Exemplary data analysis

Author

Julius Fenn

Published

May 10, 2025

Background Information

This is an R Markdown document. Instructions for writing these documents and background information can be found in the book written by Xie, Allaire, and Grolemund (2018) When you execute code within the document, the results appear beneath the code.

This file contains the pre-processing step (clean, transform data), and the analysis step (test hypotheses and exploratory analyses). In larger projects you would split this file into multiple subfiles like data processing and data analyses steps, which follows the classical data-analysis pipeline (see Peng and Matsui 2016; Wickham and Grolemund 2017).

Notes

Remark:

## global variables
cutOff <- 1 # cutoff value for building extreme groups

get packages, raw data, functions

### install and load packages
#  if packages are not already installed, the function will install and activate them
usePackage <- function(p) {
  if (!is.element(p, installed.packages()[,1]))
    install.packages(p, dep = TRUE, repos = "http://cran.us.r-project.org")
  require(p, character.only = TRUE)
}

usePackage("haven") # load SPSS, ... data 
usePackage("tidyverse") # data cleaning and summarizing
usePackage("psych") # psychometric analysis (EFA)

## psychometric analysis
usePackage("moments") # skewness, kurtosis

## outputs
usePackage("stargazer") # create tables
usePackage("report") # get reports of statistical tests in APA7

usePackage("lavaan") # for CFA

rm(usePackage)


### load data files
## change working directory
setwd("data")
## load data
dat <- haven::read_spss(file = "ESS1-9e01_1.sav")


### load functions
# print(getwd())
setwd("../functions")
for(i in 1:length(dir())){
  # print(dir()[i])
  source(dir()[i], encoding = "utf-8")
}

rm(i)

data preperation

compute mean scores

### data preparation
dat$cntry <- NULL

# reverse coded items
dat$imsmetn <- 5 - dat$imsmetn 
dat$imdfetn <- 5 - dat$imdfetn
dat$impcntr <- 5 - dat$impcntr


### create mean scores
# !!! normally you would need to run multiple analysis to check if building mean scores make sense (EFAs, ...)

# > Immigration bad or good for country's economy
# > Country's cultural life undermined or enriched by immigrants
# > Immigrants make country worse or better place to live
sel_var <- c("imbgeco", "imueclt", "imwbcnt")
dat$mean_imEnrich <- rowMeans(x = dat[, sel_var], na.rm = TRUE)
# > Allow many/few immigrants of same race/ethnic group as majority
# > Allow many/few immigrants of different race/ethnic group from majority
# > Allow many/few immigrants from poorer countries outside Europe
sel_var <- c("imsmetn", "imdfetn", "impcntr")
dat$mean_imAllow <- rowMeans(x = dat[, sel_var], na.rm = TRUE)
# > Trust
sel_var <- str_detect(string = colnames(dat), pattern = "^trst")
dat$mean_trst <- rowMeans(x = dat[, sel_var], na.rm = TRUE)
# > Satisfaction (personally, government)
sel_var <- str_detect(string = colnames(dat), pattern = "^stf")
dat$mean_stf <- rowMeans(x = dat[, sel_var], na.rm = TRUE)
dat$sd_stf <- dat %>%
  select(matches(match = "^stf")) %>%
  apply(.,1, sd, na.rm = TRUE)

get extreme groups for `lrscale` variable

Aim to get two extreme groups according to the lrscale (left, right scale) variable:

dat$lrscale_scaled <- scale(x = dat$lrscale, center = TRUE, scale = TRUE)
mean_upper <- mean(dat$lrscale_scaled[dat$lrscale_scaled > cutOff], na.rm = TRUE)
mean_lower <- mean(dat$lrscale_scaled[dat$lrscale_scaled < cutOff * -1], na.rm = TRUE)
hist(dat$lrscale_scaled)
# add vertical line
abline(v=mean_upper, col = "red")
abline(v=mean_lower, col = "red")

# save subsets
dat_upper <-dat %>%
  filter(dat$lrscale_scaled > mean_upper)
dat_lower <-dat %>%
  filter(dat$lrscale_scaled < mean_lower)


### get dummy
dat$lrscale_dummy <- ifelse(test = dat$lrscale_scaled > mean_upper, yes = 2, no =
         ifelse(test = dat$lrscale_scaled < mean_lower, yes = 1, no = 0))
table(dat$lrscale_dummy)


   0    1    2 
1977  159  125

Introduction

Migration ‘mother of all political problems,’ says German Interior Minister Horst Seehofer. Hort Seehofer’s 2018 statement¹ after the protests in Chemnitz, which sees migration at the heart of society’s disillusionment, shows how charged the debate about migration is in Germany.

Background

…

Quoting (please remove this for your report!)

How to cite literature within an markdown document:

Blah blah (see Newman 2018, 33–35; also Skrondal and Rabe-Hesketh 2004, ch. 1).
Blah blah (Newman 2018, 33–35).
Blah blah (Newman 2018; Skrondal and Rabe-Hesketh 2004).
Rutkowski et al. says blah (2018).
Newman (2018) says blah.

Methods

Hypothesis

Are different factors relevant to the perceived threat of migrants by people with a high or low left/right orientation?

The following sub-hypothesis could be derived from literature:

…

Results

Descriptive Statisticss

First glimpse at the loaded data:

glimpse(dat)

Rows: 2,358
Columns: 41
$ cname          <chr> "ESS1-9e01", "ESS1-9e01", "ESS1-9e01", "ESS1-9e01", "ES…
$ cedition       <chr> "1.0", "1.0", "1.0", "1.0", "1.0", "1.0", "1.0", "1.0",…
$ cproddat       <chr> "10.12.2020", "10.12.2020", "10.12.2020", "10.12.2020",…
$ cseqno         <dbl> 101403, 101404, 101405, 101406, 101407, 101408, 101409,…
$ name           <chr> "ESS9e03", "ESS9e03", "ESS9e03", "ESS9e03", "ESS9e03", …
$ essround       <dbl+lbl> 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, …
$ edition        <chr> "3", "3", "3", "3", "3", "3", "3", "3", "3", "3", "3", …
$ idno           <dbl> 9, 10, 64, 65, 91, 119, 150, 212, 255, 270, 279, 304, 3…
$ dweight        <dbl> 0.9994662, 0.9994662, 0.9994662, 0.9994662, 0.9994662, …
$ pspwght        <dbl> 1.2750090, 0.8540229, 0.7596949, 1.0794106, 1.2697877, …
$ pweight        <dbl> 3.037345, 3.037345, 3.037345, 3.037345, 3.037345, 3.037…
$ anweight       <dbl> 3.872642, 2.593962, 2.307456, 3.278542, 3.856783, 3.872…
$ trstprl        <dbl+lbl>  2,  7,  3,  3,  4,  9, 10,  5,  5,  7, NA,  6,  6,…
$ trstlgl        <dbl+lbl>  4,  8,  5,  4,  5,  7, 10,  7,  8,  8,  5,  9,  7,…
$ trstplc        <dbl+lbl>  5,  8,  6,  4,  7,  7, 10,  7,  9,  8,  7,  9,  7,…
$ trstplt        <dbl+lbl>  0,  6,  3,  3,  5,  8, 10,  5,  5,  6,  3,  5,  6,…
$ trstprt        <dbl+lbl> 2, 6, 5, 3, 5, 8, 4, 5, 5, 6, 1, 5, 3, 7, 9, 4, 3, …
$ trstep         <dbl+lbl>  3,  4,  5,  2,  4, 10, 10,  6,  3,  7,  3,  5,  5,…
$ trstun         <dbl+lbl>  0,  5,  6,  2,  5, 10, 10,  6,  7,  7, NA,  7,  5,…
$ lrscale        <dbl+lbl> 5, 5, 3, 2, 1, 5, 5, 2, 3, 5, 1, 4, 5, 6, 4, 3, 0, …
$ stflife        <dbl+lbl> 10,  8,  8,  6,  9,  9, 10,  8,  4,  9, 10,  9,  9,…
$ stfeco         <dbl+lbl> 10,  8,  5,  6,  9,  8, 10,  8,  5,  9,  7,  9,  9,…
$ stfgov         <dbl+lbl>  7,  5,  6,  2,  5, NA,  5,  7,  4,  6, NA,  6,  8,…
$ stfdem         <dbl+lbl>  7,  9,  6,  4,  5, 10, 10,  7,  6,  9, NA,  5,  9,…
$ imsmetn        <dbl> 4, 4, 4, 3, 4, 3, 3, 4, 4, 4, 2, 3, 4, 3, 3, 4, 4, 3, 4…
$ imdfetn        <dbl> 4, 4, 4, 3, NA, 3, 3, 4, 3, 3, 2, 3, 3, 3, 3, NA, NA, 3…
$ impcntr        <dbl> 4, 4, 4, 3, NA, 4, 2, 4, NA, 2, 2, 2, 3, 3, 3, 3, NA, 1…
$ imbgeco        <dbl+lbl> NA, 10,  9,  4,  8,  8, 10,  8,  7,  7,  0,  9, 10,…
$ imueclt        <dbl+lbl>  8,  5,  8,  4,  8,  8, 10,  8,  7,  4,  0,  9, 10,…
$ imwbcnt        <dbl+lbl> 5, 5, 8, 3, 8, 7, 6, 8, 7, 5, 0, 5, 5, 5, 5, 7, 4, …
$ happy          <dbl+lbl> 10,  8, 10,  6,  9,  9,  9,  8,  5,  9, 10,  9,  8,…
$ rlgdgr         <dbl+lbl>  9,  7,  9,  1,  5,  9,  5,  0,  3,  9,  5,  0, 10,…
$ gndr           <dbl+lbl> 2, 2, 2, 1, 2, 2, 2, 1, 1, 1, 2, 2, 1, 1, 1, 2, 2, …
$ agea           <dbl+lbl> 26, 65, 74, 64, 54, 20, 71, 41, 62, 65, 67, 47, 67,…
$ mean_imEnrich  <dbl> 6.500000, 6.666667, 8.333333, 3.666667, 8.000000, 7.666…
$ mean_imAllow   <dbl> 4.000000, 4.000000, 4.000000, 3.000000, 4.000000, 3.333…
$ mean_trst      <dbl> 2.285714, 6.285714, 4.714286, 3.000000, 5.000000, 8.428…
$ mean_stf       <dbl> 8.50, 7.50, 6.25, 4.50, 7.00, 9.00, 8.75, 7.50, 4.75, 8…
$ sd_stf         <dbl> 1.7320508, 1.7320508, 1.2583057, 1.9148542, 2.3094011, …
$ lrscale_scaled <dbl[,1]> <matrix[26 x 1]>
$ lrscale_dummy  <dbl[,1]> <matrix[26 x 1]>

summary(dat)

    cname             cedition           cproddat             cseqno      
 Length:2358        Length:2358        Length:2358        Min.   :101403  
 Class :character   Class :character   Class :character   1st Qu.:101992  
 Mode  :character   Mode  :character   Mode  :character   Median :102582  
                                                          Mean   :102582  
                                                          3rd Qu.:103171  
                                                          Max.   :103760  
                                                                          
     name              essround   edition               idno      
 Length:2358        Min.   :9   Length:2358        Min.   :    9  
 Class :character   1st Qu.:9   Class :character   1st Qu.:17194  
 Mode  :character   Median :9   Mode  :character   Median :34640  
                    Mean   :9                      Mean   :34894  
                    3rd Qu.:9                      3rd Qu.:52408  
                    Max.   :9                      Max.   :69956  
                                                                  
    dweight          pspwght          pweight         anweight     
 Min.   :0.9995   Min.   :0.4300   Min.   :3.037   Min.   : 1.306  
 1st Qu.:0.9995   1st Qu.:0.7410   1st Qu.:3.037   1st Qu.: 2.251  
 Median :0.9995   Median :0.9423   Median :3.037   Median : 2.862  
 Mean   :1.0000   Mean   :1.0000   Mean   :3.037   Mean   : 3.037  
 3rd Qu.:0.9995   3rd Qu.:1.1026   3rd Qu.:3.037   3rd Qu.: 3.349  
 Max.   :1.6288   Max.   :3.7891   Max.   :3.037   Max.   :11.509  
                                                                   
    trstprl          trstlgl          trstplc          trstplt      
 Min.   : 0.000   Min.   : 0.000   Min.   : 0.000   Min.   : 0.000  
 1st Qu.: 3.000   1st Qu.: 5.000   1st Qu.: 6.000   1st Qu.: 2.000  
 Median : 5.000   Median : 7.000   Median : 8.000   Median : 4.000  
 Mean   : 5.099   Mean   : 6.128   Mean   : 7.103   Mean   : 3.964  
 3rd Qu.: 7.000   3rd Qu.: 8.000   3rd Qu.: 9.000   3rd Qu.: 6.000  
 Max.   :10.000   Max.   :10.000   Max.   :10.000   Max.   :10.000  
 NA's   :31       NA's   :21       NA's   :5        NA's   :19      
    trstprt           trstep           trstun          lrscale      
 Min.   : 0.000   Min.   : 0.000   Min.   : 0.000   Min.   : 0.000  
 1st Qu.: 2.000   1st Qu.: 3.000   1st Qu.: 3.000   1st Qu.: 3.000  
 Median : 4.000   Median : 5.000   Median : 5.000   Median : 5.000  
 Mean   : 3.993   Mean   : 4.562   Mean   : 4.903   Mean   : 4.388  
 3rd Qu.: 5.000   3rd Qu.: 6.000   3rd Qu.: 7.000   3rd Qu.: 5.000  
 Max.   :10.000   Max.   :10.000   Max.   :10.000   Max.   :10.000  
 NA's   :22       NA's   :81       NA's   :104      NA's   :97      
    stflife           stfeco           stfgov          stfdem      
 Min.   : 0.000   Min.   : 0.000   Min.   : 0.00   Min.   : 0.000  
 1st Qu.: 7.000   1st Qu.: 5.000   1st Qu.: 3.00   1st Qu.: 4.000  
 Median : 8.000   Median : 7.000   Median : 4.00   Median : 6.000  
 Mean   : 7.664   Mean   : 6.769   Mean   : 4.28   Mean   : 5.887  
 3rd Qu.: 9.000   3rd Qu.: 8.000   3rd Qu.: 6.00   3rd Qu.: 8.000  
 Max.   :10.000   Max.   :10.000   Max.   :10.00   Max.   :10.000  
 NA's   :6        NA's   :36       NA's   :66      NA's   :37      
    imsmetn         imdfetn         impcntr         imbgeco      
 Min.   :1.000   Min.   :1.000   Min.   :1.000   Min.   : 0.000  
 1st Qu.:3.000   1st Qu.:2.000   1st Qu.:2.000   1st Qu.: 5.000  
 Median :3.000   Median :3.000   Median :3.000   Median : 6.000  
 Mean   :3.335   Mean   :2.918   Mean   :2.835   Mean   : 6.125  
 3rd Qu.:4.000   3rd Qu.:3.000   3rd Qu.:3.000   3rd Qu.: 8.000  
 Max.   :4.000   Max.   :4.000   Max.   :4.000   Max.   :10.000  
 NA's   :27      NA's   :30      NA's   :30      NA's   :33      
    imueclt          imwbcnt           happy            rlgdgr      
 Min.   : 0.000   Min.   : 0.000   Min.   : 0.000   Min.   : 0.000  
 1st Qu.: 5.000   1st Qu.: 4.000   1st Qu.: 7.000   1st Qu.: 1.000  
 Median : 6.000   Median : 5.000   Median : 8.000   Median : 5.000  
 Mean   : 6.023   Mean   : 5.347   Mean   : 7.818   Mean   : 4.164  
 3rd Qu.: 8.000   3rd Qu.: 7.000   3rd Qu.: 9.000   3rd Qu.: 7.000  
 Max.   :10.000   Max.   :10.000   Max.   :10.000   Max.   :10.000  
 NA's   :19       NA's   :29       NA's   :3        NA's   :7       
      gndr            agea       mean_imEnrich     mean_imAllow  
 Min.   :1.000   Min.   :15.00   Min.   : 0.000   Min.   :1.000  
 1st Qu.:1.000   1st Qu.:34.00   1st Qu.: 4.667   1st Qu.:2.667  
 Median :1.000   Median :51.00   Median : 6.000   Median :3.000  
 Mean   :1.486   Mean   :49.65   Mean   : 5.834   Mean   :3.031  
 3rd Qu.:2.000   3rd Qu.:64.00   3rd Qu.: 7.333   3rd Qu.:3.333  
 Max.   :2.000   Max.   :90.00   Max.   :10.000   Max.   :4.000  
                 NA's   :4       NA's   :9        NA's   :15     
   mean_trst         mean_stf          sd_stf      lrscale_scaled.V1 
 Min.   : 0.000   Min.   : 0.250   Min.   :0.000   Min.   :-2.30234  
 1st Qu.: 3.857   1st Qu.: 5.250   1st Qu.:1.258   1st Qu.:-0.72823  
 Median : 5.286   Median : 6.250   Median :1.893   Median : 0.32118  
 Mean   : 5.116   Mean   : 6.163   Mean   :1.982   Mean   : 0.00000  
 3rd Qu.: 6.571   3rd Qu.: 7.250   3rd Qu.:2.630   3rd Qu.: 0.32118  
 Max.   :10.000   Max.   :10.000   Max.   :6.364   Max.   : 2.94470  
 NA's   :2        NA's   :1        NA's   :9       NA's   :97        
 lrscale_dummy.V1 
 Min.   :0.00000  
 1st Qu.:0.00000  
 Median :0.00000  
 Mean   :0.18089  
 3rd Qu.:0.00000  
 Max.   :2.00000  
 NA's   :97

Basic Inferential Statisticss

Combining statistical tests like cor.test or t.test with the respective plot, check the assumptions of every test procedure you are using:

cor.test(dat$mean_stf, dat$mean_imEnrich, use = "complete")


    Pearson's product-moment correlation

data:  dat$mean_stf and dat$mean_imEnrich
t = 21.905, df = 2346, p-value < 2.2e-16
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 0.3779243 0.4451088
sample estimates:
      cor 
0.4120765

report::report(cor.test(dat$mean_stf, dat$mean_imEnrich, use = "complete"))

Effect sizes were labelled following Funder's (2019) recommendations.

The Pearson's product-moment correlation between dat$mean_stf and
dat$mean_imEnrich is positive, statistically significant, and very large (r =
0.41, 95% CI [0.38, 0.45], t(2346) = 21.91, p < .001)

plot(dat$mean_stf, dat$mean_imEnrich)

t.test(dat$mean_stf ~ dat$gndr)


    Welch Two Sample t-test

data:  dat$mean_stf by dat$gndr
t = 1.8892, df = 2349.3, p-value = 0.05899
alternative hypothesis: true difference in means between group 1 and group 2 is not equal to 0
95 percent confidence interval:
 -0.004760463  0.255262839
sample estimates:
mean in group 1 mean in group 2 
       6.223941        6.098690

t.test(dat$mean_stf ~ dat$gndr, var.equal = TRUE)


    Two Sample t-test

data:  dat$mean_stf by dat$gndr
t = 1.8888, df = 2355, p-value = 0.05905
alternative hypothesis: true difference in means between group 1 and group 2 is not equal to 0
95 percent confidence interval:
 -0.004788142  0.255290517
sample estimates:
mean in group 1 mean in group 2 
       6.223941        6.098690

report::report(t.test(dat$mean_stf ~ dat$gndr))

Effect sizes were labelled following Cohen's (1988) recommendations.

The Welch Two Sample t-test testing the difference of dat$mean_stf by dat$gndr
(mean in group 1 = 6.22, mean in group 2 = 6.10) suggests that the effect is
positive, statistically not significant, and very small (difference = 0.13, 95%
CI [-4.76e-03, 0.26], t(2349.27) = 1.89, p = 0.059; Cohen's d = 0.08, 95% CI
[-2.96e-03, 0.16])

boxplot(dat$mean_stf ~ dat$gndr)

p <- ggstatsplot::ggbetweenstats(data = dat, x = gndr, y = mean_stf)
p + xlab(label = "Hallo")

analyses of extreme groups for lrscale variable

Descriptive Statisticss

tmp_desc <- dat %>%
  group_by(lrscale_dummy) %>%
  summarise(N = n(),
            meanEnrich = mean(mean_imEnrich, na.rm = TRUE),
            sdEnrich = sd(mean_imEnrich, na.rm = TRUE),
            meanAllow = mean(mean_imAllow, na.rm = TRUE),
            sdAllow = sd(mean_imAllow, na.rm = TRUE),
            meanStf = mean(mean_stf, na.rm = TRUE),
            sdStf = sd(mean_stf, na.rm = TRUE),
            meanTrst = mean(mean_trst, na.rm = TRUE),
            sdTrst = sd(mean_trst, na.rm = TRUE))
tmp_desc <- round(x = tmp_desc, digits = 2)

tmp_desc

# A tibble: 4 × 10
  lrscale_dummy[,1]     N meanEnrich sdEnrich meanAllow sdAllow meanStf sdStf
              <dbl> <dbl>      <dbl>    <dbl>     <dbl>   <dbl>   <dbl> <dbl>
1                 0  1977       5.9      1.99      3.04    0.64    6.2   1.55
2                 1   159       6.34     2.06      3.24    0.69    5.9   1.67
3                 2   125       4.72     2.57      2.73    0.65    6.1   1.82
4                NA    97       5.11     2.42      2.87    0.78    5.91  2.32
# ℹ 2 more variables: meanTrst <dbl>, sdTrst <dbl>

Using the stargazer package you can create nice tables. You sometimes need to limit the number of digits using the function round():

### set up summary dataset yourself
stargazer(tmp_desc, type = "html", summary = FALSE)


	lrscale_dummy	N	meanEnrich	sdEnrich	meanAllow	sdAllow	meanStf	sdStf	meanTrst	sdTrst

1	0	1977	5.9	1.99	3.04	0.64	6.2	1.55	5.18	1.76
2	1	159	6.34	2.06	3.24	0.69	5.9	1.67	4.86	1.94
3	2	125	4.72	2.57	2.73	0.65	6.1	1.82	4.72	2.04
4	NA	97	5.11	2.42	2.87	0.78	5.91	2.32	4.65	2.25

### using summary function within stargazer
tmp_desc_stargazeer <- as.data.frame(dat[, str_subset(string = colnames(dat), pattern = "mean_")])
tmp_desc_stargazeer <- na.omit(tmp_desc_stargazeer)
stargazer(x =tmp_desc_stargazeer, type = "html", summary = TRUE, digits = 2)


Statistic	N	Mean	St. Dev.	Min	Max

mean_imEnrich	2,335	5.84	2.07	0.00	10.00
mean_imAllow	2,335	3.03	0.66	1.00	4.00
mean_trst	2,335	5.12	1.81	0.00	10.00
mean_stf	2,335	6.17	1.60	0.25	10.00

#> output to html
setwd("outputs")
stargazer(tmp_desc, type = "html", summary = FALSE, out = "summaryTable.html")


	lrscale_dummy	N	meanEnrich	sdEnrich	meanAllow	sdAllow	meanStf	sdStf	meanTrst	sdTrst

1	0	1977	5.9	1.99	3.04	0.64	6.2	1.55	5.18	1.76
2	1	159	6.34	2.06	3.24	0.69	5.9	1.67	4.86	1.94
3	2	125	4.72	2.57	2.73	0.65	6.1	1.82	4.72	2.04
4	NA	97	5.11	2.42	2.87	0.78	5.91	2.32	4.65	2.25

Basic Inferential Statisticss

lm_lower <- lm(formula = mean_imEnrich ~ mean_trst + mean_stf + happy + agea + gndr, data = dat_lower)
lm_upper <- lm(formula = mean_imEnrich ~ mean_trst + mean_stf + happy + agea + gndr, data = dat_upper)
summary(lm_lower)


Call:
lm(formula = mean_imEnrich ~ mean_trst + mean_stf + happy + agea + 
    gndr, data = dat_lower)

Residuals:
    Min      1Q  Median      3Q     Max 
-5.3869 -1.0797  0.0966  1.1228  4.0886 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept)  5.172446   0.911014   5.678 6.73e-08 ***
mean_trst    0.451803   0.102439   4.410 1.94e-05 ***
mean_stf    -0.182405   0.131175  -1.391    0.166    
happy        0.105915   0.094284   1.123    0.263    
agea        -0.001638   0.007501  -0.218    0.827    
gndr        -0.451923   0.321711  -1.405    0.162    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 1.939 on 152 degrees of freedom
  (1 Beobachtung als fehlend gelöscht)
Multiple R-squared:  0.1389,    Adjusted R-squared:  0.1106 
F-statistic: 4.905 on 5 and 152 DF,  p-value: 0.0003442

summary(lm_upper)


Call:
lm(formula = mean_imEnrich ~ mean_trst + mean_stf + happy + agea + 
    gndr, data = dat_upper)

Residuals:
    Min      1Q  Median      3Q     Max 
-4.7007 -1.6438  0.1496  1.4679  6.7869 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)   
(Intercept) -1.28886    1.13532  -1.135  0.25856   
mean_trst    0.28955    0.13520   2.142  0.03427 * 
mean_stf     0.53544    0.16619   3.222  0.00164 **
happy       -0.00867    0.10892  -0.080  0.93669   
agea         0.01027    0.01021   1.007  0.31620   
gndr         0.61951    0.38910   1.592  0.11400   
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 2.122 on 119 degrees of freedom
Multiple R-squared:  0.3445,    Adjusted R-squared:  0.317 
F-statistic: 12.51 on 5 and 119 DF,  p-value: 9.165e-10

Again we can use the stargazer package, which identifies lm_upper for example as an lm-object in R and creates a wonderful table for the model results:

stargazer(lm_lower, type = "html")


	Dependent variable:

	mean_imEnrich

mean_trst	0.452^***
	(0.102)

mean_stf	-0.182
	(0.131)

happy	0.106
	(0.094)

agea	-0.002
	(0.008)

gndr	-0.452
	(0.322)

Constant	5.172^***
	(0.911)


Observations	158
R²	0.139
Adjusted R²	0.111
Residual Std. Error	1.939 (df = 152)
F Statistic	4.905^*** (df = 5; 152)

Note:	p<0.1; p<0.05; p<0.01

stargazer(lm_upper, type = "html")


	Dependent variable:

	mean_imEnrich

mean_trst	0.290^**
	(0.135)

mean_stf	0.535^***
	(0.166)

happy	-0.009
	(0.109)

agea	0.010
	(0.010)

gndr	0.620
	(0.389)

Constant	-1.289
	(1.135)


Observations	125
R²	0.345
Adjusted R²	0.317
Residual Std. Error	2.122 (df = 119)
F Statistic	12.511^*** (df = 5; 119)

Note:	p<0.1; p<0.05; p<0.01

Appendix

Test for unidimensionality, CFA

Here we could apply a self-written function for example to check the reliability and amount of explained variance for the first factor:

get correlation plot, descriptive plot, EFA, CFA

regEx <- "^trst"
nameScale <- "Trust Scale"
nameVariable <- "mean_TrustItems"

sum(str_detect(string = colnames(dat), pattern = regEx))

[1] 7

tmp_dat <- na.omit(dat[,str_detect(string = colnames(dat), pattern = regEx)])


tmp <- CFAstats(dataset = tmp_dat, regularExp = regEx, labelLatent = str_remove(string = nameVariable, pattern = "mean_"), 
                showPlots = TRUE, 
                computeEFA = TRUE, 
                computeCFA = TRUE, 
                computeCFAMplus = FALSE)



descriptive statistics: 
        Mean   SD Median CoeffofVariation Minimum Maximun Lower Quantile
trstprl 5.13 2.47      5             0.48       0      10              0
trstlgl 6.16 2.48      7             0.40       0      10              0
trstplc 7.10 2.14      8             0.30       0      10              0
trstplt 3.97 2.25      4             0.57       0      10              0
trstprt 4.02 2.13      4             0.53       0      10              0
trstep  4.58 2.39      5             0.52       0      10              0
trstun  4.91 2.35      5             0.48       0      10              0
        Upper Quantile Skewness Kurtosis(-3) KS-Test
trstprl             10    -0.25        -0.57       0
trstlgl             10    -0.58        -0.33       0
trstplc             10    -1.02         0.91       0
trstplt             10    -0.05        -0.60       0
trstprt             10    -0.05        -0.50       0
trstep              10    -0.18        -0.55       0
trstun              10    -0.25        -0.44       0


variables under investigation:  trstprl trstlgl trstplc trstplt trstprt trstep trstun 

Cronbachs Alpha: 0.89 
Error in polychoric(x, correct = correct) : 
  You have more than8 categories for your items, polychoric is probably not needed
[1] "use instead of polychoric correlations pearson correlations"

Parallel analysis suggests that the number of factors =  3  and the number of components =  1 
TrustItems 
Number of components:  1 

Error in polychoric(tmp_dat) : 
  You have more than8 categories for your items, polychoric is probably not needed
[1] "use instead of polychoric correlations pearson correlations"


EFA factor loadings (1 factor solution): 

Loadings:
        MR1  
trstprl 0.806
trstlgl 0.678
trstplc 0.495
trstplt 0.850
trstprt 0.838
trstep  0.802
trstun  0.685

                 MR1
SS loadings    3.892
Proportion Var 0.556
CFA summary and fit statistics: 
lavaan 0.6.17 ended normally after 28 iterations

  Estimator                                         ML
  Optimization method                           NLMINB
  Number of model parameters                        14

  Number of observations                          2202

Model Test User Model:
                                              Standard      Scaled
  Test Statistic                               964.099     547.943
  Degrees of freedom                                14          14
  P-value (Chi-square)                           0.000       0.000
  Scaling correction factor                                  1.759
    Yuan-Bentler correction (Mplus variant)                       

Model Test Baseline Model:

  Test statistic                              9130.044    5090.118
  Degrees of freedom                                21          21
  P-value                                        0.000       0.000
  Scaling correction factor                                  1.794

User Model versus Baseline Model:

  Comparative Fit Index (CFI)                    0.896       0.895
  Tucker-Lewis Index (TLI)                       0.844       0.842
                                                                  
  Robust Comparative Fit Index (CFI)                         0.897
  Robust Tucker-Lewis Index (TLI)                            0.845

Loglikelihood and Information Criteria:

  Loglikelihood user model (H0)             -30701.274  -30701.274
  Scaling correction factor                                  1.357
      for the MLR correction                                      
  Loglikelihood unrestricted model (H1)             NA          NA
  Scaling correction factor                                  1.558
      for the MLR correction                                      
                                                                  
  Akaike (AIC)                               61430.547   61430.547
  Bayesian (BIC)                             61510.307   61510.307
  Sample-size adjusted Bayesian (SABIC)      61465.827   61465.827

Root Mean Square Error of Approximation:

  RMSEA                                          0.176       0.132
  90 Percent confidence interval - lower         0.166       0.125
  90 Percent confidence interval - upper         0.185       0.139
  P-value H_0: RMSEA <= 0.050                    0.000       0.000
  P-value H_0: RMSEA >= 0.080                    1.000       1.000
                                                                  
  Robust RMSEA                                               0.175
  90 Percent confidence interval - lower                     0.162
  90 Percent confidence interval - upper                     0.187
  P-value H_0: Robust RMSEA <= 0.050                         0.000
  P-value H_0: Robust RMSEA >= 0.080                         1.000

Standardized Root Mean Square Residual:

  SRMR                                           0.067       0.067

Parameter Estimates:

  Standard errors                             Sandwich
  Information bread                           Observed
  Observed information based on                Hessian

Latent Variables:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
  TrustItems =~                                                         
    trstprl           1.000                               1.978    0.801
    trstlgl           0.798    0.025   31.815    0.000    1.578    0.638
    trstplc           0.501    0.027   18.834    0.000    0.991    0.462
    trstplt           0.997    0.021   47.008    0.000    1.972    0.877
    trstprt           0.933    0.022   42.309    0.000    1.846    0.868
    trstep            0.957    0.023   41.358    0.000    1.893    0.793
    trstun            0.800    0.025   31.400    0.000    1.582    0.673

Variances:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
   .trstprl           2.193    0.113   19.485    0.000    2.193    0.359
   .trstlgl           3.633    0.127   28.590    0.000    3.633    0.593
   .trstplc           3.615    0.131   27.681    0.000    3.615    0.786
   .trstplt           1.163    0.077   15.008    0.000    1.163    0.230
   .trstprt           1.118    0.071   15.803    0.000    1.118    0.247
   .trstep            2.119    0.102   20.683    0.000    2.119    0.371
   .trstun            3.029    0.119   25.373    0.000    3.029    0.548
    TrustItems        3.914    0.168   23.347    0.000    1.000    1.000



CFA first 6 Modification Indices: 
       lhs op     rhs      mi    epc sepc.lv sepc.all sepc.nox
22 trstlgl ~~ trstplc 438.788  1.692   1.692    0.467    0.467
36  trstep ~~  trstun 271.209  1.023   1.023    0.404    0.404
31 trstplt ~~ trstprt 259.067  0.703   0.703    0.616    0.616
16 trstprl ~~ trstlgl  70.977  0.580   0.580    0.206    0.206
33 trstplt ~~  trstun  59.919 -0.404  -0.404   -0.215   -0.215
32 trstplt ~~  trstep  55.450 -0.366  -0.366   -0.233   -0.233

Save final files

setwd("outputs")
## save as .xlsx file
xlsx::write.xlsx2(x = dat, file = "dat.xlsx")
## save as .csv file
write.csv2(x = dat, file = "dat.csv")
## save as R object
saveRDS(dat, file = "dat.rds")

References

Newman, Mark. 2018. Networks: An Introduction. Oxford University Press.

Peng, Roger D., and Elizabeth Matsui. 2016. The Art of Data Science: A Guide for Anyone Who Works with Data. Lulu.com. https://bookdown.org/rdpeng/artofdatascience/.

Skrondal, Anders, and Sophia Rabe-Hesketh. 2004. Generalized Latent Variable Modeling: Multilevel, Longitudinal, and Structural Equation Models. New York: Chapman; Hall/CRC. https://doi.org/10.1201/9780203489437.

Wickham, Hadley, and Garrett Grolemund. 2017. R for Data Science: Import, Tidy, Transform, Visualize, and Model Data. "O’Reilly Media, Inc.". https://r4ds.had.co.nz/.

Xie, Yihui, J. J. Allaire, and Garrett Grolemund. 2018. R Markdown: The Definitive Guide. New York: Chapman; Hall/CRC. https://doi.org/10.1201/9781138359444.

Footnotes

see https://www.dw.com/en/migration-mother-of-all-political-problems-says-german-interior-minister-horst-seehofer/a-45378092, retrieved 9 February 2022↩︎

Background Information

Notes

get packages, raw data, functions

data preperation

get extreme groups for lrscale variable

Introduction

Background

Quoting (please remove this for your report!)

Methods

Hypothesis

Results

Descriptive Statisticss

Basic Inferential Statisticss

analyses of extreme groups for lrscale variable

Descriptive Statisticss

Basic Inferential Statisticss

Appendix

Test for unidimensionality, CFA

Save final files

References

Footnotes

get extreme groups for `lrscale` variable