical/Sciences (N = 565)- Mixed/Social (N = 423)

► Grade 11 (N = 2871 – 24 schools)- Economical/Languages (N = 579)- Economical/Sciences (N = 405)- Classical/Languages (N = 304)- Classical/Sciences (N = 900) >>> Reference Category- Mixed/Social (N = 684)


4. Data

► Student level variables- Gender (0=Male / 1=Female)- SES (1 factor score: Income/Cultural capital/Occupational Level/Highest Diploma)- Academic self-concept (1 factor score: 9 items)- Dutch & Mathematics achievement (IRT – Grade 8 & Grade 10)- Numerical & Verbal intelligence (GETLOV scores – Grade 7)- Interest in Business – Sciences – Social - Literature (OII – Grade 7&Grade 12)

► School Level variables- SES composition- Gender composition- Math composition


5. Method

• Multinomial Multilevel Regression • Estimation method: Markov Chain Monte Carlo

(MCMC)- PQL1 starting values- 50 000 iterations - orthogonal parameterization

• Missing data: EM algorithm

• Software: MLwiN


5. Method

1. Logistic regression: A short introduction

► Unordered categorical dependent variable (option choice)► We will apply one of the most widely used transformations of probabilities, that is, the log odds:

► Interpretation: an increase of 1 of predictor x, increases the odds of choosing A versus not-A with a

factor eβPresentation Earli Sig Interest Group 18 (Leuven)

2010

( )1

Logit Ln x

5. Method

2. Estimation Method► Multinomial models cannot be estimated with ML methods in MLwiN

► Alternative: Marginal Quasi-Likelihood (MQL) and Penalized Quasi-Likelihood (PQL) in combination with a first or second order Taylor-series approximation (e.g., MQL1 vs MQL2):

* MQL1: raw estimates, downwardly biased fixed and random estimates* MQL2 and PQL1: only small improvements* PQL2: generally considered as best Pseudo-Likelihood estimator.

However, computationally less stable

► Recently: Bayesian MCMC methods offer an improvement on PQL2 methods (Browne & Draper, 2006)


5. Method

3. Multinomial warnings► Results rely heavenly on the chosen reference category

- Objective criterium: largest category

► When the number of categories grows: number of parameters gets doubled, tripled…

- Convergence problems!

► Option choices were clustered

- Supply-demand: some option choices are offered by some schools and not by others- Too many clusters: scattered results/interpretation meaningless- Some option choices are very alike (e.g., EC-MA & EC-SC)


6. Results (Final Model Grade 9)Parameter β S.E. Exp (β)

FIXED EFFECTS (student level)

Cons_Classical/Languages - 0.503 3.203Cons_Classical/Sciences 2.274 1.792

Cons_Economical/Languages - 3.535 1.850

Cons_Mixed/Social - 2.995 3.871

Girls_Classical/Languages 0.233 0.304Girls_Classical/Sciences - 0.251 0.206Girls_Economical/Languages 0.474 ** 0.194 1.60 **Girls_Mixed/Social 0.668 ** 0.218 1.95 **

SES_Classical/Languages 0.320 ** 0.092 1.38 **SES_Classical/Sciences 0.418 ** 0.073 1.52 **SES_Economical/Languages - 0.197 ** 0.071 0.82 **SES_Mixed/Social 0.021 0.073

Self-concept2_Classical/Languages 0.018 0.089Self-concept2_Classical/Sciences 0.112 0.074

Self-concept2_Economical/Languages - 0.283 ** 0.068 0.75 **Self-concept2_Mixed/Social - 0.029 0.072


6. Results (Grade 9 - Continued)Parameter β S.E. Exp (β)


Achievement Dutch2_Classical/Languages 1.263 ** 0.165 3.54 **Achievement Dutch2_Classical/Sciences 1.219 ** 0.126 3.38 **Achievement Dutch2_Economical/Languages - 0.131 0.083Achievement Dutch2_Mixed/Social - 0.059 0.098

Achievement Math2_Classical/Languages 0.012 0.127Achievement Math2_Classical/Sciences 0.660 ** 0.107 1.93 **Achievement Math2_Economical/Languages - 0.458 ** 0.080 0.63 **Achievement Math2_Mixed/Social - 0.084 0.091

Verbal Intelligence_Classical/Languages 0.333 ** 0.110 1.40 **

Verbal Intelligence_Classical/Sciences 0.215 ** 0.088 1.24 **

Verbal Intelligence_Economical/Languages 0.032 0.077

Verbal Intelligence_Mixed/Social 0.145 0.086

Numeric Intelligence_Classical/Languages - 0.180 0.107Numeric Intelligence_Classical/Sciences 0.095 0.087

Numeric Intelligence_Economical/Languages - 0.423 ** 0.079 0.66 **Numeric Intelligence_Mixed/Social - 0.139 0.086




Interest Business1_Classical/Languages - 0.029 0.091

Interest Business1_Classical/Sciences - 0.164 ** 0.072 0.85 **

Interest Business1_Economical/Languages - 0.139 ** 0.069 0.87 **

Interest Business1_Mixed/Social - 0.353 ** 0.073 0.70 **

Interest Sciences1_Classical/Languages 0.102 0.111

Interest Sciences1_Classical/Sciences 0.098 0.087

Interest Sciences1_Economical/Languages - 0.284 ** 0.082 0.75 **

Interest Sciences1_Mixed/Social - 0.188 ** 0.088 0.83 **

Interest Social1_Classical/Languages 0.159 0.109

Interest Social1_Classical/Sciences 0.086 0.089Interest Social1_Economical/Languages 0.001 0.082

Interest Social1_Mixed/Social 0.008 0.088

Interest Literature1_Classical/Languages 0.702 ** 0.104 2.02 **

Interest Literature1_Classical/Sciences 0.222 ** 0.079 1.25 **Interest Literature1_Economical/Languages 0.195 ** 0.075 1.22 **

Interest Literature1_Mixed/Social 0.280 ** 0.081 1.32 **



FIXED EFFECTS (school level)

SES-composition_Classical/Languages 0.200 0.563

SES-composition_Classical/Sciences - 0.036 0.317

SES-composition_Economical/Languages 0.343 0.332

SES-composition_Mixed/Social 0.420 0.700

Girls school_Classical/Languages - 1.274 1.230

Girls school_Classical/Sciences - 0.185 0.733

Girls school_Economical/Languages - 0.329 0.759

Girls school_Mixed/Social - 2.167 1.473

Mixed school_Classical/Languages - 1.993 1.165

Mixed school_Classical/Sciences - 0.301 0.663Mixed school_Economical/Languages 0.016 0.677

Mixed school_Mixed/Social - 1.293 1.337

Math composition_Classical/Languages - 0.834 1.375

Math composition_Classical/Sciences - 2.412 ** 0.724 0.09 **Math composition_Economical/Languages 1.067 0.733

Math composition_Mixed/Social 0.958 1.444


6. Results (Grade 9 - Continued)S.E.

RANDOM EFFECTS

Level 3 – School level

Cons_Classical/Languages.Cons_Classical/Languages 2.325 1.064

Cons_Classical/Sciences.Cons_Classical/Sciences 0.704 0.290

Cons_Economical/Languages.Cons_Economical/Languages 0.749 0.300

Cons_Mixed/Social.Cons_Mixed/Social 2.856 1.314

Cons_Classical/Languages.Cons_Economical/Languages 0.945 0.454

Cons_Classical/Sciences.Cons_Classical/Languages 0.885 0.445

Cons_Classical/Sciences.Cons_Economical/Languages 0.650 0.273

Cons_Mixed/Social.Cons_Classical/Languages 0.990 0.743

Cons_Mixed/Social.Cons_Classical/Sciences 0.551 0.416

Cons_Mixed/Social.Cons_Economical/Languages 0.852 0.462

Level 2 – Student Level 1.000 0.000

Level 1 – Multinomial Variance 1.000 0.000


2( )m 01

6. Results (Final Model Grade 11)Parameter β S.E. Exp (β)


Cons_Classical/Languages - 0.909 2.001Cons_Economical/Languages 0.694 1.774

Cons_Economical/Sciences 0.225 1.773

Cons_Mixed/Social 0.741 3.138

Girls_Classical/Languages - 0.262 0.239Girls_Economical/Languages - 0.127 0.202Girls_Economical/Sciences 0.127 0.203Girls_Mixed/Social - 0.062 0.189

SES_Classical/Languages - 0.114 0.086SES_Economical/Languages - 0.431 ** 0.078 0.65 ** SES_Economical/Sciences - 0.452 ** 0.079 0.64 ** SES_Mixed/Social - 0.432 ** 0.070 0.65 **

Self-concept4_Classical/Languages - 0.105 0.084Self-concept4_Economical/Languages - 0.066 0.075

Self-concept4_Economical/Sciences - 0.026 0.077Self-concept4_Mixed/Social - 0.244 ** 0.069 0.78 **




Achievement Dutch4_Classical/Languages 0.266 ** 0.112 1.30 **Achievement Dutch4_Economical/Languages - 0.448 ** 0.095 0.64 **Achievement Dutch4_Economical/Sciences - 0.676 ** 0.096 0.51 **Achievement Dutch4_Mixed/Social - 0.541 ** 0.088 0.58 **

Achievement Math4_Classical/Languages - 1.114 ** 0.106 0.33 **Achievement Math4_Economical/Languages - 1.161 ** 0.097 0.31 ** Achievement Math4_Economical/Sciences - 0.023 0.107 Achievement Math4_Mixed/Social - 0.870 ** 0.094 0.42 **

Verbal Intelligence_Classical/Languages - 0.104 0.099

Verbal Intelligence_Economical/Languages - 0.296 ** 0.090 0.74 **

Verbal Intelligence_Economical/Sciences - 0.280 ** 0.090 0.76 **

Verbal Intelligence_Mixed/Social - 0.235 ** 0.082 0.79 **

Numeric Intelligence_Classical/Languages - 0.288 ** 0.098 0.75 **Numeric Intelligence_Economical/Languages - 0.443 ** 0.087 0.64 **

Numeric Intelligence_Economical/Sciences - 0.221 ** 0.091 0.80 **Numeric Intelligence_Mixed/Social - 0.323 ** 0.081 0.72 **




Interest Business6_Classical/Languages 0.205 ** 0.083 1.23 **

Interest Business6_Economical/Languages 0.638 ** 0.076 1.89 **

Interest Business6_Economical/Sciences 0.663 ** 0.079 1.94 **

Interest Business6_Mixed/Social - 0.101 0.068

Interest Sciences6_Classical/Languages - 0.855 ** 0.108 0.43 **

Interest Sciences6_Economical/Languages - 1.053 ** 0.097 0.35 **

Interest Sciences6_Economical/Sciences - 0.888 ** 0.097 0.41 **

Interest Sciences6_Mixed/Social - 0.776 ** 0.087 0.46 **

Interest Social6_Classical/Languages - 0.079 0.098

Interest Social6_Economical/Languages - 0.327 ** 0.087 0.72 **Interest Social6_Economical/Sciences - 0.218 ** 0.088 0.80 **

Interest Social6_Mixed/Social 0.133 0.081

Interest Literature6_Classical/Languages 0.757 ** 0.101 2.13 **

Interest Literature6_Economical/Languages 0.316 ** 0.082 1.37 ** Interest Literature6_Economical/Sciences - 0.107 0.082

Interest Literature6_Mixed/Social 0.300 ** 0.075 1.35 **



FIXED EFFECTS (school level)

SES-composition_Classical/Languages 0.138 0.362

SES-composition_Economical/Languages - 0.077 0.332

SES-composition_Economical/Sciences - 0.111 0.323

SES-composition_Mixed/Social 0.034 0.586

Girls school_Classical/Languages - 0.538 0.824

Girls school_Economical/Languages - 0.300 0.715

Girls school_Economical/Sciences - 0.579 0.662

Girls school_Mixed/Social - 1.230 1.295

Mixed school_Classical/Languages - 1.395 0.720

Mixed school_Economical/Languages - 1.250 0.622Mixed school_Economical/Sciences - 0.852 0.619

Mixed school_Mixed/Social - 1.729 1.141

Math composition_Classical/Languages 0.874 0.624

Math composition_Economical/Languages 0.842 0.564Math composition_Economical/Sciences 0.702 0.532

Math composition_Mixed/Social 1.106 1.007


6. Results (Grade 11 - Continued)S.E.

RANDOM EFFECTS

Level 3 – School level

Cons_Classical/Languages.Cons_Classical/Languages 0.744 0.326

Cons_Economical/Languages.Cons_Economical/Languages 0.552 0.236

Cons_Economical/Sciences.Cons_Economical/Sciences 0.460 0.208

Cons_Mixed/Social.Cons_Mixed/Social 2.032 0.847

Cons_Classical/Languages.Cons_Economical/Languages 0.433 0.226

Cons_Classical/Languages.Cons_Economical/Sciences - 0.117 0.176

Cons_Economical/Sciences.Cons_Economical/Languages 0.220 0.169

Cons_Mixed/Social.Cons_Classical/Languages 0.774 0.409

Cons_Mixed/Social.Cons_Economical/Languages 0.854 0.400

Cons_Mixed/Social.Cons_Economical/Sciences 0.412 0.313

Level 2 – Student Level 1.000 0.000

Level 1 – Multinomial Variance 1.000 0.000


2( )m 01

7. Conclusions and discussion

• Almost no effect of academic self-concept on option choice• Option choice in secondary school is mainly determined by student

level factors• In 9th grade: girls tend to choose the options economical/Languages

& Mixed/social more often (in comparison with economical/Sciences)

• In 11th grade: the effect of gender on option choice disappeared completely after the inclusion of interest in sciences

• In both 9th and 11th grade: opting for Mixed/Social seems to be a negative choice (no effect of interest in social service)

• Relative importance of achievement (Grade 9)Example 1. Economical/Languages VS Economical/Sciences: Those students do

not perform better in Dutch but they perform significantly worse in math. But: greater interest in literature and less interest in sciences

Example 2. Classical/Languages VS Classical/Sciences: Those students do not perform better in Dutch but they perform significantly worse in math. But greater interest in literature Presentation Earli Sig Interest Group 18 (Leuven)

2010

7. Conclusion and discussion

• From an achievement point of view: strong hierarchy between option choices with classical studies at the top

• From a SES point of view: student with higher socio-economical background tend to choose classical studies over economical or social oriented option choices

BUT

1. Chicken or the egg? Interest or option choice?2. Positive or negative choice?

! Educational option choice is a complex jigsaw puzzle !


References

• Ayalon, H., & Yogev, A. (1997). Students, schools, and enrollment in science and humanities courses in Israeli secondary education. Educational Evaluation and Policy Analysis, 19, 339-353.

• Browne, W. J., & Draper, D. (2006). A comparison of Bayesian and likelihood-based methods for fitting multilevel models. Bayesian Analysis, 1 (3), 473-514.

• Colley, A., & Comber, C. (2003). School subject preferences: age and gender differences revisited. Educational Studies, 29, 59-67.

• Daly, P., & Ainley, J. (1999). Student participation in mathematics courses in Australian secondary schools. The Irish Journal of Education, 30, 77-95.

• Dickhauser, O., Reuter, M., & Hilling, C. (2005). Coursework selection: A frame of reference approach using structural equation modeling. British Journal of Educational Psychology, 75, 673-688.

• Dryler, H. (1999).The impact of school and classroom characteristics on educational choices by boys and girls: A multilevel analysis. Acta Sociologica, 42, 299-318.

• Elsworth, G. R., Harvey-Beavis, A., Ainley, J., & Fabris, S. (1999). Generic interests and school subject choice. Educational Research and Evaluation, 5, 290-318.


References

• Lamb, S. (1996). Gender differences in mathematics participation in Australian schools: Some relationships with social class and school policy. British Educational Research Journal, 22, 223-240.

• Miller, L., & Budd, J. (1999). The development of occupational sex-role stereotypes, occupational preferences and academic subject preferences in children at ages 8, 12 and 16. Educational Psychology, 19, 17-35.

• Smyth, E., & Hannan, C. (2006). School Effects and Subject Choice: The uptake of scientific subjects in Ireland. School Effectiveness and School Improvement,17, 303-327.

• Stokking, K. M. (2000). Predicting the choice of physics in secondary education. International Journal of Science Education, 22, 1261-1283.

• van Langen, A., Rekers-Mombarg, L., & Dekkers, H. (2006a). Sex-related differences in the determinants and process of science and mathematics choice in pre-university education. International Journal of Science Education, 28, 71-94.

• van Langen, A., Rekers-Mombarg, L., & Dekkers, H. (2006b). Group-related differences in the choice of mathematics and science subjects. Educational Research and Evaluation, 12, 27-51.


Thank you!

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