To complete the analysis on the significance of the sector on the salary for different occupational groups in Sweden I will in this post examine the correlation between salary and sector using statistics for education.

The F-value from the Anova table is used as the single value to discriminate how much the region and salary correlates. For exploratory analysis, the Anova value seems good enough.

First, define libraries and functions.

library (tidyverse)
## -- Attaching packages --------------------------------------------------- tidyverse 1.3.0 --
## v ggplot2 3.2.1     v purrr   0.3.3
## v tibble  2.1.3     v dplyr   0.8.3
## v tidyr   1.0.2     v stringr 1.4.0
## v readr   1.3.1     v forcats 0.4.0
## -- Conflicts ------------------------------------------------------ tidyverse_conflicts() --
## x dplyr::filter() masks stats::filter()
## x dplyr::lag()    masks stats::lag()
library (broom)
library (car)
## Loading required package: carData
## 
## Attaching package: 'car'
## The following object is masked from 'package:dplyr':
## 
##     recode
## The following object is masked from 'package:purrr':
## 
##     some
library (sjPlot)
## Registered S3 methods overwritten by 'lme4':
##   method                          from
##   cooks.distance.influence.merMod car 
##   influence.merMod                car 
##   dfbeta.influence.merMod         car 
##   dfbetas.influence.merMod        car
## Learn more about sjPlot with 'browseVignettes("sjPlot")'.
readfile <- function (file1){read_csv (file1, col_types = cols(), locale = readr::locale (encoding = "latin1"), na = c("..", "NA")) %>%
  gather (starts_with("19"), starts_with("20"), key = "year", value = salary) %>%
  drop_na() %>%
  mutate (year_n = parse_number (year))
}

The data table is downloaded from Statistics Sweden. It is saved as a comma-delimited file without heading, 000000CY.csv, http://www.statistikdatabasen.scb.se/pxweb/en/ssd/.

I have renamed the file to 000000CY_sector.csv because the filename 000000CY.csv was used in a previous post.

The table: Average basic salary, monthly salary and women´s salary as a percentage of men´s salary by sector, occupational group (SSYK 2012), sex and educational level (SUN). Year 2014 – 2018 Monthly salary 1-3 public sector 4-5 private sector

In the plot and tables, you can also find information on how the increase in salaries per year for each occupational group is affected when the interactions are taken into account.

tb <- readfile("000000CY_sector.csv") %>% 
  mutate(edulevel = `level of education`)

numedulevel <- read.csv("edulevel.csv") 

numedulevel %>%
  knitr::kable(
  booktabs = TRUE,
  caption = 'Initial approach, length of education') 

tbnum <- tb %>% 
  right_join(numedulevel, by = c("level of education" = "level.of.education")) %>%
  filter(!is.na(eduyears)) %>%
  mutate(eduyears = factor(eduyears))
## Warning: Column `level of education`/`level.of.education` joining character
## vector and factor, coercing into character vector
summary_table = vector()
anova_table = vector()

for (i in unique(tbnum$`occuptional  (SSYK 2012)`)){
  temp <- filter(tbnum, `occuptional  (SSYK 2012)` == i)
  if (dim(temp)[1] > 90){
    model <- lm(log(salary) ~ edulevel + sex + year_n + sector, data = temp)
    summary_table <- rbind (summary_table, mutate (tidy (summary (model)), ssyk = i, interaction = "none"))
    anova_table <- rbind (anova_table, mutate (tidy (Anova (model, type = 2)), ssyk = i, interaction = "none"))  
  
    model <- lm(log(salary) ~ edulevel * sector + sex + year_n, data = temp)
    summary_table <- rbind (summary_table, mutate (tidy (summary (model)), ssyk = i, interaction = "sector and edulevel"))
    anova_table <- rbind (anova_table, mutate (tidy (Anova (model, type = 2)), ssyk = i, interaction = "sector and edulevel"))  
    
    model <- lm(log(salary) ~ edulevel + sector * sex + year_n, data = temp)
    summary_table <- rbind (summary_table, mutate (tidy (summary (model)), ssyk = i, interaction = "sector and sex"))
    anova_table <- rbind (anova_table, mutate (tidy (Anova (model, type = 2)), ssyk = i, interaction = "sector and sex"))  
    
    model <- lm(log(salary) ~ edulevel +  year_n * sector + sex, data = temp)
    summary_table <- rbind (summary_table, mutate (tidy (summary (model)), ssyk = i, interaction = "sector and year"))
    anova_table <- rbind (anova_table, mutate (tidy (Anova (model, type = 2)), ssyk = i, interaction = "sector and year"))  
    
    model <- lm(log(salary) ~ edulevel * sector * sex * year_n, data = temp)
    summary_table <- rbind (summary_table, mutate (tidy (summary (model)), ssyk = i, interaction = "sector, year, edulevel and sex"))
    anova_table <- rbind (anova_table, mutate (tidy (Anova (model, type = 2)), ssyk = i, interaction = "sector, year, edulevel and sex"))      
  }
}
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
anova_table <- anova_table %>% rowwise() %>% mutate(contcol = str_count(term, ":")) 

summary_table <- summary_table %>% rowwise() %>% mutate(contcol = str_count(term, ":"))

merge(summary_table, anova_table, by = c("ssyk", "interaction"), all = TRUE) %>%
  filter (term.x == "year_n") %>%
  filter (term.y == "sector") %>%    
  filter (interaction == "none") %>%
  
  mutate (estimate = (exp(estimate) - 1) * 100) %>%  
  ggplot () +
    geom_point (mapping = aes(x = estimate, y = statistic.y, colour = interaction)) +
    labs(
      x = "Increase in salaries (% / year)",
      y = "F-value for sector"
    )   

Figure 1: The significance of the sector on the salary in Sweden, a comparison between different occupational groups, Year 2014 – 2018

merge(summary_table, anova_table, by = c("ssyk", "interaction"), all = TRUE) %>%
  filter (term.x == "year_n") %>%
  filter (contcol.y > 0) %>%    
  # only look at the interactions between all four variables in the case with interaction sector, year, edulevel and sex
  filter (!(contcol.y < 3 & interaction == "sector, year, edulevel and sex")) %>% 
  
  mutate (estimate = (exp(estimate) - 1) * 100) %>%  
  ggplot () +
    geom_point (mapping = aes(x = estimate, y = statistic.y, colour = interaction)) +
    labs(
      x = "Increase in salaries (% / year)",
      y = "F-value for interaction"
    ) 

Figure 2: The significance of the interaction between sector, edulevel, year and sex on the salary in Sweden, a comparison between different occupational groups, Year 2014 – 2018

The tables with all occupational groups sorted by F-value in descending order.

merge(summary_table, anova_table, c("ssyk", "interaction"), all = TRUE) %>%
  filter (term.x == "year_n") %>%
  filter (term.y == "sector") %>%   
  filter (interaction == "none") %>%
  mutate (estimate = (exp(estimate) - 1) * 100) %>%  
  select (ssyk, estimate, statistic.y, interaction) %>%
  rename (`F-value` = statistic.y) %>%
  rename (`Increase in salary` = estimate) %>%
  arrange (desc (`F-value`)) %>%
  knitr::kable(
    booktabs = TRUE,
    caption = 'Correlation for F-value (sector) and the yearly increase in salaries')

merge(summary_table, anova_table, c("ssyk", "interaction"), all = TRUE) %>%
  filter (term.x == "year_n") %>%
  filter (contcol.y > 0) %>%   
  filter (interaction == "sector and sex") %>%
  mutate (estimate = (exp(estimate) - 1) * 100) %>%  
  select (ssyk, estimate, statistic.y, interaction) %>%
  rename (`F-value` = statistic.y) %>%
  rename (`Increase in salary` = estimate) %>%
  arrange (desc (`F-value`)) %>%
  knitr::kable(
    booktabs = TRUE,
    caption = 'Correlation for F-value (sector and sex) and the yearly increase in salaries')

merge(summary_table, anova_table, c("ssyk", "interaction"), all = TRUE) %>%
  filter (term.x == "year_n") %>%
  filter (contcol.y > 0) %>%   
  filter (interaction == "sector and edulevel") %>%
  mutate (estimate = (exp(estimate) - 1) * 100) %>%  
  select (ssyk, estimate, statistic.y, interaction) %>%
  rename (`F-value` = statistic.y) %>%
  rename (`Increase in salary` = estimate) %>%
  arrange (desc (`F-value`)) %>%
  knitr::kable(
    booktabs = TRUE,
    caption = 'Correlation for F-value (sector and edulevel) and the yearly increase in salaries')

merge(summary_table, anova_table, c("ssyk", "interaction"), all = TRUE) %>%
  filter (term.x == "year_n") %>%
  filter (contcol.y > 0) %>%   
  filter (interaction == "sector and year") %>%
  mutate (estimate = (exp(estimate) - 1) * 100) %>%  
  select (ssyk, estimate, statistic.y, interaction) %>%
  rename (`F-value` = statistic.y) %>%
  rename (`Increase in salary` = estimate) %>%
  arrange (desc (`F-value`)) %>%
  knitr::kable(
    booktabs = TRUE,
    caption = 'Correlation for F-value (sector and year) and the yearly increase in salaries')

merge(summary_table, anova_table, c("ssyk", "interaction"), all = TRUE) %>%
  filter (term.x == "year_n") %>%
  filter (contcol.y > 1) %>%   
  filter (interaction == "sector, year, edulevel and sex") %>%
  filter (!(contcol.y < 3 & interaction == "sector, year, edulevel and sex")) %>%  
  mutate (estimate = (exp(estimate) - 1) * 100) %>%  
  select (ssyk, estimate, statistic.y, interaction) %>%
  rename (`F-value` = statistic.y) %>%
  rename (`Increase in salary` = estimate) %>%
  arrange (desc (`F-value`)) %>%
  knitr::kable(
    booktabs = TRUE,
    caption = 'Correlation for F-value (sector, year, edulevel and sex) and the yearly increase in salaries')

Let’s check what we have found.

temp <- tbnum %>%
  filter(`occuptional  (SSYK 2012)` == "242 Organisation analysts, policy administrators and human resource specialists")
 
model <- lm (log(salary) ~ year_n + eduyears + sector + sex, data = temp) 
 
plot_model(model, type = "pred", terms = c("eduyears", "sector"))
## Model has log-transformed response. Back-transforming predictions to original response scale. Standard errors are still on the log-scale.

Figure 3: Highest F-value sector, Organisation analysts, policy administrators and human resource specialists

temp <- tbnum %>%
  filter(`occuptional  (SSYK 2012)` == "941 Fast-food workers, food preparation assistants")
 
model <-lm (log(salary) ~ year_n + eduyears + sector + sex, data = temp) 
 
plot_model(model, type = "pred", terms = c("eduyears", "sector"))
## Model has log-transformed response. Back-transforming predictions to original response scale. Standard errors are still on the log-scale.

Figure 4: Lowest F-value sector, Fast-food workers, food preparation assistants

temp <- tbnum %>%
  filter(`occuptional  (SSYK 2012)` == "911 Cleaners and helpers")
 
model <- lm (log(salary) ~ year_n + eduyears + sector * sex, data = temp) 
 
plot_model(model, type = "pred", terms = c("eduyears", "sex", "sector"))
## Model has log-transformed response. Back-transforming predictions to original response scale. Standard errors are still on the log-scale.

Figure 5: Highest F-value interaction sector and gender, Cleaners and helpers

temp <- tbnum %>%
  filter(`occuptional  (SSYK 2012)` == "411 Office assistants and other secretaries")
 
model <- lm (log(salary) ~ year_n + eduyears + sector * sex, data = temp) 
 
plot_model(model, type = "pred", terms = c("eduyears", "sex", "sector"))
## Model has log-transformed response. Back-transforming predictions to original response scale. Standard errors are still on the log-scale.

Figure 6: Lowest F-value interaction sector and gender, Office assistants and other secretaries

temp <- tbnum %>%
  filter(`occuptional  (SSYK 2012)` == "335 Tax and related government associate professionals")
 
model <- lm (log(salary) ~ year_n + eduyears * sector + sex, data = temp) 
 
plot_model(model, type = "pred", terms = c("eduyears", "sector"))
## Warning in predict.lm(model, newdata = fitfram, type = "response", se.fit =
## se, : prediction from a rank-deficient fit may be misleading
## Model has log-transformed response. Back-transforming predictions to original response scale. Standard errors are still on the log-scale.

Figure 7: Highest F-value interaction sector and edulevel, Tax and related government associate professionals

temp <- tbnum %>%
  filter(`occuptional  (SSYK 2012)` == "911 Cleaners and helpers")
 
model <- lm (log(salary) ~ year_n + eduyears * sector + sex, data = temp) 
 
plot_model(model, type = "pred", terms = c("eduyears", "sector"))
## Warning in predict.lm(model, newdata = fitfram, type = "response", se.fit =
## se, : prediction from a rank-deficient fit may be misleading
## Model has log-transformed response. Back-transforming predictions to original response scale. Standard errors are still on the log-scale.

Figure 8: Lowest F-value interaction sector and edulevel, Cleaners and helpers

temp <- tbnum %>%
  filter(`occuptional  (SSYK 2012)` == "129 Administration and service managers not elsewhere classified")
 
model <- lm (log(salary) ~ year_n * sector + eduyears + sex, data = temp) 
 
plot_model(model, type = "pred", terms = c("eduyears", "year_n", "sector"))
## Model has log-transformed response. Back-transforming predictions to original response scale. Standard errors are still on the log-scale.

Figure 9: Highest F-value interaction sector and year, Administration and service managers not elsewhere classified

temp <- tbnum %>%
  filter(`occuptional  (SSYK 2012)` == "159 Other social services managers")
 
model <- lm (log(salary) ~ year_n * sector + eduyears + sex, data = temp) 
 
plot_model(model, type = "pred", terms = c("eduyears", "year_n", "sector"))
## Model has log-transformed response. Back-transforming predictions to original response scale. Standard errors are still on the log-scale.

Figure 10: Lowest F-value interaction sector and year, Other social services managers

temp <- tbnum %>%
  filter(`occuptional  (SSYK 2012)` == "264 Authors, journalists and linguists")
 
model <- lm (log(salary) ~ year_n * eduyears * sector * sex, data = temp) 
 
plot_model(model, type = "pred", terms = c("eduyears", "year_n", "sex", "sector"))
## Warning in predict.lm(model, newdata = fitfram, type = "response", se.fit =
## se, : prediction from a rank-deficient fit may be misleading
## Model has log-transformed response. Back-transforming predictions to original response scale. Standard errors are still on the log-scale.

Figure 11: Highest F-value interaction sector, edulevel, year and gender, Authors, journalists and linguists

## TableGrob (2 x 1) "arrange": 2 grobs
##   z     cells    name           grob
## 1 1 (1-1,1-1) arrange gtable[layout]
## 2 2 (2-2,1-1) arrange gtable[layout]
temp <- tbnum %>%
  filter(`occuptional  (SSYK 2012)` == "534 Attendants, personal assistants and related workers")
 
model <- lm (log(salary) ~ year_n * eduyears * sector * sex, data = temp) 
 
plot_model(model, type = "pred", terms = c("eduyears", "year_n", "sex", "sector"))
## Warning in predict.lm(model, newdata = fitfram, type = "response", se.fit =
## se, : prediction from a rank-deficient fit may be misleading
## Model has log-transformed response. Back-transforming predictions to original response scale. Standard errors are still on the log-scale.

Figure 12: Lowest F-value interaction sector, edulevel, year and gender, Attendants, personal assistants and related workers

## TableGrob (2 x 1) "arrange": 2 grobs
##   z     cells    name           grob
## 1 1 (1-1,1-1) arrange gtable[layout]
## 2 2 (2-2,1-1) arrange gtable[layout]