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## brief Chiu2012
:::success
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.
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**Jack Tsai**
2021/4/6
<!-- Put the link to this slide here so people can follow -->
slide: https://hackmd.io/@nccudoc/SJEtRimQ_
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### 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 </br> 2. ==high== corr b/w Ach, ==low== corr b/w SC (non-matching) </br> 3. social comparison theory | 1. multi-dim academic self-concept </br> 2. social comparison theory
| indivisual lv | group lv |
---
### Intro (4/4) Example
|||
|:--:|:--:|
|![](https://i.imgur.com/V3gZtxF.png)|Marsh & Hau (2004)|
|![](https://i.imgur.com/1YCf9lm.png)|Chiu (2008)|
|![](https://i.imgur.com/nJbUlGh.png)|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
![](https://i.imgur.com/b6s5oFY.png)
#### 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
1) Individuals' self-concept in a domain is influenced by comparing their performance in other domains.
2) The BFLPE precisely captured the essence of social comparison theory.
---
### Question
1) Why multilevel researches usually present so many model results? (even if they only need a few of these models to test their hypo?)
2) 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?
3) What kind of situation should we use random slope effect or interaction effect to interpret data?
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