Advanced quantitative data analysis

class: center, middle, inverse, title-slide

.title[
# Advanced quantitative data analysis
]
.subtitle[
## OLS with interaction
]
.author[
### Mengni Chen
]
.institute[
### Department of Sociology, University of Copenhagen
]

---

#Let's get ready

```r
library(tidyverse) # Add the tidyverse package to my current library.
library(haven) # Import data.
library(Hmisc) # Weighting
library(ggplot2) # Allows us to create nice figures.
library(estimatr) # Allows us to estimate (cluster-)robust standard errors.
library(texreg) # Allows us to make nicely-formatted Html & Latex regression tables.
```

---
#Model the relationship between marital status and life satisfaction
- [Prepare data](https://rpubs.com/fancycmn/1094159)
  - a dataset of age, sex,  marital status, years of education, life satisfaction, weight
    - DV: life satisfaction
    - IV: age, sex, **marital status**, years of education

---
#Running an OLS

```r
ols3_cat <- lm_robust(formula = sat6 ~ age + marital1, data = wave1c, weights = cdweight)
```

```r
texreg::screenreg(list(ols3_cat), 
                  include.ci = FALSE, digits = 3)
```

```
## 
## ==============================
##                   Model 1     
## ------------------------------
## (Intercept)          8.549 ***
##                     (0.093)   
## age                 -0.045 ***
##                     (0.004)   
## marital1Married      0.735 ***
##                     (0.078)   
## marital1Divorced    -0.528 ** 
##                     (0.169)   
## ------------------------------
## R^2                  0.047    
## Adj. R^2             0.046    
## Num. obs.         6135        
## RMSE                 1.756    
## ==============================
## *** p < 0.001; ** p < 0.01; * p < 0.05
```

---
#Running an OLS: make it beautiful

```r
ols3_cat <- lm_robust(formula = sat6 ~ age + marital1, data = wave1c, weights = cdweight)
```

```r
texreg::screenreg(list(ols3_cat), 
                  custom.model.names="OLS", #change the model name
                  custom.coef.names=c( #change the variable name
                    "Intercept",
                    "Age",
                    "Married",
                    "Divorced"
                  ),
                  include.ci = FALSE, digits = 3)
```

```
## 
## =======================
##            OLS         
## -----------------------
## Intercept     8.549 ***
##              (0.093)   
## Age          -0.045 ***
##              (0.004)   
## Married       0.735 ***
##              (0.078)   
## Divorced     -0.528 ** 
##              (0.169)   
## -----------------------
## R^2           0.047    
## Adj. R^2      0.046    
## Num. obs.  6135        
## RMSE          1.756    
## =======================
## *** p < 0.001; ** p < 0.01; * p < 0.05
```

---
#Running an OLS: make it beautiful

Export to html

```r
texreg::htmlreg(list(ols3_cat),
                custom.model.names="OLS",
                custom.coef.names=c(
                  "Intercept",
                    "Age",
                    "Married",
                    "Divorced"
                ),
                include.ci = FALSE, 
                file = "Nice fomatted result.html") #html
```

```
## The table was written to the file 'Nice fomatted result.html'.
```
---
#Interpretation of OLS
- what does the intercept "8.549" mean?
  - does it mean the life satisfaction of those never married?!

```r
texreg::screenreg(list(ols3_cat),
                  custom.model.names="OLS", #change the model name
                  custom.coef.names=c("Intercept","Age","Married","Divorced"), #change the variable name
                  include.ci = FALSE, digits = 3)
```

- it means that a person who is aged 0 and never married, his/her life satisfaction is 8.544.
  - does it make sense? a person aged 0 never existed in the pairfam survey.

---
#Interpretation of OLS
- Take those divorced as the reference group
  - What does the coefficient of never married (i.e. 0.528) mean here

```r
wave1c$marital1 <- fct_relevel(wave1c$marital1, "Divorced", "Nevermarried", "Married")
#use fct_level function to re-level marital1, now divorced is the first level and will be treated as the reference category
ols3_cat_relevel <- lm_robust(formula = sat6 ~ age + marital1, data = wave1c, weights = cdweight)
texreg::screenreg(list(ols3_cat_relevel), 
                  include.ci = FALSE, digits = 3)
```

```
## 
## ==================================
##                       Model 1     
## ----------------------------------
## (Intercept)              8.021 ***
##                         (0.216)   
## age                     -0.045 ***
##                         (0.004)   
## marital1Nevermarried     0.528 ** 
##                         (0.169)   
## marital1Married          1.263 ***
##                         (0.162)   
## ----------------------------------
## R^2                      0.047    
## Adj. R^2                 0.046    
## Num. obs.             6135        
## RMSE                     1.756    
## ==================================
## *** p < 0.001; ** p < 0.01; * p < 0.05
```

--
  - It means when the age is controlled, a person who is never married has a higher life satisfaction score than a person who is divorced, by the amount of 0.528.

---
#OLS with interaction: interaction betwen two categorical
- Does the relationship between marital status and life satisfaction vary across men and women?

```r
#as we re-level marital1 in last slides, we now re-level it back
wave1c$marital1 <- fct_relevel(wave1c$marital1,"Nevermarried",  "Married","Divorced") 
ols4_interactsex <- lm_robust(formula = sat6 ~ age +  marital1*sex_gen, data = wave1c, weights = cdweight)
# use * to specific the interaction
texreg::screenreg(list(ols4_interactsex), 
                  include.ci = FALSE, digits = 3, single.row = TRUE)#single.row= TRUE is to make the standard error in the same row with coef.
```

```
## 
## ======================================================
##                                   Model 1             
## ------------------------------------------------------
## (Intercept)                          8.522 (0.097) ***
## age                                 -0.044 (0.004) ***
## marital1Married                      0.770 (0.102) ***
## marital1Divorced                    -0.674 (0.293) *  
## sex_gen2 Female                      0.053 (0.062)    
## marital1Married:sex_gen2 Female     -0.074 (0.111)    
## marital1Divorced:sex_gen2 Female     0.234 (0.337)    
## ------------------------------------------------------
## R^2                                  0.047            
## Adj. R^2                             0.046            
## Num. obs.                         6135                
## RMSE                                 1.756            
## ======================================================
## *** p < 0.001; ** p < 0.01; * p < 0.05
```
---
#Interpreting interaction betwen two categorical
- `$$sat6=8.522 -0.044age +0.770married -0.674divorced + 0.053female $$`
`$$-0.074married*female + 0.234divorced*female $$`

- A man aged 20 and never married, what his life satisfaction? age=20, married=0, divorced=0, female=0
`$$sat6=8.522 -0.044*\color{red}{20}$$`
--

- A man aged 20 and divorced, what his life satisfaction? age=20, married=0, divorced=1, female=0
`$$sat6=8.522 -0.044*\color{red}{20} -0.674*\color{red}{1}$$`
--

- A female aged 20 and never married, what her life satisfaction? age=20, married=0, divorced=0, female=1
`$$sat6=8.522 -0.044*\color{red}{20} + 0.053*\color{red}{1}$$`

- A female aged 20 and divorced, what her life satisfaction? age=20, married=0, divorced=1, female=1
`$$sat6=8.522 -0.044*\color{red}{20} -0.674*\color{red}{1} + 0.053*\color{red}{1}+ 0.234*\color{red}{1}*\color{red}{1}$$`

---
#Interpreting interaction betwen two categorical
Given that age is the average level of age in the sample:
<img src="https://github.com/fancycmn/2023advancequant_intro/blob/main/interaction1.png?raw=true" width="80%" style="display: block; margin: auto;" >

---
##OLS with interaction: interaction betwen one categorical and one continuous
- Does the relationship between age and life satisfaction vary across marital status?

```r
ols5_interactage <- lm_robust(formula = sat6 ~ age*marital1 + sex_gen , data = wave1c, weights = cdweight)
texreg::screenreg(list(ols5_interactage), 
                  include.ci = FALSE, digits = 3,single.row = TRUE)
```

```
## 
## ==========================================
##                       Model 1             
## ------------------------------------------
## (Intercept)              8.690 (0.104) ***
## age                     -0.052 (0.005) ***
## marital1Married         -0.949 (0.363) ** 
## marital1Divorced        -1.947 (1.438)    
## sex_gen2 Female          0.055 (0.051)    
## age:marital1Married      0.052 (0.011) ***
## age:marital1Divorced     0.043 (0.041)    
## ------------------------------------------
## R^2                      0.051            
## Adj. R^2                 0.050            
## Num. obs.             6135                
## RMSE                     1.752            
## ==========================================
## *** p < 0.001; ** p < 0.01; * p < 0.05
```
`$$sat6=8.690 -0.052age -0.949married -1.947divorced +0.055female +0.052married*age $$`
`$$+ 0.043divorced*age$$`

---
##interpreting interaction betwen one categorical and one continuous
`$$sat6=8.690 -0.052age -0.949married -1.947divorced +0.055female +0.052married*age $$`
`$$+ 0.043divorced*age$$`
- Does the relationship between age and life satisfaction vary across marital status?
  - supposed that A-a never married man is aging, B-a divorced man is aging
  
  - the association between age and life satisfaction is not constant at -0.052
  
  - for A, with 1-year increase in the age, sat6 decreases by -0.052
  
  - for B, with 1-year increase in the age, sat6 decreases by -0.052+0.043

---
##interpreting interaction betwen one categorical and one continuous
`$$sat6=8.690 -0.052age -0.949married -1.947divorced +0.055female +0.052married*age $$`
`$$+ 0.043divorced*age$$`

Given that the marital status is the reference level, i.e."never-married":
.pull-left[
male

<img src="https://github.com/fancycmn/2023advancequant_intro/blob/main/interaction2_male.png?raw=true" width="110%" style="display: block; margin: auto;" >
]

.pull-right[
female

]
---
#Take home
1. Modify the output of your regression
2. OLS with interaction
    - Interaction between two categorical variables
    - Interaction between one categorical variable and one continous variable
    - Interpret OLS with interactions

---
class: center, middle
#[Exercise](https://rpubs.com/fancycmn/1095087)