The Integration Paradox

class: center, middle, inverse, title-slide

.title[
# The Integration Paradox
]
.subtitle[
## First Results from a Meta-Analysis & Proposal of a New Experimental Design
]
.author[
### Merlin Schaeffer & Judith Kas
]
.date[
### 2023-04-21
]

---

layout: true
# Tocqueville's Paradox

.push-right[.center[
<img src="https://upload.wikimedia.org/wikipedia/commons/a/aa/Alexis_de_tocqueville.jpg" width="67%" style="display: block; margin: auto;" />
]]

---

.push-left[
 
 
 
> The hatred that men bear to privilege increases in proportion as privileges become fewer and less considerable

> [...]

> the love of equality should constantly increase together with equality itself [...]

> -- Alexis de Tocqueville (2015 [1840])
]

---

.push-left[.center[
<img src="media/FRA_2.png" width="100%" style="display: block; margin: auto;" />
.backgrnote[.center[
*Source*: European Union Agency for Fundamental Rights. (2014)
]]
]]

---
layout: false
# The integration paradox

.left-column[
 
> [...] greater familiarity with the culture and language and economic advancement can lead to greater consciousness of the reality of discrimination.

> -- Portes, Parker, and Cobas (1980)
]

.right-column[
 
 
<img src="media/Conceptual-model.png" width="100%" style="display: block; margin: auto;" />
]

---
class: clear
layout: true
# Meta-analysis .font60[Which reliable patterns has the literature produced so far?]

.push-left[
.center[.font150[**Sample definition**]]
1. **Outcome**: perceived (ethnic) discrimination.
2. **Population**: Immigrants, descendants of immigrants, or members of an ethnic, religious, or racial minority.
3. **Correlation or regression coefficient & associated inference statistic**: Perceived discrimination and one of the following types of indicators of immigrant integration: 
  + Education, length of residence or generational status, 
  + Labor market attainment (e.g., income), exposure to persons of native-born parents (e.g., neighborhood share), 
  + Indicators of familiarity with public discourse (e.g., news media consumption), 
  + Indicators of (downward) social mobility
4. **Published in English** & no MA theses.
]

---

.push-right[
 
 
 
<img src="media/Conceptual-model.png" width="100%" style="display: block; margin: auto;" />
]

---
.push-right[
.center[.font150[**Sampling**]]
- 766 non-duplicate studies from WoS & Google Scholar via search string, 7 April 2021:
> .font70[
("integration paradox" OR "Paradox of Integration") AND discrimination
]

]

---
layout: false
# Sample of studies .font60[Cleaning & pre-reg training]

.left-column[
<img src="SOFI_files/figure-html/dag3-1.png" width="100%" style="display: block; margin: auto;" />

]

.right-column[
<img src="https://www.cos.io/hs-fs/hubfs/badges_stacked.original.png?width=417&name=badges_stacked.original.png" width="60%" style="display: block; margin: auto;" />
.center[[osf.io/dmsc6](https://osf.io/dmsc6/?view_only=4bcac52a1b9c49f8b240c387855a052d)]
]

---
# Meta-analysis

.push-left[
.center[.font150[**Outcome**]]

`$$\begin{align*}
      \rho_{yx \cdot z} &= \frac{\text{Cov}(e_{x \cdot z}, e_{y \cdot z})}{\text{SD}_{e_{x \cdot z}} \text{SD}_{e_{y \cdot z}}}, \\
      &= \frac{t}{\sqrt{t^2 + \text{df}}}.
    \end{align*}$$`
.backgrnote[.center[
*Source*: Gustafson (1961)
]]

.backgrnote[
*Advantage*: Can get `$t$` and `$\text{df}$` from every kind of model (e.g., logit, probit, poisson, OLS).

*Disadvantages*: `$\rho_{yx \cdot z}$` depends on `$z$` & is probably not accurate for estimates from GLMs.
]]

.push-right[
.center[.font150[**Overall meta-estimate and meta regression**]]
`$$\begin{align*}
\bar{\rho}_{yx \cdot z} &= \frac{\sum_{i=1}^n \color{orange}{w_{i}}\rho_{(yx \cdot z)i}}{\color{orange}{w_{i}}}, \\
\min \text{RSS} &= \min \sum_{i=1}^{n} \color{orange}{w_{i}} R_{i}^{2}, \\
w_{i} &= \frac{1}{\color{orange}{\text{Var}(\rho_{(yx \cdot z)i})} + \tau^2}. 
 \end{align*}$$`
.backgrnote[
Where `$\tau^2$` is the between-studies variance of `$\rho_{(yx \cdot z)i}$` estimated via REML.
]

```r
rma.mv(yi = yi, V = as.matrix(vi), 
       data = meta_data, test = "t", 
       mods = ~ pred + mipex,
       random = list(~ 1 | Study_ID/ID,
                     ~ 1 | data,
                     ~ 1 | cntryear))
```
.backgrnote[
Multilevel random effects meta-analytic models (Konstantopoulos, 2011), as implemented in *R*'s *metafor* package (Viechtbauer, 2010).
]]

---
class: clear

.left-column[
 
.red[.font200[**Overall meta-estimate**]]

.center[.backgrnote[
*Note*: 79 partial correlation coefficients and overall meta-estimate with associated 95% confidence intervals, based on 30 coded studies.
]]
]

.right-column[
<img src="media/Figure_2-postregistration.svg" width="88%" style="display: block; margin: auto;" />
]

---
# Signs of mediation?

.push-left[
<img src="media/Figure_5-postreg.svg" width="100%" style="display: block; margin: auto;" />
.center[.backgrnote[
*Note*: n = 95 partial correlations. Results are based on a multilevel random effects meta-analyses with cross−classified random effects for the 30 studies in which estimates were published and the 27 data sets used.
]]
]

.push-right[
<img src="media/Figure_5_model.png" width="90%" style="display: block; margin: auto;" />
]

---
class: clear
# Scope condition .font70[Citizenship rights for immigrants?]

.left-column[
<img src="media/Figure_6_modelc.png" width="100%" style="display: block; margin: auto;" />
]

.right-column[
<img src="media/Figure_6-postregistration.svg" width="100%" style="display: block; margin: auto;" />
.center[.backgrnote[
*Note*: Results are based on a multilevel random effects meta analysis with controls for integration predictor used and visibility of immigrant group studied, as well as cross-classified random effects for 21 studies, 20 data sets used, and 14 country-year combinations of collected data. n = 62 partial correlation coefficients.]]
]

---
# Fundamental flaw of prior research

.left-column[
 
> [...] greater familiarity with the culture and language and some economic advancement can lead to greater .alert[consciousness of the reality] of discrimination.

> -- Portes, Parker, and Cobas (1980)
]

.right-column[
.center[.alert[**False Consciousness**: Are the less integrated under-perceiving the true extent of discrimination they face?]]
 
<img src="media/Conceptual-model-2.png" width="100%" style="display: block; margin: auto;" />
]

---
# Limitation of correspondence studies

.left-column[
.center[.alert[Fake CV's have no experiences and perceptions]]
<img src="https://www.docdroid.net/thumbnail/d9fU64e/1500,1500/fake-cv-pdf.jpg" width="100%" style="display: block; margin: auto;" />
]

.right-column[
 
 
<img src="media/Conceptual-model-2a.png" width="100%" style="display: block; margin: auto;" />
]

---
# A new experimental design

.right-column[
.center[**The Trust game** 
Two persons' *mutual* evaluation of their trustworthiness 
.backgrnote[We'll have endowments of €10 
Respondents will play both roles & we define actual role randomly afterwards]]
<img src="media/trust-game.gif" width="100%" style="display: block; margin: auto;" />
]

.left-column[
.center[**Non-anonymous games** 
Profile photo & spoken sentence]
<img src="media/Non-anonymous-trust-game.png" width="100%" style="display: block; margin: auto;" />
]

---
# Actual discrimination

.left-column[
.center[**Non-anonymous games** 
Profile photo & spoken sentence]
<img src="media/Non-anonymous-trust-game.png" width="100%" style="display: block; margin: auto;" />
]

.right-column[
<img src="media/Actual-discrimination.png" width="100%" style="display: block; margin: auto;" />
1. `$€_{\text{Judith}} - \bar{€}_{\text{Co-ethnics}}$`, or `$€_{\text{Judith}} - €_{\text{anonymous}}.$`
2. After all 11 games: Which two games do you want paid out?
]

---
# Expected & perceived discrimination

.left-column[
.center[**Non-anonymous games** 
Profile photo & spoken sentence]
<img src="media/Non-anonymous-trust-game.png" width="100%" style="display: block; margin: auto;" />
]

.right-column[
.center[**Expected discrimination** After all games are played ]
1. Expected `$\Delta€$` .backgrnote[(incentivized, €4 for correct guess)]
.backgrnote[
 - How much did that game partner send you? `$\rightarrow$` €3
- How much did that game partner send other players? `$\rightarrow$` €5
- Why did that game partner send you €2 less than the others?
]
2. Expectation, did game partner choose this game to be paid out? .backgrnote[(incentivized, €2 for correct guess)]

.center[**Perceived discrimination** After aggregate personal and overall payoffs]
1. Why did you make less / more than the average?
]

---
# Implementation in three steps
.left-column[
#### 1) Recruitment phase June 2021
 - Photo & recorded sentence.
 - Online survey on integration.
 - Berlin, Hamburg, Cologne, Frankfurt, Munich.
 - 1,500 Germans with native-born parents.
 - 900 immigrants or children of immigrants.
 - 600 Turkish immigrants or children of Turkish immigrants.
]

.right-column[
<img src="media/Conceptual-model-3.png" width="100%" style="display: block; margin: auto;" />
]

---
# Implementation in three steps
.left-column[
#### 2) Online trust games October 2021
 - n = 2,000.
 - Not simultaneously but strategy method.
 - Guaranteed €20, Average win €60, maximum €100.
]

.right-column[
<img src="media/Conceptual-model-4.png" width="100%" style="display: block; margin: auto;" />
]

---
# Implementation in three steps
.left-column[
#### 3) Final survey January 2022
 - Information about personal and overall payoffs.
 - Survey on perceived discrimination.
]

.right-column[
<img src="media/Conceptual-model-5.png" width="100%" style="display: block; margin: auto;" />
]

---
# Conclusion

.push-left[
- *Tocqueville's / integration paradox*
  + Interesting and potentially pervasive phenomenon.
  + Meta-analysis suggests it is credible.
  
  
- *(Marxist) claims about false consciousness*
  + No established toolbox to empirically study these claims.
  + Hefty implications for interview/survey based studies and reports.
]

.push-right[
- *The new experimental design*
 - Artificial, but *first* attempt to measure & predict individuals' under- and over-perceived discrimination.
 - Mis-perceptions may also be used as predictor, e.g. of political mobilization.
 
]

.font150[.center[.alert[Thank you for your attention!]]]

---
# References

.font70[
European Union Agency for Fundamental Rights. (2014). _Violence against women :an EU wide survey :
results at a glance._ LU: Publications Office.

Gustafson, R. L. (1961). "Partial Correlations in Regression Computations". In: _Journal of the
American Statistical Association_, pp. 363-367.

Konstantopoulos, S. (2011). "Fixed effects and variance components estimation in three-level
meta-analysis". In: _Research Synthesis Methods_, pp. 61-76.

Portes, A., R. N. Parker, and J. A. Cobas (1980). "Assimilation or Consciousness". In: _Social
Forces_, pp. 200-224.

Tocqueville, A. d. (2015). _Democracy in America - Vol. I. and II._ Read Books Ltd.

Viechtbauer, W. (2010). "Conducting Meta-Analyses in R with the metafor Package". In: _Journal of
Statistical Software_, pp. 1-48.
]

---
class: center middle

.alert[.font200[Appendix]]

---
# Best integration indicator

<img src="media/Figure_3.svg" width="75%" style="display: block; margin: auto;" />
.center[.backgrnote[
*Note*: n = 79 partial correlations. Results are based on a multilevel random effects meta-analyses with cross−classified random effects for the 30 studies in which estimates were published and the 27 data sets used.

]]

---
class: clear

.left-column[
 
.red[.font190[**Publication bias?** *P*-curve analysis]]

.font70[

```r
# Sample definition
#------------------
pubbias_sample <- sample_1 %>%
 mutate(
 pred_num = case_when(
 pred == "Education" ~ 3,
 pred == "Generation" ~ 2,
 TRUE ~ 1)) %>%
 # Within each independent sample:
 group_by(study_ID, data, pop, context) %>%
 # Use preferable predictor,
 filter(pred_num == 
 max(pred_num, na.rm = TRUE)) %>%
 # Finally, choose one at random.
 sample_n(1) %>%
 ungroup()
```
]]

.right-column[
<img src="media/Figure_7.svg" width="83%" style="display: block; margin: auto;" />
.center[.backgrnote[
*Note*: n = 20, 2, & 22 (left column), and 15, 13, & 2 (right column) *p*-values respectively.]]
]

---
class: clear
# Small-sample publication bias? .font60[Trim and fill analysis]

.push-left[
<img src="media/Tim_n_fill1.png" width="100%" style="display: block; margin: auto;" />
]

.push-right[
<img src="media/Tim_n_fill2.png" width="100%" style="display: block; margin: auto;" />
.center[.backgrnote[
*Note*: Results are based on (multilevel, Original model) random effects meta analyses.]]
]

---
# Envisioned data .font60[n = 1,500 X 8 = 12,000]

| Minority     | Pot. discriminator | `$€_{i} - \bar{€}_{j(\text{Co-ethnics})}$` | Exp. `$\Delta_i€$` | `$j$` selected `$i$` | `$i$` exp. selection | `$i$` Education | `$i$` ...
|-------------:|:------------------:|:----------------------------------------:|:----------------:|:----------------:|:------------------:|:--:|:--|
| `$i=1$` (Judith)  | `$j=1$` (Merlin)  | -3                                       | -5               |0                 |0                   |... |...|
| `$i=1$` (Judith)  | `$j=2$`           | 0                                        |0                 |1                 |0                   |... |...|
| `$i=1$` (Judith)  | `$j=3$`           | 1                                        |0                 |1                 |0                   |... |...|
| `$i=1$` (Judith)  | `$j=4$`           | -1                                       |0                 |1                 |1                   |... |...|
| `$i=1$` (Judith)  | `$j=5$`           | -2                                       |0                 |1                 |0                   |... |...|
| `$i=1$` (Judith)  | `$j=6$`           | -4                                       |0                 |1                 |0                   |... |...|
| `$i=1$` (Judith)  | `$j=7$`           | 3                                        |0                 |0                 |0                   |... |...|
| `$i=1$` (Judith)  | `$j=8$`           | 0                                        |0                 |0                 |0                   |... |...|
| `$i=2$`           | `$j=1$` (Merlin)  | ...                                      |...               |...               |...                 |... |...|
| `$i=2$`           | `$j=4$`           | ...                                      |...               |...               |...                 |... |...|
| `$i=2$`           | `$j=9$`           | ...                                      |...               |...               |...                 |... |...|
| `$i=2$`           | `$j=10$`          | ...                                      |...               |...               |...                 |... |...|

---
# Coding

.push-left[
.center[.font150[**Predictors**]]

- Original predictor:
  + Broad indicators of integration
      + Education   
      + Generation
      + Length of residence
  + Social exposure
      + Contact to mainstream members
      + Labor market attainment
  + Awareness
      + Media consumption
      + Language skills
  + Disillusion & relative deprivation
      + Downward social mobility
- Identifiability of immigrant population studied
- MIPEX by country-year

.backgrnote[
- Data analyzed.
- Nr. of good/bad controls.
- Nr. mediators.
- ...
]
]

.push-right[
.center[.font150[**Nested estimates**]]
1. Code estimates for: 
  + strongest dummy contrast,
  + full-sample, unless subsamples informative about identifiability,
  + racial > ethnic > national > religious > linguistic discrimination,
  + composite scale if available,
  + max demographic (e.g., gender) & min subsequent outcomes (e.g., mental health) & altern. predictors as controls,
  + No moderated/conditional coefficients.
2. Use *multilevel random effects meta-analytic models* (Konstantopoulos, 2011), as implemented in *R*'s *metafor* package (Viechtbauer, 2010).

]