The significance of the region on the salary of engineers in Sweden

So far I have analysed the effect of experience, education, gender and year on the salary of engineers in Sweden. In this post, I will have a look at the effect of the region on the salary of engineers in Sweden.

Statistics Sweden use NUTS (Nomenclature des Unités Territoriales Statistiques), which is the EU’s hierarchical regional division, to specify the regions.

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 (swemaps) # devtools::install_github('reinholdsson/swemaps')
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

## Install package "strengejacke" from GitHub (`devtools::install_github("strengejacke/strengejacke")`) to load all sj-packages at once!

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))
}
nuts <- read.csv("nuts.csv") %>%
  mutate(NUTS2_sh = substr(NUTS2, 1, 4))

map_ln_n <- map_ln %>%
  mutate(lnkod_n = as.numeric(lnkod)) 

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

The table: Average basic salary, monthly salary and women´s salary as a percentage of men´s salary by region, sector, occupational group (SSYK 2012) and sex. Year 2014 - 2018 Monthly salary All sectors

We expect that the region is an important factor in salaries. As a null hypothesis, we assume that the region is not related to the salary and examine if we can reject this hypothesis with the data from Statistics Sweden.

tb <- readfile ("000000CG.csv") %>%
  filter (`occuptional  (SSYK 2012)` == "214 Engineering professionals") %>% 
  left_join(nuts %>% distinct (NUTS2_en, NUTS2_sh), by = c("region" = "NUTS2_en")) 

## Warning: Column `region`/`NUTS2_en` joining character vector and factor,
## coercing into character vector

tb_map <- readfile ("000000CG.csv") %>%
  filter (`occuptional  (SSYK 2012)` == "214 Engineering professionals") %>%
  left_join(nuts, by = c("region" = "NUTS2_en")) 

## Warning: Column `region`/`NUTS2_en` joining character vector and factor,
## coercing into character vector

tb_map %>%
  filter (sex == "men") %>%
  right_join(map_ln_n, by = c("Länskod" = "lnkod_n")) %>%
  ggplot() +
    geom_polygon(mapping = aes(x = ggplot_long, y = ggplot_lat, group = lnkod, fill = salary)) +
      facet_grid(. ~ year) + 
    coord_equal() 

tb_map %>%
  filter (sex == "women") %>%
  right_join(map_ln_n, by = c("Länskod" = "lnkod_n")) %>%
  ggplot() +
    geom_polygon(mapping = aes(x = ggplot_long, y = ggplot_lat, group = lnkod, fill = salary)) +
      facet_grid(. ~ year) + 
    coord_equal() 

tb %>%
  ggplot () +  
    geom_point (mapping = aes(x = year_n, y = salary, colour = region, shape=sex)) + 
  labs(
    x = "Year",
    y = "Salary (SEK/month)"
  )

The F-value from the Anova table for the region is 40 (Pr(>F) < 2.2e-16), sufficient for rejecting the null hypothesis that the region has no effect on the salary holding year as constant. The adjusted R-squared value is 0,882 implying a good fit of the model.

model <-lm (log(salary) ~ year_n + sex + region , data = tb)

tb <- bind_cols(tb, as_tibble(exp(predict(model, tb, interval = "confidence"))))

tb %>%
  ggplot () +  
    geom_point (mapping = aes(x = year_n,y = fit, colour = region, shape=sex)) + 
  labs(
    x = "Year",
    y = "Salary (SEK/month)"
  )

summary(model) %>%  
  tidy() %>%
  knitr::kable( 
  booktabs = TRUE,
  caption = 'Summary from linear model fit')

Table 1: Summary from linear model fit

term	estimate	std.error	statistic	p.value
(Intercept)	-29.2269335	3.7348614	-7.825440	0.00e+00
year_n	0.0198303	0.0018526	10.703985	0.00e+00
sexwomen	-0.0587056	0.0052400	-11.203449	0.00e+00
regionSE12 East-Central Sweden	-0.0574855	0.0104799	-5.485297	6.00e-07
regionSE21 Småland and islands	-0.1286385	0.0104799	-12.274762	0.00e+00
regionSE22 South Sweden	-0.0457725	0.0104799	-4.367642	4.26e-05
regionSE23 West Sweden	-0.0513546	0.0104799	-4.900285	6.00e-06
regionSE31 North-Central Sweden	-0.0948080	0.0104799	-9.046630	0.00e+00
regionSE32 Central Norrland	-0.1099716	0.0104799	-10.493550	0.00e+00
regionSE33 Upper Norrland	-0.1360235	0.0104799	-12.979443	0.00e+00

summary(model)$r.squared

## [1] 0.8817871

Anova(model, type=2) %>% 
  tidy() %>% 
  knitr::kable( 
  booktabs = TRUE,
  caption = 'Anova report from linear model fit')

Table 1: Anova report from linear model fit

term	sumsq	df	statistic	p.value
year_n	0.0629183	1	114.57530	0
sex	0.0689270	1	125.51728	0
region	0.1548911	7	40.29419	0
Residuals	0.0384401	70	NA	NA

Let’s check what we have found.

model <-lm (log(salary) ~ year_n + sex + NUTS2_sh , data = tb) 
 
plot_model(model, type = "pred", terms = c("NUTS2_sh"))

## Model has log-transformed response. Back-transforming predictions to original response scale. Standard errors are still on the log-scale.

plot(model, which = 1)

tb[38,]

## # A tibble: 1 x 11
##   region sector `occuptional  (~ sex   year  salary year_n NUTS2_sh    fit
##   <chr>  <chr>  <chr>            <chr> <chr>  <dbl>  <dbl> <chr>     <dbl>
## 1 SE21 ~ 0 all~ 214 Engineering~ women 2016   34700   2016 SE21     38698.
## # ... with 2 more variables: lwr <dbl>, upr <dbl>

tb[27,]

## # A tibble: 1 x 11
##   region sector `occuptional  (~ sex   year  salary year_n NUTS2_sh    fit
##   <chr>  <chr>  <chr>            <chr> <chr>  <dbl>  <dbl> <chr>     <dbl>
## 1 SE31 ~ 0 all~ 214 Engineering~ men   2015   38100   2015 SE31     41616.
## # ... with 2 more variables: lwr <dbl>, upr <dbl>

tb[5,]

## # A tibble: 1 x 11
##   region sector `occuptional  (~ sex   year  salary year_n NUTS2_sh    fit
##   <chr>  <chr>  <chr>            <chr> <chr>  <dbl>  <dbl> <chr>     <dbl>
## 1 SE21 ~ 0 all~ 214 Engineering~ men   2014   41500   2014 SE21     39442.
## # ... with 2 more variables: lwr <dbl>, upr <dbl>

Also examine the interaction between gender and region. The F-value from the Anova table for the interaction is 2,7 (Pr(>F) < 0.017) implying a relation to 95 % significance.

model <-lm (log(salary) ~ year_n + sex * NUTS2_sh , data = tb) 

summary(model) %>%  
  tidy() %>%
  knitr::kable( 
  booktabs = TRUE,
  caption = 'Summary from linear model fit')

Table 2: Summary from linear model fit

term	estimate	std.error	statistic	p.value
(Intercept)	-29.2212864	3.4559410	-8.4553776	0.0000000
year_n	0.0198303	0.0017142	11.5678970	0.0000000
sexwomen	-0.0699998	0.0137140	-5.1042618	0.0000033
NUTS2_shSE12	-0.0755067	0.0137140	-5.5058132	0.0000007
NUTS2_shSE21	-0.1161490	0.0137140	-8.4693756	0.0000000
NUTS2_shSE22	-0.0520542	0.0137140	-3.7957018	0.0003332
NUTS2_shSE23	-0.0535387	0.0137140	-3.9039471	0.0002331
NUTS2_shSE31	-0.1099009	0.0137140	-8.0137791	0.0000000
NUTS2_shSE32	-0.1293018	0.0137140	-9.4284543	0.0000000
NUTS2_shSE33	-0.1327796	0.0137140	-9.6820490	0.0000000
sexwomen:NUTS2_shSE12	0.0360425	0.0193945	1.8583838	0.0677877
sexwomen:NUTS2_shSE21	-0.0249791	0.0193945	-1.2879441	0.2024762
sexwomen:NUTS2_shSE22	0.0125634	0.0193945	0.6477815	0.5194801
sexwomen:NUTS2_shSE23	0.0043683	0.0193945	0.2252313	0.8225283
sexwomen:NUTS2_shSE31	0.0301860	0.0193945	1.5564170	0.1246186
sexwomen:NUTS2_shSE32	0.0386605	0.0193945	1.9933706	0.0505553
sexwomen:NUTS2_shSE33	-0.0064879	0.0193945	-0.3345206	0.7390979

summary(model)$r.squared

## [1] 0.908906

Anova(model, type=2) %>% 
  tidy() %>% 
  knitr::kable( 
  booktabs = TRUE,
  caption = 'Anova report from linear model fit')

Table 2: Anova report from linear model fit

term	sumsq	df	statistic	p.value
year_n	0.0629183	1	133.816241	0.0000000
sex	0.0689270	1	146.595736	0.0000000
NUTS2_sh	0.1548911	7	47.060909	0.0000000
sex:NUTS2_sh	0.0088184	7	2.679327	0.0170929
Residuals	0.0296216	63	NA	NA

plot_model(model, type = "pred", terms = c("NUTS2_sh", "sex"))

## Model has log-transformed response. Back-transforming predictions to original response scale. Standard errors are still on the log-scale.

plot(model, which = 1)

tb[37,]

## # A tibble: 1 x 11
##   region sector `occuptional  (~ sex   year  salary year_n NUTS2_sh    fit
##   <chr>  <chr>  <chr>            <chr> <chr>  <dbl>  <dbl> <chr>     <dbl>
## 1 SE21 ~ 0 all~ 214 Engineering~ men   2016   40100   2016 SE21     41037.
## # ... with 2 more variables: lwr <dbl>, upr <dbl>

And the interaction between year and region. The F-value from the Anova table for the region is 0,57 (Pr(>F) < 0,77) implying no significant relation.

model <-lm (log(salary) ~ year_n * NUTS2_sh + sex , data = tb) 
 
summary(model) %>%  
  tidy() %>%
  knitr::kable( 
  booktabs = TRUE,
  caption = 'Summary from linear model fit')

Table 3: Summary from linear model fit

term	estimate	std.error	statistic	p.value
(Intercept)	-32.1955668	10.7951966	-2.9823975	0.0040635
year_n	0.0213028	0.0053548	3.9782933	0.0001818
NUTS2_shSE12	-4.0204905	15.2667129	-0.2633501	0.7931402
NUTS2_shSE21	0.6481345	15.2667129	0.0424541	0.9662710
NUTS2_shSE22	18.2873103	15.2667129	1.1978551	0.2354607
NUTS2_shSE23	7.7565167	15.2667129	0.5080672	0.6131806
NUTS2_shSE31	-5.4895464	15.2667129	-0.3595762	0.7203666
NUTS2_shSE32	-3.2845607	15.2667129	-0.2151452	0.8303490
NUTS2_shSE33	9.2276482	15.2667129	0.6044293	0.5477290
sexwomen	-0.0587056	0.0053548	-10.9632632	0.0000000
year_n:NUTS2_shSE12	0.0019658	0.0075728	0.2595848	0.7960305
year_n:NUTS2_shSE21	-0.0003853	0.0075728	-0.0508802	0.9595820
year_n:NUTS2_shSE22	-0.0090938	0.0075728	-1.2008536	0.2343036
year_n:NUTS2_shSE23	-0.0038730	0.0075728	-0.5114312	0.6108371
year_n:NUTS2_shSE31	0.0026760	0.0075728	0.3533662	0.7249937
year_n:NUTS2_shSE32	0.0015747	0.0075728	0.2079419	0.8359451
year_n:NUTS2_shSE33	-0.0046447	0.0075728	-0.6133392	0.5418602

summary(model)$r.squared

## [1] 0.8888956

Anova(model, type=2) %>% 
  tidy() %>% 
  knitr::kable( 
  booktabs = TRUE,
  caption = 'Anova report from linear model fit')

Table 3: Anova report from linear model fit

term	sumsq	df	statistic	p.value
year_n	0.0629183	1	109.7152945	0.0000000
NUTS2_sh	0.1548911	7	38.5850132	0.0000000
sex	0.0689270	1	120.1931409	0.0000000
year_n:NUTS2_sh	0.0023115	7	0.5758246	0.7728945
Residuals	0.0361285	63	NA	NA

plot_model(model, type = "pred", terms = c("NUTS2_sh", "year_n"))

## Model has log-transformed response. Back-transforming predictions to original response scale. Standard errors are still on the log-scale.

plot(model, which = 1)

Finally the interaction between gender, year and region, the only significant interaction is between the region and gender, F-value from the Anova table for the interaction is 2,4 (Pr(>F) < 0.033)

model <-lm (log(salary) ~ year_n * NUTS2_sh * sex , data = tb) 
 
summary(model) %>%  
  tidy() %>%
  knitr::kable( 
  booktabs = TRUE,
  caption = 'Summary from linear model fit')

Table 4: Summary from linear model fit

term	estimate	std.error	statistic	p.value
(Intercept)	-34.6715204	14.5497427	-2.3829645	0.0211805
year_n	0.0225338	0.0072171	3.1222585	0.0030380
NUTS2_shSE12	5.2021839	20.5764435	0.2528223	0.8014851
NUTS2_shSE21	5.5082002	20.5764435	0.2676945	0.7900815
NUTS2_shSE22	25.5308721	20.5764435	1.2407816	0.2207168
NUTS2_shSE23	16.1162328	20.5764435	0.7832370	0.4373355
NUTS2_shSE31	-18.4371634	20.5764435	-0.8960326	0.3747072
NUTS2_shSE32	7.6855067	20.5764435	0.3735100	0.7104136
NUTS2_shSE33	5.0530040	20.5764435	0.2455723	0.8070603
sexwomen	4.8932017	20.5764435	0.2378060	0.8130438
year_n:NUTS2_shSE12	-0.0026179	0.0102066	-0.2564919	0.7986672
year_n:NUTS2_shSE21	-0.0027899	0.0102066	-0.2733393	0.7857651
year_n:NUTS2_shSE22	-0.0126899	0.0102066	-1.2433117	0.2197916
year_n:NUTS2_shSE23	-0.0080207	0.0102066	-0.7858392	0.4358239
year_n:NUTS2_shSE31	0.0090909	0.0102066	0.8906917	0.3775375
year_n:NUTS2_shSE32	-0.0038764	0.0102066	-0.3797940	0.7057736
year_n:NUTS2_shSE33	-0.0025723	0.0102066	-0.2520253	0.8020975
year_n:sexwomen	-0.0024619	0.0102066	-0.2412080	0.8104213
NUTS2_shSE12:sexwomen	-18.4453487	29.0994854	-0.6338720	0.5291736
NUTS2_shSE21:sexwomen	-9.7201315	29.0994854	-0.3340310	0.7398112
NUTS2_shSE22:sexwomen	-14.4871236	29.0994854	-0.4978481	0.6208644
NUTS2_shSE23:sexwomen	-16.7194322	29.0994854	-0.5745611	0.5682714
NUTS2_shSE31:sexwomen	25.8952341	29.0994854	0.8898863	0.3779654
NUTS2_shSE32:sexwomen	-21.9401348	29.0994854	-0.7539699	0.4545502
NUTS2_shSE33:sexwomen	8.3492884	29.0994854	0.2869222	0.7754068
year_n:NUTS2_shSE12:sexwomen	0.0091674	0.0144343	0.6351107	0.5283723
year_n:NUTS2_shSE21:sexwomen	0.0048091	0.0144343	0.3331727	0.7404549
year_n:NUTS2_shSE22:sexwomen	0.0071923	0.0144343	0.4982800	0.6205623
year_n:NUTS2_shSE23:sexwomen	0.0082955	0.0144343	0.5747113	0.5681705
year_n:NUTS2_shSE31:sexwomen	-0.0128299	0.0144343	-0.8888492	0.3785170
year_n:NUTS2_shSE32:sexwomen	0.0109022	0.0144343	0.7552986	0.4537602
year_n:NUTS2_shSE33:sexwomen	-0.0041447	0.0144343	-0.2871452	0.7752371

summary(model)$r.squared

## [1] 0.9231133

Anova(model, type=2) %>% 
  tidy() %>% 
  knitr::kable( 
  booktabs = TRUE,
  caption = 'Anova report from linear model fit')

Table 4: Anova report from linear model fit

term	sumsq	df	statistic	p.value
year_n	0.0629183	1	120.7946290	0.0000000
NUTS2_sh	0.1637127	14	22.4504512	0.0000000
sex	0.0777463	8	18.6578050	0.0000000
year_n:NUTS2_sh	0.0023115	7	0.6339728	0.7254512
year_n:sex	0.0000085	1	0.0163969	0.8986442
NUTS2_sh:sex	0.0088184	7	2.4186030	0.0332038
year_n:NUTS2_sh:sex	0.0022998	7	0.6307550	0.7280524
Residuals	0.0250018	48	NA	NA

plot_model(model, type = "pred", terms = c("NUTS2_sh", "year_n", "sex"))

## Model has log-transformed response. Back-transforming predictions to original response scale. Standard errors are still on the log-scale.

plot(model, which = 1)