brief Chiu2012
Chiu, M. S. (2012). The internal/external frame of reference model, big-fish-little-pond effect, and combined model for mathematics and science. Journal of Educational Psychology, 104(1), 87-107.
Jack Tsai
2021/4/6
Intro (1/4) Internal/External of Refernce (I/E) Model
- academic self-concept -> SC in diff domains (e.g. math, science, English)
- Positive effect: Achievement and self-concept are matching. (internal comparison)
- MAch(+) -> MSC(+)
- VAch(+) -> VSC(+)
- Negtive effect: Achievement and self-concept are non-matching. (external comparison)
- MAch(+) -> VSC(-)
- VAch(+) -> MSC(-)
Intro (2/4) Big-Fish-Little-Pond Efeect (BFLPE)
- focused on academic self-concept either in general or particular domian.
- students:
- achieving group (+) -> self-concept (-)
- achieving group (-) -> self-concept (+)
Intro (3/4) Combine model
- Internal comparison (individual lv) (I/E model)
- Ach <-> SC
- External comparison (group lv) (BFLPE)
- self <-> group average
| I/E model | BFLPE |
|---|---|
| 1. multi-dim academic self-concept 2. high corr b/w Ach, low corr b/w SC (non-matching) 3. social comparison theory |
1. multi-dim academic self-concept 2. social comparison theory |
| indivisual lv | group lv |
Intro (4/4) Example
 |
Marsh & Hau (2004) |
 |
Chiu (2008) |
 |
Chiu (2012) |
Method (1/2)
Sample
- student lv: 139,174
- school lv: 4,231
- country lv: 27
Measures
- student lv: L1MAch, L1SAch, L1MSC, L1SSC
- school lv: L2MAch, L2SAch
- country lv: L3MAch, L3SAch
Method (2/2) Statistical Analysis
random intercept model
- only interpret the intercept (the level of
L1MSC) - do not consider the interaction effect b/w variables
- do not consider other interpretations on slope level.
Results (1/2) math self-concept
- Hypo 1/ Model 2: L1MSC <- (+)L1MAch + (-)L1SAch + SSC
- Hypo 3/ Model 4: L1MSC <- (-)L2MAch + L1MAch
- Hypo 5/ Model 7: L1MSC <- (+)L1MAch + (-)L1SAch + (-)L2MAch + L1SSC
| L1MSC ~ . | model 2 | model 4 | model 7 |
|---|---|---|---|
| (fixed) | |||
| L1MAch | .81*** | .80*** | .86*** |
| L1SAch | -.17*** | -.14*** | |
| L1SSC | .09** | .08* | |
| L2MAch | -.50*** | -.45*** | |
| L2SAch | |||
| L3MAch | |||
| (random) | |||
| L1 | .73 | .74 | .73 |
| L2 | .09 | .05 | .05 |
| L3 | .36 | .11 | .10 |
Results (2/2) science self-concept
- Hypo 2/ Model 10: L1SSC <- (+)L1SAch + (-)L1MAch + MSC
- Hypo 4/ Model 12: L1SSC <- (-)L2SAch + L1SAch
- Hypo 6/ Model 15: L1SSC <- (+)L1SAch + (-)L1MAch + (-)L2SAch + L1MSC
| L1SSC ~ . | model 10 | model 12 | model 15 |
|---|---|---|---|
| (fixed) | |||
| L1MAch | -.09* | -.07 | |
| L1SAch | .52*** | .54*** | .54*** |
| L1MSC | .09** | .09* | |
| L2MAch | |||
| L2SAch | -.28*** | -.24*** | |
| L3MAch | |||
| (random) | |||
| L1 | .77 | .77 | .76 |
| L2 | .09 | .07 | .07 |
| L3 | .23 | .13 | .11 |
Discussion (1/1) combined model
- Individuals' self-concept in a domain is influenced by comparing their performance in other domains.
- The BFLPE precisely captured the essence of social comparison theory.
Question
- Why multilevel researches usually present so many model results? (even if they only need a few of these models to test their hypo?)
- In this paper, the author only set random effects on intercept (i.e., mean of math/science self-concept). If L2Ach and L3Ach are only explained to L1SC, why does it appear in the fixed effect?(what do they mean?) I am a little confused?
- What kind of situation should we use random slope effect or interaction effect to interpret data?
brief Chiu2012 Chiu, M. S. (2012). The internal/external frame of reference model, big-fish-little-pond effect, and combined model for mathematics and science. Journal of Educational Psychology, 104 (1), 87-107. Jack Tsai 2021/4/6 slide: https://hackmd.io/@nccudoc/SJEtRimQ_
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