The Integration Paradox

class: center, middle, inverse, title-slide

.title[
# The Integration Paradox
]
.subtitle[
## First Results of a Meta-Analysis & Proposal of a New Experimental Design
]
.author[
### Merlin Schaeffer & Judith Kas (WZB)
]
.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_1.png" width="89%" style="display: block; margin: auto;" />
.backgrnote[.center[
*Source*: European Union Agency for Fundamental Rights. (2014)
]]]]

---

.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: true
# An integration paradox?

.push-right[.center[
<img src="https://www.tagesspiegel.de/images/rudow/1251998/2-format43.jpg" width="100%" style="display: block; margin: auto;" />
Single family home in Berlin's suburb Rudow
]]

---

.push-left[.center[.font120[
 
 
 
 
Do immigrants and their descendants who established themselves among the middle-class mainstream report .alert[less or more] discrimination than those who remain at the margins of society?
]]]

---

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

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

---
layout: false
class: clear
# The integration paradox .font60[Synthesized theoretical model]

---
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 .font60[Cleaning & pre-reg training]

.left-column[
<img src="Nuffield_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;" />
]

---
# Coding

.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)
]]
*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[**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.
- ...
]
]

---
# Meta-analysis

.push-left[

`$$\begin{align*}
\bar{\rho}_{yx \cdot z} &= \frac{\sum_{i=1}^n \color{orange}{w_{i}}\rho_{(yx \cdot z)i}}{\color{orange}{w_{i}}}, \\
\min \text{RSS} &= \min \sum_{i=1}^{n} \color{orange}{w_{i}} R_{i}^{2}.
  \end{align*}$$`

1. *Fixed effects*: `$w_{i} = \frac{1}{\color{orange}{\text{Var}(\rho_{(yx \cdot z)i})}}.$`

2. *Random effects*: `$w_{i} = \frac{1}{\text{Var}(\rho_{(yx \cdot z)i}) \color{orange}{+ \tau^2}},$`

where `$\tau^2$` is the between-studies variance of `$\rho_{(yx \cdot z)i}$`. Commonly, `$\tau^2$` is estimated via REML.
]

.push-right[
**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).

```r
rma.mv(yi = yi, V = as.matrix(vi), 
       data = sample_1, test = "t",
       mods = ~ pred,
*      random = list(~ 1 | Study_ID/ID), ~ 1 | data))
```
]

---
layout: true
# Overall meta-estimate

.left-column[.font70[

```r
# Sample definition
#------------------
sample_1 <- meta_data %>%
 # Only broad integration indicators,
 filter(pred == "Education" | 
 pred == "Generation" |
 pred == "Length of residency") %>%
 # Within each indep. sample & type of predictor,
 group_by(study_ID, data, context, pred) %>%
 # Use sub-sample if available,
 filter(full_sample_num == 
 max(full_sample_num, na.rm = TRUE)) %>%
 # Use model with least number of mediators
 filter(nr_mediators == min(nr_mediators)) %>%
 # Use model with min number of bad controls
 filter(nr_bad_controls == min(nr_bad_controls)) %>%
 # Use model with max number of good controls
 filter(nr_good_controls == max(nr_good_controls)) %>%
 # Use model with minimum number of integration predictors
 filter(nr_preds == min(nr_preds)) %>%
 ungroup()
```
]]

---

---
.right-column[
<img src="media/Figure_1.svg" width="100%" style="display: block; margin: auto;" />
.center[.backgrnote[
*Note*: 20 partial correlation coefficients and overall meta-estimate with associated 95% confidence intervals, based on five coded studies.]]
]

---

.right-column[
<img src="media/Figure_2.svg" width="100%" style="display: block; margin: auto;" />
.center[.backgrnote[
*Note*: Results are based on a multilevel random effects meta analysis. n = 20 partial correlation coefficients based on five coded studies and five different data sets.]]
]

---
layout: false
# Signs of mediation?

.left-column[.font70[

```r
# Sample definition
#------------------
sample_2 <- meta_data %>%
 # Only broad integration indicators,
 filter(pred == "Education" | 
 pred == "Generation" |
 pred == "Length of residency") %>%
 # Within each indep. sample & type of predictor,
 group_by(study_ID, data, context, pred) %>%
 # Use sub-sample if available,
 filter(full_sample_num == 
 max(full_sample_num, na.rm = TRUE)) %>%
 # Use model with least number of mediators
* # filter(nr_mediators == min(nr_mediators)) %>%
 # Use model with min number of bad controls
 filter(nr_bad_controls == min(nr_bad_controls)) %>%
 # Use model with max number of good controls
 filter(nr_good_controls == max(nr_good_controls)) %>%
 # Use model with minimum number of integration predictors
 filter(nr_preds == min(nr_preds)) %>%
 ungroup()
```
]]

.right-column[
<img src="media/Figure_4.svg" width="100%" style="display: block; margin: auto;" />
.center[.backgrnote[
*Note*: Results are based on a multilevel random effects meta analysis. n = 27 partial correlation coefficients based on five coded studies and five different data sets.]]
]

---
# Scope condition .font70[Citizenship rights?]

<img src="media/Figure_5.svg" width="75%" style="display: block; margin: auto;" />
.center[.backgrnote[
*Note*: Results are based on a multilevel random effects meta analysis. n = 20 partial correlation coefficients based on five coded studies and five different data sets.]]

---
# Publication bias? .font70[*p*-curve analysis]

.left-column[.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_6.svg" width="100%" style="display: block; margin: auto;" />
.center[.backgrnote[
*Note*: n = 12 and 6 *p*-values respectively.]]
]

---
# Synthesized theoretical model

.left-column[
 
> [...] greater familiarity with the culture and language and some 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;" />
]
---
# 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 feelings]]
<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-2.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 `$€_{\text{Judith}} - €_{\text{anonymous}}$`
 + Single measure: May be ethnic or not.
 + Aggregated across 10 game partners: Ethnic discrimination.
2. After all 11 games: Which two of the overall ten (non-anonymous) games do you want to have 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: What do you think,
1. Expected `$\Delta€$` (incentivized, €4 for correct guess)
  - 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. Do you think, that game partner chose your game as one of the two that are being paid out (incentivized, €2 for correct guess)

.center[**Perceived discrimination**]
Three months later, respondents are informed about their aggregate personal and overall average payoffs.
1. Why did you make less / more?
]

---
# Implementation in three steps
.left-column[
#### 1) Pre-game online survey May 2021
 - Photo & recorded sentence.
 - 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.
]

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

---
# 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)  | ...                                      |...               |...               |...                 |... |...|
| `$i=2$`           | `$j=4$`           | ...                                      |...               |...               |...                 |... |...|
| `$i=2$`           | `$j=9$`           | ...                                      |...               |...               |...                 |... |...|
| `$i=2$`           | `$j=10$`          | ...                                      |...               |...               |...                 |... |...|

---
# Conclusion

- Tocqueville's / integration paradox: 
  + Interesting phenomenon & maybe rather pervasive.
  + Related to (Marxist) claims about false consciousness.
  + Hefty implications for interview/survey based reports.
  + No good toolbox to study these phenomena.
  
  
- Training pre-reg (multilevel) meta-analysis:
  + Interesting tool for sociology despite violated assumptions?
  + Integration paradox seems credible.
  
  
- 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]]

---
# Which social / psychological process?

.left-column[.font80[

```r
## Sample definition
sample_3 <- meta_data %>%
 # Only broad integration indicators and full samples.
* filter(pred == "Social exposure" |
* pred == "Labor market attainment" |
* pred == "Cognitive awareness" |
* pred == "Disillusion") %>%
 # Within each independent sample & type of predictor,
 group_by(study_ID, data, context, pred) %>%
 # Use sub-sample if available,
 filter(full_sample_num == max(full_sample_num, na.rm = TRUE)) %>%
 # Use model with least number of mediators
 filter(nr_mediators == min(nr_mediators)) %>%
 # Use model with min number of bad controls
 filter(nr_bad_controls == min(nr_bad_controls)) %>%
 # Use model with max number of good controls
 filter(nr_good_controls == max(nr_good_controls)) %>%
 # Use model with minimum number of integration predictors
* # filter(nr_preds == min(nr_preds)) %>%
 ungroup()
```
]]

.right-column[
<img src="media/Figure_3.svg" width="100%" style="display: block; margin: auto;" />
.center[.backgrnote[
*Note*: n = 34 partial correlation coefficients based on five coded studies and five different data sets.]]
]

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

.center[
<img src="media/Tim_n_fill.png" width="80%" style="display: block; margin: auto;" />
.center[.backgrnote[
*Note*: Results are based on (multilevel, Original model) random effects meta analyses.]]
]