The significance of gender on the salary of engineers in Sweden

December 27, 2019
By

[This article was first published on R Analystatistics Sweden , and kindly contributed to R-bloggers]. (You can report issue about the content on this page here)
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In my previous posts, I have shown that there exists a correlation between salaries and experience as well as between salaries and education within many occupational groups. Within the data I used from Statistics Sweden there was also information about gender. Some of the models and graphs also showed that there is a difference in salaries between the different genders.

In this post, I will examine the interaction between the predictors. Apart from gender the interaction between year also needs to be investigated.

It would have been very interesting to examine the interaction between experience and education. However, this information is not available at Statistics Sweden, at least not for free.

First, define libraries and functions.

library (tidyverse) 
## -- Attaching packages --------------------------------------- tidyverse 1.2.1 --
## v ggplot2 3.2.0     v purrr   0.3.2
## v tibble  2.1.3     v dplyr   0.8.3
## v tidyr   1.0.0     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 (splines)
#install_github("ZheyuanLi/SplinesUtils")
library(SplinesUtils)
library(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, 00000031.csv, http://www.statistikdatabasen.scb.se/pxweb/en/ssd/.

Average monthly pay (total pay), non-manual workers private sector (SLP), SEK by occupational group (SSYK), age, sex and year. Year 2014 – 2018

There are no women in the age group 65-66 years which explains the uncertainty for this group.

We are interested to see if the interaction terms between gender, age and year are important factors in salaries. As a null hypothesis, we assume that the interaction terms between gender, age and year is not related to the salary and examine if we can reject this hypothesis with the data from Statistics Sweden.

tb <- readfile("00000031.csv") %>% 
  rowwise() %>% 
  mutate(age_l = unlist(lapply(strsplit(substr(age, 1, 5), "-"), strtoi))[1]) %>%
  rowwise() %>% 
  mutate(age_h = unlist(lapply(strsplit(substr(age, 1, 5), "-"), strtoi))[2]) %>%
  mutate(age_n = (age_l + age_h) / 2) 
   
tb %>%
  ggplot () +  
    geom_point (mapping = aes(x = year_n,y = salary, colour = age, shape = sex)) + 
  labs(
    x = "Year",
    y = "Salary (SEK/month)"
  )

SSYK 214, Architects, engineers and related professionals, Year 2014 - 2018

Figure 1: SSYK 214, Architects, engineers and related professionals, Year 2014 – 2018

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

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) -28.1818327 3.5502758 -7.937928 0
year_n 0.0190896 0.0017610 10.839936 0
sexwomen -0.0338702 0.0051006 -6.640420 0
age25-29 years 0.1194646 0.0108200 11.041048 0
age30-34 years 0.2670157 0.0108200 24.677885 0
age35-39 years 0.3798043 0.0108200 35.101929 0
age40-44 years 0.4507298 0.0108200 41.656942 0
age45-49 years 0.4826082 0.0108200 44.603178 0
age50-54 years 0.4957858 0.0108200 45.821064 0
age55-59 years 0.4999386 0.0108200 46.204870 0
age60-64 years 0.4926852 0.0108200 45.534501 0
age65-66 years 0.4850540 0.0145457 33.346995 0
summary(model)$adj.r.squared  
## [1] 0.9817476
Anova(model, type = 2)
## Anova Table (Type II tests)
## 
## Response: log(salary)
##            Sum Sq Df F value    Pr(>F)    
## year_n    0.06878  1 117.504 < 2.2e-16 ***
## sex       0.02581  1  44.095 3.166e-09 ***
## age       2.81366  9 534.074 < 2.2e-16 ***
## Residuals 0.04800 82                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
plot(model, which = 1)

SSYK 214, Architects, engineers and related professionals, Year 2014 - 2018

Figure 2: SSYK 214, Architects, engineers and related professionals, Year 2014 – 2018

tb[38,]
## Source: local data frame [1 x 9]
## Groups: 
## 
## # A tibble: 1 x 9
##   `occuptional  (SSYK 2012~ age      sex   year  salary year_n age_l age_h age_n
##                                    
## 1 214 Engineering professi~ 18-24 y~ men   2016   27300   2016    18    24    21
tb[56,]
## Source: local data frame [1 x 9]
## Groups: 
## 
## # A tibble: 1 x 9
##   `occuptional  (SSYK 2012~ age      sex   year  salary year_n age_l age_h age_n
##                                    
## 1 214 Engineering professi~ 65-66 y~ men   2016   51500   2016    65    66  65.5
tb[72,]
## Source: local data frame [1 x 9]
## Groups: 
## 
## # A tibble: 1 x 9
##   `occuptional  (SSYK 2012~ age      sex   year  salary year_n age_l age_h age_n
##                                    
## 1 214 Engineering professi~ 55-59 y~ women 2017   45000   2017    55    59    57

I will examine models with both the categorical and continuous predictors to see if they can make the same predictions. The models with continuous predictors show approximately the same as the models with categorical predictors as you can see below.

We start by examining the interaction between year and age. We find that the only significant interaction between age and year is in the age group 65-66 years old.

model <- lm (log(salary) ~ sex + year_n * age, 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) -41.8453794 10.9079056 -3.8362433 0.0002631
sexwomen -0.0338702 0.0051012 -6.6396284 0.0000000
year_n 0.0258672 0.0054107 4.7807733 0.0000088
age25-29 years 14.3621579 15.4261077 0.9310293 0.3549073
age30-34 years 27.5176359 15.4261077 1.7838353 0.0786064
age35-39 years 20.9934100 15.4261077 1.3609013 0.1777316
age40-44 years 16.2491631 15.4261077 1.0533547 0.2956526
age45-49 years 5.7537717 15.4261077 0.3729892 0.7102373
age50-54 years 0.6906147 15.4261077 0.0447692 0.9644135
age55-59 years 14.2039759 15.4261077 0.9207751 0.3602008
age60-64 years 13.3026500 15.4261077 0.8623465 0.3913210
age65-66 years 44.0644781 19.7739637 2.2284090 0.0289332
year_n:age25-29 years -0.0070648 0.0076518 -0.9232852 0.3589003
year_n:age30-34 years -0.0135172 0.0076518 -1.7665264 0.0814879
year_n:age35-39 years -0.0102250 0.0076518 -1.3362808 0.1856080
year_n:age40-44 years -0.0078365 0.0076518 -1.0241363 0.3091527
year_n:age45-49 years -0.0026147 0.0076518 -0.3417041 0.7335553
year_n:age50-54 years -0.0000966 0.0076518 -0.0126298 0.9899576
year_n:age55-59 years -0.0067976 0.0076518 -0.8883667 0.3772614
year_n:age60-64 years -0.0063541 0.0076518 -0.8304083 0.4090156
year_n:age65-66 years -0.0216149 0.0098077 -2.2038822 0.0306865
summary(model)$adj.r.squared  
## [1] 0.9817432
Anova(model, type = 2)
## Anova Table (Type II tests)
## 
## Response: log(salary)
##             Sum Sq Df  F value    Pr(>F)    
## sex        0.02581  1  44.0847 4.817e-09 ***
## year_n     0.06878  1 117.4762 < 2.2e-16 ***
## age        2.81366  9 533.9464 < 2.2e-16 ***
## year_n:age 0.00526  9   0.9978    0.4497    
## Residuals  0.04274 73                       
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
plot_model(model, type = "pred", terms = c("year_n", "age"), colors = "Set3")
## Model has log-transformed response. Back-transforming predictions to original response scale. Standard errors are still on the log-scale.

SSYK 214, Architects, engineers and related professionals, Year 2014 - 2018

Figure 3: SSYK 214, Architects, engineers and related professionals, Year 2014 – 2018

plot(model, which = 1)

SSYK 214, Architects, engineers and related professionals, Year 2014 - 2018

Figure 4: SSYK 214, Architects, engineers and related professionals, Year 2014 – 2018

model <- lm (log(salary) ~ sex + year_n * bs(age_n, knots = c(35, 50)), 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) -42.2169094 10.4483489 -4.0405340 0.0001206
sexwomen -0.0339907 0.0048836 -6.9601677 0.0000000
year_n 0.0260513 0.0051827 5.0265834 0.0000029
bs(age_n, knots = c(35, 50))1 15.9469335 23.8937700 0.6674097 0.5064075
bs(age_n, knots = c(35, 50))2 37.3855896 23.7587981 1.5735472 0.1194903
bs(age_n, knots = c(35, 50))3 -8.1493593 25.1608613 -0.3238903 0.7468559
bs(age_n, knots = c(35, 50))4 8.6142351 22.3328612 0.3857202 0.7007151
bs(age_n, knots = c(35, 50))5 37.8153976 18.0285162 2.0975324 0.0390644
year_n:bs(age_n, knots = c(35, 50))1 -0.0078854 0.0118521 -0.6653159 0.5077385
year_n:bs(age_n, knots = c(35, 50))2 -0.0183302 0.0117851 -1.5553743 0.1237557
year_n:bs(age_n, knots = c(35, 50))3 0.0042939 0.0124805 0.3440519 0.7316989
year_n:bs(age_n, knots = c(35, 50))4 -0.0040248 0.0110776 -0.3633240 0.7173094
year_n:bs(age_n, knots = c(35, 50))5 -0.0185161 0.0089421 -2.0706713 0.0415743
summary(model)$adj.r.squared  
## [1] 0.98315
Anova(model, type = 2)
## Anova Table (Type II tests)
## 
## Response: log(salary)
##                                      Sum Sq Df   F value    Pr(>F)    
## sex                                 0.02618  1   48.4439 8.049e-10 ***
## year_n                              0.06883  1  127.3747 < 2.2e-16 ***
## bs(age_n, knots = c(35, 50))        2.81344  5 1041.2680 < 2.2e-16 ***
## year_n:bs(age_n, knots = c(35, 50)) 0.00445  5    1.6454    0.1574    
## Residuals                           0.04377 81                        
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
plot_model(model, type = "pred", terms = c("age_n", "year_n"))
## Model has log-transformed response. Back-transforming predictions to original response scale. Standard errors are still on the log-scale.

SSYK 214, Architects, engineers and related professionals, Year 2014 - 2018

Figure 5: SSYK 214, Architects, engineers and related professionals, Year 2014 – 2018

plot(model, which = 1)

SSYK 214, Architects, engineers and related professionals, Year 2014 - 2018

Figure 6: SSYK 214, Architects, engineers and related professionals, Year 2014 – 2018

Examine the interaction between gender and age. We can see that women have a significantly lower salary for the age groups 35-39 years, 45-49 years, 50-54 years, 55-59 years and 60-64 years.

The F-value from the Anova table for the interaction term between gender and age is 3,2 (Pr(>F) < 0.003564), sufficient for rejecting the null hypothesis that the interaction between gender and age has no effect on the salary holding year as constant.

model <- lm (log(salary) ~ year_n + sex * age, 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) -28.2022208 3.2212924 -8.7549396 0.0000000
year_n 0.0190896 0.0015979 11.9470190 0.0000000
sexwomen 0.0069060 0.0138839 0.4974127 0.6203728
age25-29 years 0.1287635 0.0138839 9.2743148 0.0000000
age30-34 years 0.2841357 0.0138839 20.4651381 0.0000000
age35-39 years 0.3994082 0.0138839 28.7677512 0.0000000
age40-44 years 0.4652656 0.0138839 33.5111890 0.0000000
age45-49 years 0.5076384 0.0138839 36.5631348 0.0000000
age50-54 years 0.5175734 0.0138839 37.2787098 0.0000000
age55-59 years 0.5389253 0.0138839 38.8166009 0.0000000
age60-64 years 0.5298153 0.0138839 38.1604449 0.0000000
age65-66 years 0.5054421 0.0147315 34.3102881 0.0000000
sexwomen:age25-29 years -0.0185979 0.0196348 -0.9471913 0.3466242
sexwomen:age30-34 years -0.0342399 0.0196348 -1.7438372 0.0853402
sexwomen:age35-39 years -0.0392078 0.0196348 -1.9968533 0.0495192
sexwomen:age40-44 years -0.0290715 0.0196348 -1.4806107 0.1429556
sexwomen:age45-49 years -0.0500604 0.0196348 -2.5495786 0.0128556
sexwomen:age50-54 years -0.0435752 0.0196348 -2.2192866 0.0295322
sexwomen:age55-59 years -0.0779734 0.0196348 -3.9711888 0.0001643
sexwomen:age60-64 years -0.0742603 0.0196348 -3.7820779 0.0003131
summary(model)$adj.r.squared  
## [1] 0.9849736
Anova(model, type = 2)
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Anova Table (Type II tests)
## 
## Response: log(salary)
##            Sum Sq Df  F value    Pr(>F)    
## year_n    0.06878  1 142.7313 < 2.2e-16 ***
## sex       0.02581  1  53.5620 2.492e-10 ***
## age       2.81366  9 648.7344 < 2.2e-16 ***
## sex:age   0.01234  8   3.2006  0.003564 ** 
## Residuals 0.03566 74                       
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
plot_model(model, type = "pred", terms = c("age", "sex"))
## 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.

SSYK 214, Architects, engineers and related professionals, Year 2014 - 2018

Figure 7: SSYK 214, Architects, engineers and related professionals, Year 2014 – 2018

plot(model, which = 1)

SSYK 214, Architects, engineers and related professionals, Year 2014 - 2018

Figure 8: SSYK 214, Architects, engineers and related professionals, Year 2014 – 2018

tb[75,]
## Source: local data frame [1 x 9]
## Groups: 
## 
## # A tibble: 1 x 9
##   `occuptional  (SSYK 2012~ age      sex   year  salary year_n age_l age_h age_n
##                                    
## 1 214 Engineering professi~ 65-66 y~ men   2017   46500   2017    65    66  65.5
model <- lm (log(salary) ~ year_n + sex * bs(age_n, knots = c(35, 50)), 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) -28.2038536 3.1195378 -9.0410359 0.0000000
year_n 0.0190902 0.0015474 12.3371071 0.0000000
sexwomen 0.0071007 0.0134078 0.5295958 0.5978408
bs(age_n, knots = c(35, 50))1 0.0569146 0.0216453 2.6294148 0.0102324
bs(age_n, knots = c(35, 50))2 0.4595799 0.0214465 21.4291344 0.0000000
bs(age_n, knots = c(35, 50))3 0.5131788 0.0225545 22.7528180 0.0000000
bs(age_n, knots = c(35, 50))4 0.5585990 0.0195443 28.5811988 0.0000000
bs(age_n, knots = c(35, 50))5 0.5056993 0.0139459 36.2613732 0.0000000
sexwomen:bs(age_n, knots = c(35, 50))1 -0.0156019 0.0309691 -0.5037899 0.6157765
sexwomen:bs(age_n, knots = c(35, 50))2 -0.0520644 0.0314890 -1.6534151 0.1021172
sexwomen:bs(age_n, knots = c(35, 50))3 -0.0173455 0.0347256 -0.4995018 0.6187800
sexwomen:bs(age_n, knots = c(35, 50))4 -0.1083142 0.0346022 -3.1302674 0.0024289
sexwomen:bs(age_n, knots = c(35, 50))5 -0.0509037 0.0386819 -1.3159563 0.1919009
summary(model)$adj.r.squared  
## [1] 0.9859063
Anova(model, type = 2)
## Anova Table (Type II tests)
## 
## Response: log(salary)
##                                   Sum Sq Df   F value    Pr(>F)    
## year_n                           0.06880  1  152.2042 < 2.2e-16 ***
## sex                              0.02612  1   57.7814 4.558e-11 ***
## bs(age_n, knots = c(35, 50))     2.81344  5 1244.9030 < 2.2e-16 ***
## sex:bs(age_n, knots = c(35, 50)) 0.01161  5    5.1354 0.0003844 ***
## Residuals                        0.03661 81                        
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
plot_model(model, type = "pred", terms = c("age_n", "sex"))
## Model has log-transformed response. Back-transforming predictions to original response scale. Standard errors are still on the log-scale.

SSYK 214, Architects, engineers and related professionals, Year 2014 - 2018

Figure 9: SSYK 214, Architects, engineers and related professionals, Year 2014 – 2018

plot(model, which = 1)

SSYK 214, Architects, engineers and related professionals, Year 2014 - 2018

Figure 10: SSYK 214, Architects, engineers and related professionals, Year 2014 – 2018

Examine the interaction between gender and year. Both the model with categorical predictors and the model with continuous predictors indicates that women’s salaries increase more than men’s salaries.

The F-value from the Anova table for the interaction term between gender and year is 3,1 (Pr(>F) < 0.08053), with 90 % significance we can reject the null hypothesis that the interaction between gender and year has no effect on the salary holding age as constant.

model <- lm (log(salary) ~ year_n * sex + age, 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) -22.2600278 4.8457687 -4.593704 0.0000158
year_n 0.0161522 0.0024037 6.719863 0.0000000
sexwomen -12.4532110 7.0175325 -1.774585 0.0797236
age25-29 years 0.1194646 0.0106821 11.183664 0.0000000
age30-34 years 0.2670157 0.0106821 24.996646 0.0000000
age35-39 years 0.3798043 0.0106821 35.555336 0.0000000
age40-44 years 0.4507298 0.0106821 42.195020 0.0000000
age45-49 years 0.4826082 0.0106821 45.179312 0.0000000
age50-54 years 0.4957858 0.0106821 46.412928 0.0000000
age55-59 years 0.4999386 0.0106821 46.801692 0.0000000
age60-64 years 0.4926852 0.0106821 46.122664 0.0000000
age65-66 years 0.4857883 0.0143662 33.814759 0.0000000
year_n:sexwomen 0.0061604 0.0034809 1.769759 0.0805306
summary(model)$adj.r.squared  
## [1] 0.9822101
Anova(model, type = 2)
## Anova Table (Type II tests)
## 
## Response: log(salary)
##             Sum Sq Df F value    Pr(>F)    
## year_n     0.06878  1 120.559 < 2.2e-16 ***
## sex        0.02581  1  45.242 2.266e-09 ***
## age        2.81430  9 548.084 < 2.2e-16 ***
## year_n:sex 0.00179  1   3.132   0.08053 .  
## Residuals  0.04621 81                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
plot_model(model, type = "pred", terms = c("year_n", "sex"))
## Model has log-transformed response. Back-transforming predictions to original response scale. Standard errors are still on the log-scale.

SSYK 214, Architects, engineers and related professionals, Year 2014 - 2018

Figure 11: SSYK 214, Architects, engineers and related professionals, Year 2014 – 2018

model <- lm (log(salary) ~ year_n * sex + bs(age_n, knots = c(35, 50)), 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) -22.2810163 4.7408239 -4.699819 0.0000099
year_n 0.0161625 0.0023516 6.872990 0.0000000
sexwomen -12.4325740 6.8662746 -1.810672 0.0737248
bs(age_n, knots = c(35, 50))1 0.0497887 0.0168608 2.952920 0.0040694
bs(age_n, knots = c(35, 50))2 0.4323307 0.0167836 25.759071 0.0000000
bs(age_n, knots = c(35, 50))3 0.5064797 0.0178110 28.436385 0.0000000
bs(age_n, knots = c(35, 50))4 0.5014488 0.0159182 31.501692 0.0000000
bs(age_n, knots = c(35, 50))5 0.4850317 0.0132343 36.649526 0.0000000
year_n:sexwomen 0.0061501 0.0034059 1.805728 0.0745008
summary(model)$adj.r.squared  
## [1] 0.9829655
Anova(model, type = 2)
## Anova Table (Type II tests)
## 
## Response: log(salary)
##                               Sum Sq Df   F value    Pr(>F)    
## year_n                       0.06883  1  125.9950 < 2.2e-16 ***
## sex                          0.02612  1   47.8063 8.182e-10 ***
## bs(age_n, knots = c(35, 50)) 2.81407  5 1030.2198 < 2.2e-16 ***
## year_n:sex                   0.00178  1    3.2607    0.0745 .  
## Residuals                    0.04644 85                        
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
plot_model(model, type = "pred", terms = c("year_n", "sex"))
## Model has log-transformed response. Back-transforming predictions to original response scale. Standard errors are still on the log-scale.

SSYK 214, Architects, engineers and related professionals, Year 2014 - 2018

Figure 12: SSYK 214, Architects, engineers and related professionals, Year 2014 – 2018

Examine the interaction between year, gender and age. It’s becoming a bit difficult to make any significant predictions about the interactions from the model, the data is not sufficiently large, the degrees of freedom has been reduced from 82 in the model with no interaction terms to 56.

The following interaction terms are significant to 90 %.

year_n:sexwomen

sexwomen:age35-39 years

year_n:sexwomen:age35-39 years

In the graph below you can that the salaries for men in the age group 35-39 years has increased more than for women.

The F-value from the Anova table for the interaction term between gender and age is 3,3 (Pr(>F) < 0.00373), sufficient for rejecting the null hypothesis that the interaction between gender and age has no effect on the salary holding year as constant.

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

summary(model) %>%  
  tidy() %>%
  knitr::kable( 
  booktabs = TRUE,
  caption = 'Summary from linear model fit')
Table 5: Summary from linear model fit
term estimate std.error statistic p.value
(Intercept) -23.0500250 13.7844076 -1.6721810 0.1000676
year_n 0.0165340 0.0068375 2.4181290 0.0188783
sexwomen -37.6245789 19.4940962 -1.9300499 0.0586714
age25-29 years 0.3057247 19.4940962 0.0156829 0.9875431
age30-34 years 13.4212323 19.4940962 0.6884768 0.4939950
age35-39 years -6.4835219 19.4940962 -0.3325890 0.7406864
age40-44 years -4.3559249 19.4940962 -0.2234484 0.8239997
age45-49 years -8.7690292 19.4940962 -0.4498300 0.6545695
age50-54 years -0.8787263 19.4940962 -0.0450765 0.9642067
age55-59 years -6.3664653 19.4940962 -0.3265843 0.7451998
age60-64 years 2.4331505 19.4940962 0.1248147 0.9011172
age65-66 years 25.2691238 20.1796414 1.2522088 0.2156985
year_n:sexwomen 0.0186664 0.0096697 1.9304047 0.0586265
year_n:age25-29 years -0.0000878 0.0096697 -0.0090777 0.9927894
year_n:age30-34 years -0.0065164 0.0096697 -0.6739015 0.5031462
year_n:age35-39 years 0.0034142 0.0096697 0.3530778 0.7253558
year_n:age40-44 years 0.0023915 0.0096697 0.2473155 0.8055686
year_n:age45-49 years 0.0046015 0.0096697 0.4758707 0.6360177
year_n:age50-54 years 0.0006926 0.0096697 0.0716268 0.9431541
year_n:age55-59 years 0.0034253 0.0096697 0.3542299 0.7244970
year_n:age60-64 years -0.0009441 0.0096697 -0.0976365 0.9225696
year_n:age65-66 years -0.0122817 0.0100091 -1.2270593 0.2249341
sexwomen:age25-29 years 28.1128665 27.5688152 1.0197343 0.3122398
sexwomen:age30-34 years 28.1928073 27.5688152 1.0226340 0.3108784
sexwomen:age35-39 years 54.9538639 27.5688152 1.9933343 0.0511051
sexwomen:age40-44 years 41.2101760 27.5688152 1.4948113 0.1405778
sexwomen:age45-49 years 29.0456019 27.5688152 1.0535673 0.2966058
sexwomen:age50-54 years 3.1386820 27.5688152 0.1138490 0.9097647
sexwomen:age55-59 years 41.1408823 27.5688152 1.4922978 0.1412337
sexwomen:age60-64 years 21.7389989 27.5688152 0.7885358 0.4337089
year_n:sexwomen:age25-29 years -0.0139541 0.0136750 -1.0204092 0.3119226
year_n:sexwomen:age30-34 years -0.0140015 0.0136750 -1.0238762 0.3102964
year_n:sexwomen:age35-39 years -0.0272783 0.0136750 -1.9947569 0.0509451
year_n:sexwomen:age40-44 years -0.0204560 0.0136750 -1.4958662 0.1403033
year_n:sexwomen:age45-49 years -0.0144324 0.0136750 -1.0553834 0.2957821
year_n:sexwomen:age50-54 years -0.0015785 0.0136750 -0.1154296 0.9085175
year_n:sexwomen:age55-59 years -0.0204459 0.0136750 -1.4951265 0.1404958
year_n:sexwomen:age60-64 years -0.0108201 0.0136750 -0.7912297 0.4321485
summary(model)$adj.r.squared  
## [1] 0.9854223
Anova(model, type = 2)
## Note: model has aliased coefficients
##       sums of squares computed by model comparison
## Anova Table (Type II tests)
## 
## Response: log(salary)
##                 Sum Sq Df  F value    Pr(>F)    
## year_n         0.06878  1 147.1250 < 2.2e-16 ***
## sex            0.02581  1  55.2108 6.727e-10 ***
## age            2.81430  9 668.8557 < 2.2e-16 ***
## year_n:sex     0.00113  1   2.4097   0.12622    
## year_n:age     0.00460  9   1.0927   0.38295    
## sex:age        0.01234  8   3.2991   0.00373 ** 
## year_n:sex:age 0.00310  8   0.8277   0.58192    
## Residuals      0.02618 56                       
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
plot_model(model, type = "pred", terms = c("year_n", "age", "sex"))
## 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.
## Warning in RColorBrewer::brewer.pal(n, pal): n too large, allowed maximum for palette Set1 is 9
## Returning the palette you asked for with that many colors
## Warning: Removed 10 rows containing missing values (geom_path).

SSYK 214, Architects, engineers and related professionals, Year 2014 - 2018

Figure 13: SSYK 214, Architects, engineers and related professionals, Year 2014 – 2018

plot(model, which = 1)

SSYK 214, Architects, engineers and related professionals, Year 2014 - 2018

Figure 14: SSYK 214, Architects, engineers and related professionals, Year 2014 – 2018

model <- lm (log(salary) ~ year_n * sex * bs(age_n, knots = c(35, 50)), data = tb)

summary(model) %>%  
  tidy() %>%
  knitr::kable( 
  booktabs = TRUE,
  caption = 'Summary from linear model fit')
Table 5: Summary from linear model fit
term estimate std.error statistic p.value
(Intercept) -24.0868942 12.7931370 -1.8827981 0.0638836
year_n 0.0170481 0.0063458 2.6865147 0.0090115
sexwomen -35.9593922 18.0942402 -1.9873392 0.0507987
bs(age_n, knots = c(35, 50))1 13.5471021 29.2057808 0.4638500 0.6441944
bs(age_n, knots = c(35, 50))2 -3.5308622 28.9253132 -0.1220682 0.9031947
bs(age_n, knots = c(35, 50))3 -3.0003750 30.3944067 -0.0987147 0.9216469
bs(age_n, knots = c(35, 50))4 -10.6818355 26.2596260 -0.4067779 0.6854122
bs(age_n, knots = c(35, 50))5 24.6956649 18.4012753 1.3420627 0.1839126
year_n:sexwomen 0.0178405 0.0089753 1.9877332 0.0507540
year_n:bs(age_n, knots = c(35, 50))1 -0.0066913 0.0144870 -0.4618860 0.6455954
year_n:bs(age_n, knots = c(35, 50))2 0.0019790 0.0143478 0.1379286 0.8906928
year_n:bs(age_n, knots = c(35, 50))3 0.0017435 0.0150765 0.1156429 0.9082666
year_n:bs(age_n, knots = c(35, 50))4 0.0055746 0.0130255 0.4279781 0.6699809
year_n:bs(age_n, knots = c(35, 50))5 -0.0119974 0.0091271 -1.3144829 0.1929745
sexwomen:bs(age_n, knots = c(35, 50))1 -3.0882433 41.7901518 -0.0738988 0.9413017
sexwomen:bs(age_n, knots = c(35, 50))2 96.0533158 42.4835588 2.2609527 0.0268729
sexwomen:bs(age_n, knots = c(35, 50))3 -33.3604447 46.8350731 -0.7122962 0.4786489
sexwomen:bs(age_n, knots = c(35, 50))4 73.5641700 46.6314260 1.5775664 0.1191741
sexwomen:bs(age_n, knots = c(35, 50))5 -29.6631727 52.0527929 -0.5698671 0.5705923
year_n:sexwomen:bs(age_n, knots = c(35, 50))1 0.0015239 0.0207292 0.0735146 0.9416063
year_n:sexwomen:bs(age_n, knots = c(35, 50))2 -0.0476709 0.0210732 -2.2621610 0.0267943
year_n:sexwomen:bs(age_n, knots = c(35, 50))3 0.0165386 0.0232316 0.7118987 0.4788935
year_n:sexwomen:bs(age_n, knots = c(35, 50))4 -0.0365429 0.0231306 -1.5798519 0.1186493
year_n:sexwomen:bs(age_n, knots = c(35, 50))5 0.0146870 0.0258196 0.5688315 0.5712911
summary(model)$adj.r.squared  
## [1] 0.9873689
Anova(model, type = 2)
## Anova Table (Type II tests)
## 
## Response: log(salary)
##                                          Sum Sq Df  F value    Pr(>F)    
## year_n                                  0.06880  1 169.8286 < 2.2e-16 ***
## sex                                     0.03780  6  15.5511 3.011e-11 ***
## bs(age_n, knots = c(35, 50))            2.82569 10 697.5506 < 2.2e-16 ***
## year_n:sex                              0.00126  1   3.1090 0.0822248 .  
## year_n:bs(age_n, knots = c(35, 50))     0.00394  5   1.9452 0.0977419 .  
## sex:bs(age_n, knots = c(35, 50))        0.01163  5   5.7405 0.0001702 ***
## year_n:sex:bs(age_n, knots = c(35, 50)) 0.00253  5   1.2489 0.2958798    
## Residuals                               0.02836 70                       
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
plot_model(model, type = "pred", terms = c("age_n", "year_n", "sex"))
## Model has log-transformed response. Back-transforming predictions to original response scale. Standard errors are still on the log-scale.

SSYK 214, Architects, engineers and related professionals, Year 2014 - 2018

Figure 15: SSYK 214, Architects, engineers and related professionals, Year 2014 – 2018

plot(model, which = 1)

SSYK 214, Architects, engineers and related professionals, Year 2014 - 2018

Figure 16: SSYK 214, Architects, engineers and related professionals, Year 2014 – 2018

Average basic salary, monthly salary and women´s salary as a percentage of men´s salary by sector, occupational group (SSYK 2012), gender and educational level (SUN). Year 2014 – 2018 Monthly salary All sectors

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

tb <- readfile("000000CY.csv") %>% 
  filter(`occuptional  (SSYK 2012)` == "214 Engineering professionals") %>%    
  mutate(edulevel = `level of education`)

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

tbnum <- tb %>% 
  right_join(numedulevel, by = c("level of education" = "level.of.education")) %>%
  filter(!is.na(eduyears))
## Warning: Column `level of education`/`level.of.education` joining character
## vector and factor, coercing into character vector
numedulevel %>%
  knitr::kable(
  booktabs = TRUE,
  caption = 'Initial approach, length of education') 
Table 6: Initial approach, length of education
level.of.education eduyears
primary and secondary education 9-10 years (ISCED97 2) 9
upper secondary education, 2 years or less (ISCED97 3C) 11
upper secondary education 3 years (ISCED97 3A) 12
post-secondary education, less than 3 years (ISCED97 4+5B) 14
post-secondary education 3 years or more (ISCED97 5A) 15
post-graduate education (ISCED97 6) 19
no information about level of educational attainment NA
tb %>%
  ggplot () +  
    geom_point (mapping = aes(x = year_n,y = salary, colour = `level of education`, shape = sex)) + 
  labs(
    x = "Year",
    y = "Salary (SEK/month)"
  )

SSYK 214, Architects, engineers and related professionals, Year 2014 - 2018

Figure 17: SSYK 214, Architects, engineers and related professionals, Year 2014 – 2018

model <- lm (log(salary) ~ year_n + sex + edulevel, data = tbnum)

summary(model) %>%  
  tidy() %>%
  knitr::kable( 
  booktabs = TRUE,
  caption = 'Summary from linear model fit')
Table 6: Summary from linear model fit
term estimate std.error statistic p.value
(Intercept) -34.8741818 4.5648337 -7.639749 0
year_n 0.0226738 0.0022643 10.013413 0
sexwomen -0.0743114 0.0063438 -11.713990 0
edulevelpost-secondary education 3 years or more (ISCED97 5A) -0.1104356 0.0108816 -10.148796 0
edulevelpost-secondary education, less than 3 years (ISCED97 4+5B) -0.1446573 0.0108816 -13.293700 0
edulevelprimary and secondary education 9-10 years (ISCED97 2) -0.2207500 0.0111971 -19.714892 0
edulevelupper secondary education 3 years (ISCED97 3A) -0.1898866 0.0108816 -17.450172 0
edulevelupper secondary education, 2 years or less (ISCED97 3C) -0.2155065 0.0108816 -19.804583 0
summary(model)$adj.r.squared  
## [1] 0.9311952
Anova(model, type = 2)
## Anova Table (Type II tests)
## 
## Response: log(salary)
##            Sum Sq Df F value    Pr(>F)    
## year_n    0.05936  1  100.27 1.232e-13 ***
## sex       0.08124  1  137.22 4.476e-16 ***
## edulevel  0.34338  5  116.00 < 2.2e-16 ***
## Residuals 0.03019 51                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
plot(model, which = 1)

SSYK 214, Architects, engineers and related professionals, Year 2014 - 2018

Figure 18: SSYK 214, Architects, engineers and related professionals, Year 2014 – 2018

tb[20,]
## # A tibble: 1 x 8
##   sector  `occuptional  (~ sex   `level of educat~ year  salary year_n edulevel 
##                                         
## 1 0 all ~ 214 Engineering~ men   no information a~ 2015   48400   2015 no infor~
tb[41,]
## # A tibble: 1 x 8
##   sector  `occuptional  (~ sex   `level of educat~ year  salary year_n edulevel 
##                                         
## 1 0 all ~ 214 Engineering~ women no information a~ 2016   39400   2016 no infor~
tb[55,]
## # A tibble: 1 x 8
##   sector  `occuptional  (~ sex   `level of educat~ year  salary year_n edulevel 
##                                         
## 1 0 all ~ 214 Engineering~ women no information a~ 2017   35300   2017 no infor~

We start by examining the interaction between year and education. The salaries for the education upper secondary education, 2 years or less increase more than other educations during the time period 2014-2018, however, this can not be shown with 95% significance from this data.

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

summary(model) %>%  
  tidy() %>%
  knitr::kable( 
  booktabs = TRUE,
  caption = 'Summary from linear model fit')
Table 7: Summary from linear model fit
term estimate std.error statistic p.value
(Intercept) -29.3041153 10.9645273 -2.6726291 0.0103775
sexwomen -0.0743499 0.0063563 -11.6971241 0.0000000
year_n 0.0199109 0.0054388 3.6609245 0.0006464
edulevelpost-secondary education 3 years or more (ISCED97 5A) 3.5092165 15.5061826 0.2263108 0.8219623
edulevelpost-secondary education, less than 3 years (ISCED97 4+5B) -3.7498523 15.5061826 -0.2418295 0.8099871
edulevelprimary and secondary education 9-10 years (ISCED97 2) -6.8196567 16.6031078 -0.4107458 0.6831661
edulevelupper secondary education 3 years (ISCED97 3A) -0.3311115 15.5061826 -0.0213535 0.9830560
edulevelupper secondary education, 2 years or less (ISCED97 3C) -27.1431543 15.5061826 -1.7504730 0.0867042
year_n:edulevelpost-secondary education 3 years or more (ISCED97 5A) -0.0017955 0.0076916 -0.2334329 0.8164610
year_n:edulevelpost-secondary education, less than 3 years (ISCED97 4+5B) 0.0017883 0.0076916 0.2325005 0.8171806
year_n:edulevelprimary and secondary education 9-10 years (ISCED97 2) 0.0032732 0.0082351 0.3974684 0.6928605
year_n:edulevelupper secondary education 3 years (ISCED97 3A) 0.0000701 0.0076916 0.0091077 0.9927726
year_n:edulevelupper secondary education, 2 years or less (ISCED97 3C) 0.0133570 0.0076916 1.7365753 0.0891557
summary(model)$adj.r.squared  
## [1] 0.9312476
Anova(model, type = 2)
## Anova Table (Type II tests)
## 
## Response: log(salary)
##                  Sum Sq Df  F value    Pr(>F)    
## sex             0.08094  1 136.8227 2.212e-15 ***
## year_n          0.05936  1 100.3448 3.853e-13 ***
## edulevel        0.34338  5 116.0852 < 2.2e-16 ***
## year_n:edulevel 0.00298  5   1.0078     0.424    
## Residuals       0.02721 46                       
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
plot_model(model, type = "pred", terms = c("year_n", "edulevel"))
## Model has log-transformed response. Back-transforming predictions to original response scale. Standard errors are still on the log-scale.

SSYK 214, Architects, engineers and related professionals, Year 2014 - 2018

Figure 19: SSYK 214, Architects, engineers and related professionals, Year 2014 – 2018

plot(model, which = 1)

SSYK 214, Architects, engineers and related professionals, Year 2014 - 2018

Figure 20: SSYK 214, Architects, engineers and related professionals, Year 2014 – 2018

tb[10,]
## # A tibble: 1 x 8
##   sector  `occuptional  (~ sex   `level of educat~ year  salary year_n edulevel 
##                                         
## 1 0 all ~ 214 Engineering~ women post-secondary e~ 2014   38800   2014 post-sec~
tb[25,]
## # A tibble: 1 x 8
##   sector  `occuptional  (~ sex   `level of educat~ year  salary year_n edulevel 
##                                         
## 1 0 all ~ 214 Engineering~ women post-secondary e~ 2015   41200   2015 post-sec~
tb[29,]
## # A tibble: 1 x 8
##   sector  `occuptional  (~ sex   `level of educat~ year  salary year_n edulevel 
##                                         
## 1 0 all ~ 214 Engineering~ men   upper secondary ~ 2016   42100   2016 upper se~
model <- lm(log(salary) ~ sex + year_n * bs(eduyears, knots = c(14)), data = tbnum)

summary(model) %>%  
  tidy() %>%
  knitr::kable( 
  booktabs = TRUE,
  caption = 'Summary from linear model fit')
Table 7: Summary from linear model fit
term estimate std.error statistic p.value
(Intercept) -37.5638852 12.5188542 -3.0005849 0.0042648
sexwomen -0.0744192 0.0064006 -11.6269343 0.0000000
year_n 0.0238981 0.0062092 3.8488437 0.0003504
bs(eduyears, knots = c(14))1 -33.5129947 34.8826450 -0.9607355 0.3415000
bs(eduyears, knots = c(14))2 52.9743796 67.5504892 0.7842190 0.4367647
bs(eduyears, knots = c(14))3 -26.1485331 82.0008933 -0.3188811 0.7512002
bs(eduyears, knots = c(14))4 8.2849059 16.6914080 0.4963575 0.6219077
year_n:bs(eduyears, knots = c(14))1 0.0166181 0.0173024 0.9604499 0.3416422
year_n:bs(eduyears, knots = c(14))2 -0.0262412 0.0335071 -0.7831529 0.4373844
year_n:bs(eduyears, knots = c(14))3 0.0130625 0.0406748 0.3211439 0.7494955
year_n:bs(eduyears, knots = c(14))4 -0.0039997 0.0082789 -0.4831182 0.6312082
summary(model)$adj.r.squared  
## [1] 0.9302821
Anova(model, type = 2)
## Anova Table (Type II tests)
## 
## Response: log(salary)
##                                     Sum Sq Df  F value    Pr(>F)    
## sex                                0.08110  1 135.1856 1.453e-15 ***
## year_n                             0.05941  1  99.0272 2.972e-13 ***
## bs(eduyears, knots = c(14))        0.34299  4 142.9343 < 2.2e-16 ***
## year_n:bs(eduyears, knots = c(14)) 0.00179  4   0.7457    0.5657    
## Residuals                          0.02880 48                       
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
plot_model(model, type = "pred", terms = c("year_n", "eduyears"))
## Model has log-transformed response. Back-transforming predictions to original response scale. Standard errors are still on the log-scale.

SSYK 214, Architects, engineers and related professionals, Year 2014 - 2018

Figure 21: SSYK 214, Architects, engineers and related professionals, Year 2014 – 2018

plot(model, which = 1)

SSYK 214, Architects, engineers and related professionals, Year 2014 - 2018

Figure 22: SSYK 214, Architects, engineers and related professionals, Year 2014 – 2018

tb[25,]
## # A tibble: 1 x 8
##   sector  `occuptional  (~ sex   `level of educat~ year  salary year_n edulevel 
##                                         
## 1 0 all ~ 214 Engineering~ women post-secondary e~ 2015   41200   2015 post-sec~

Examine the interaction between gender and education. The only significant difference in salaries for the length in education is for the group upper secondary education, 2 years or less.

The F-value from the Anova table for the interaction term between gender and education is 3,3 (Pr(>F) < 0.01195), sufficient for rejecting the null hypothesis that the interaction between gender and education has no effect on the salary holding year as constant.

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

summary(model) %>%  
  tidy() %>%
  knitr::kable( 
  booktabs = TRUE,
  caption = 'Summary from linear model fit')
Table 8: Summary from linear model fit
term estimate std.error statistic p.value
(Intercept) -34.7430460 4.1272331 -8.4179994 0.0000000
sexwomen -0.0771083 0.0138850 -5.5533508 0.0000013
edulevelpost-secondary education 3 years or more (ISCED97 5A) -0.1168022 0.0138850 -8.4121058 0.0000000
edulevelpost-secondary education, less than 3 years (ISCED97 4+5B) -0.1597128 0.0138850 -11.5025341 0.0000000
edulevelprimary and secondary education 9-10 years (ISCED97 2) -0.2251088 0.0138850 -16.2123615 0.0000000
edulevelupper secondary education 3 years (ISCED97 3A) -0.1948942 0.0138850 -14.0363072 0.0000000
edulevelupper secondary education, 2 years or less (ISCED97 3C) -0.1931089 0.0138850 -13.9077238 0.0000000
year_n 0.0226094 0.0020472 11.0438961 0.0000000
sexwomen:edulevelpost-secondary education 3 years or more (ISCED97 5A) 0.0127331 0.0196364 0.6484450 0.5199213
sexwomen:edulevelpost-secondary education, less than 3 years (ISCED97 4+5B) 0.0301109 0.0196364 1.5334243 0.1320210
sexwomen:edulevelprimary and secondary education 9-10 years (ISCED97 2) 0.0094897 0.0202666 0.4682454 0.6418203
sexwomen:edulevelupper secondary education 3 years (ISCED97 3A) 0.0100153 0.0196364 0.5100385 0.6124632
sexwomen:edulevelupper secondary education, 2 years or less (ISCED97 3C) -0.0447952 0.0196364 -2.2812368 0.0272117
summary(model)$adj.r.squared  
## [1] 0.9439866
Anova(model, type = 2)
## Anova Table (Type II tests)
## 
## Response: log(salary)
##               Sum Sq Df  F value    Pr(>F)    
## sex          0.08124  1 168.5530 < 2.2e-16 ***
## edulevel     0.34338  5 142.4863 < 2.2e-16 ***
## year_n       0.05879  1 121.9676 1.576e-14 ***
## sex:edulevel 0.00802  5   3.3293   0.01195 *  
## Residuals    0.02217 46                       
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
plot_model(model, type = "pred", terms = c("edulevel", "sex"))
## Model has log-transformed response. Back-transforming predictions to original response scale. Standard errors are still on the log-scale.

SSYK 214, Architects, engineers and related professionals, Year 2014 - 2018

Figure 23: SSYK 214, Architects, engineers and related professionals, Year 2014 – 2018

plot(model, which = 1)

SSYK 214, Architects, engineers and related professionals, Year 2014 - 2018

Figure 24: SSYK 214, Architects, engineers and related professionals, Year 2014 – 2018

tb[12,]
## # A tibble: 1 x 8
##   sector  `occuptional  (S~ sex   `level of educa~ year  salary year_n edulevel 
##                                         
## 1 0 all ~ 214 Engineering ~ women post-graduate e~ 2014   45000   2014 post-gra~
model <- lm(log(salary) ~ sex * bs(eduyears, knots = c(14)) + year_n, data = tbnum)

summary(model) %>%  
  tidy() %>%
  knitr::kable( 
  booktabs = TRUE,
  caption = 'Summary from linear model fit')
Table 8: Summary from linear model fit
term estimate std.error statistic p.value
(Intercept) -35.0137987 4.1599657 -8.4168479 0.0000000
sexwomen -0.0691630 0.0148436 -4.6594632 0.0000254
bs(eduyears, knots = c(14))1 0.0563505 0.0303035 1.8595384 0.0690857
bs(eduyears, knots = c(14))2 -0.0451702 0.0604863 -0.7467842 0.4588363
bs(eduyears, knots = c(14))3 0.2884546 0.0731010 3.9459725 0.0002585
bs(eduyears, knots = c(14))4 0.2248785 0.0139796 16.0861324 0.0000000
year_n 0.0226322 0.0020635 10.9680236 0.0000000
sexwomen:bs(eduyears, knots = c(14))1 -0.1362989 0.0434669 -3.1356935 0.0029251
sexwomen:bs(eduyears, knots = c(14))2 0.2339328 0.0855779 2.7335654 0.0087471
sexwomen:bs(eduyears, knots = c(14))3 -0.2077223 0.1036306 -2.0044483 0.0506812
sexwomen:bs(eduyears, knots = c(14))4 -0.0079140 0.0203999 -0.3879451 0.6997718
summary(model)$adj.r.squared  
## [1] 0.943092
Anova(model, type = 2)
## Anova Table (Type II tests)
## 
## Response: log(salary)
##                                  Sum Sq Df  F value    Pr(>F)    
## sex                             0.08128  1 165.9766 < 2.2e-16 ***
## bs(eduyears, knots = c(14))     0.34299  4 175.1086 < 2.2e-16 ***
## year_n                          0.05891  1 120.2975 1.128e-14 ***
## sex:bs(eduyears, knots = c(14)) 0.00708  4   3.6147   0.01181 *  
## Residuals                       0.02350 48                       
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
plot_model(model, type = "pred", terms = c("eduyears", "sex"))
## Model has log-transformed response. Back-transforming predictions to original response scale. Standard errors are still on the log-scale.

SSYK 214, Architects, engineers and related professionals, Year 2014 - 2018

Figure 25: SSYK 214, Architects, engineers and related professionals, Year 2014 – 2018

plot(model, which = 1)

SSYK 214, Architects, engineers and related professionals, Year 2014 - 2018

Figure 26: SSYK 214, Architects, engineers and related professionals, Year 2014 – 2018

Examine the interaction between gender and year There is no evidence that the salaries for men and women are interacting with year, holding education constant.

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

summary(model) %>%  
  tidy() %>%
  knitr::kable( 
  booktabs = TRUE,
  caption = 'Summary from linear model fit')
Table 9: Summary from linear model fit
term estimate std.error statistic p.value
(Intercept) -33.2392045 6.3870956 -5.2041188 0.0000037
sexwomen -3.4777309 9.2153884 -0.3773830 0.7074862
year_n 0.0218628 0.0031682 6.9007009 0.0000000
edulevelpost-secondary education 3 years or more (ISCED97 5A) -0.1104356 0.0109750 -10.0625026 0.0000000
edulevelpost-secondary education, less than 3 years (ISCED97 4+5B) -0.1446573 0.0109750 -13.1806660 0.0000000
edulevelprimary and secondary education 9-10 years (ISCED97 2) -0.2209486 0.0113059 -19.5427007 0.0000000
edulevelupper secondary education 3 years (ISCED97 3A) -0.1898866 0.0109750 -17.3017955 0.0000000
edulevelupper secondary education, 2 years or less (ISCED97 3C) -0.2155065 0.0109750 -19.6361878 0.0000000
sexwomen:year_n 0.0016882 0.0045710 0.3693193 0.7134493
summary(model)$adj.r.squared  
## [1] 0.93001
Anova(model, type = 2)
## Anova Table (Type II tests)
## 
## Response: log(salary)
##             Sum Sq Df  F value    Pr(>F)    
## sex        0.08124  1 134.8940 8.258e-16 ***
## year_n     0.05936  1  98.5705 2.047e-13 ***
## edulevel   0.34343  5 114.0493 < 2.2e-16 ***
## sex:year_n 0.00008  1   0.1364    0.7134    
## Residuals  0.03011 50                       
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
plot_model(model, type = "pred", terms = c("year_n", "sex"))
## Model has log-transformed response. Back-transforming predictions to original response scale. Standard errors are still on the log-scale.

SSYK 214, Architects, engineers and related professionals, Year 2014 - 2018

Figure 27: SSYK 214, Architects, engineers and related professionals, Year 2014 – 2018

plot(model, which = 1)

SSYK 214, Architects, engineers and related professionals, Year 2014 - 2018

Figure 28: SSYK 214, Architects, engineers and related professionals, Year 2014 – 2018

tb[18,]
## # A tibble: 1 x 8
##   sector  `occuptional  (~ sex   `level of educat~ year  salary year_n edulevel 
##                                         
## 1 0 all ~ 214 Engineering~ men   post-secondary e~ 2015   44800   2015 post-sec~
model <- lm(log(salary) ~ sex * year_n + bs(eduyears, knots = c(14)), data = tbnum)

summary(model) %>%  
  tidy() %>%
  knitr::kable( 
  booktabs = TRUE,
  caption = 'Summary from linear model fit')
Table 9: Summary from linear model fit
term estimate std.error statistic p.value
(Intercept) -33.4606036 6.3648511 -5.2570914 0.0000029
sexwomen -3.5113836 9.1831982 -0.3823704 0.7037755
year_n 0.0218628 0.0031572 6.9248186 0.0000000
bs(eduyears, knots = c(14))1 -0.0110825 0.0239981 -0.4618072 0.6461835
bs(eduyears, knots = c(14))2 0.0720456 0.0472864 1.5236020 0.1337855
bs(eduyears, knots = c(14))3 0.1853033 0.0572546 3.2364779 0.0021284
bs(eduyears, knots = c(14))4 0.2214175 0.0112515 19.6788574 0.0000000
sexwomen:year_n 0.0017049 0.0045551 0.3742767 0.7097502
summary(model)$adj.r.squared  
## [1] 0.9304967
Anova(model, type = 2)
## Anova Table (Type II tests)
## 
## Response: log(salary)
##                              Sum Sq Df  F value    Pr(>F)    
## sex                         0.08128  1 135.8986 5.361e-16 ***
## year_n                      0.05941  1  99.3330 1.446e-13 ***
## bs(eduyears, knots = c(14)) 0.34304  4 143.3973 < 2.2e-16 ***
## sex:year_n                  0.00008  1   0.1401    0.7098    
## Residuals                   0.03050 51                       
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
plot_model(model, type = "pred", terms = c("eduyears", "sex"))
## Model has log-transformed response. Back-transforming predictions to original response scale. Standard errors are still on the log-scale.

SSYK 214, Architects, engineers and related professionals, Year 2014 - 2018

Figure 29: SSYK 214, Architects, engineers and related professionals, Year 2014 – 2018

plot(model, which = 1)

SSYK 214, Architects, engineers and related professionals, Year 2014 - 2018

Figure 30: SSYK 214, Architects, engineers and related professionals, Year 2014 – 2018

Examine the interaction between year, gender and education It’s becoming a bit difficult to make any significant predictions from the model, the data is not sufficiently large, the degrees of freedom has been reduced from 51 in the model with no interaction terms to 35.

There are no significant interaction terms in the summary.

The F-value from the Anova table for the interaction term between gender and education is 3,0 (Pr(>F) < 0.02377), sufficient for rejecting the null hypothesis that the interaction between gender and education has no effect on the salary holding year as constant.

model <- lm(log(salary) ~ sex * year_n * edulevel, data = tbnum)

summary(model) %>%  
  tidy() %>%
  knitr::kable( 
  booktabs = TRUE,
  caption = 'Summary from linear model fit')
Table 10: Summary from linear model fit
term estimate std.error statistic p.value
(Intercept) -28.6598716 14.7502103 -1.9430144 0.0600924
sexwomen -1.3628373 20.8599474 -0.0653327 0.9482808
year_n 0.0195920 0.0073166 2.6777544 0.0112090
edulevelpost-secondary education 3 years or more (ISCED97 5A) 5.7063531 20.8599474 0.2735555 0.7860341
edulevelpost-secondary education, less than 3 years (ISCED97 4+5B) 1.8926757 20.8599474 0.0907325 0.9282224
edulevelprimary and secondary education 9-10 years (ISCED97 2) -6.5228901 20.8599474 -0.3126993 0.7563648
edulevelupper secondary education 3 years (ISCED97 3A) 3.4041093 20.8599474 0.1631888 0.8713084
edulevelupper secondary education, 2 years or less (ISCED97 3C) -32.8376799 20.8599474 -1.5741976 0.1244390
sexwomen:year_n 0.0006378 0.0103472 0.0616363 0.9512031
sexwomen:edulevelpost-secondary education 3 years or more (ISCED97 5A) -4.3942731 29.5004205 -0.1489563 0.8824431
sexwomen:edulevelpost-secondary education, less than 3 years (ISCED97 4+5B) -11.2850561 29.5004205 -0.3825388 0.7043750
sexwomen:edulevelprimary and secondary education 9-10 years (ISCED97 2) 1.3504648 32.9857439 0.0409409 0.9675757
sexwomen:edulevelupper secondary education 3 years (ISCED97 3A) -7.4704416 29.5004205 -0.2532317 0.8015707
sexwomen:edulevelupper secondary education, 2 years or less (ISCED97 3C) 11.3890513 29.5004205 0.3860640 0.7017862
year_n:edulevelpost-secondary education 3 years or more (ISCED97 5A) -0.0028885 0.0103472 -0.2791549 0.7817689
year_n:edulevelpost-secondary education, less than 3 years (ISCED97 4+5B) -0.0010180 0.0103472 -0.0983890 0.9221848
year_n:edulevelprimary and secondary education 9-10 years (ISCED97 2) 0.0031239 0.0103472 0.3019079 0.7645090
year_n:edulevelupper secondary education 3 years (ISCED97 3A) -0.0017852 0.0103472 -0.1725318 0.8640133
year_n:edulevelupper secondary education, 2 years or less (ISCED97 3C) 0.0161927 0.0103472 1.5649406 0.1265947
sexwomen:year_n:edulevelpost-secondary education 3 years or more (ISCED97 5A) 0.0021860 0.0146331 0.1493879 0.8821050
sexwomen:year_n:edulevelpost-secondary education, less than 3 years (ISCED97 4+5B) 0.0056127 0.0146331 0.3835596 0.7036250
sexwomen:year_n:edulevelprimary and secondary education 9-10 years (ISCED97 2) -0.0006652 0.0163603 -0.0406584 0.9677993
sexwomen:year_n:edulevelupper secondary education 3 years (ISCED97 3A) 0.0037105 0.0146331 0.2535713 0.8013105
sexwomen:year_n:edulevelupper secondary education, 2 years or less (ISCED97 3C) -0.0056716 0.0146331 -0.3875826 0.7006721
summary(model)$adj.r.squared  
## [1] 0.9377879
Anova(model, type = 2)
## Anova Table (Type II tests)
## 
## Response: log(salary)
##                      Sum Sq Df  F value    Pr(>F)    
## sex                 0.08897  6  27.6985 6.428e-12 ***
## year_n              0.05879  1 109.8150 2.456e-12 ***
## edulevel            0.35144 10  65.6498 < 2.2e-16 ***
## sex:year_n          0.00007  1   0.1338   0.71677    
## sex:edulevel        0.00800  5   2.9902   0.02377 *  
## year_n:edulevel     0.00298  5   1.1127   0.37150    
## sex:year_n:edulevel 0.00039  5   0.1445   0.98038    
## Residuals           0.01874 35                       
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
plot_model(model, type = "pred", terms = c("year_n", "edulevel","sex"))
## Model has log-transformed response. Back-transforming predictions to original response scale. Standard errors are still on the log-scale.

SSYK 214, Architects, engineers and related professionals, Year 2014 - 2018

Figure 31: SSYK 214, Architects, engineers and related professionals, Year 2014 – 2018

plot(model, which = 1)

SSYK 214, Architects, engineers and related professionals, Year 2014 - 2018

Figure 32: SSYK 214, Architects, engineers and related professionals, Year 2014 – 2018

tb[29,]
## # A tibble: 1 x 8
##   sector  `occuptional  (~ sex   `level of educat~ year  salary year_n edulevel 
##                                         
## 1 0 all ~ 214 Engineering~ men   upper secondary ~ 2016   42100   2016 upper se~
model <- lm(log(salary) ~ sex * year_n * bs(eduyears, knots = c(14)), data = tbnum)

summary(model) %>%  
  tidy() %>%
  knitr::kable( 
  booktabs = TRUE,
  caption = 'Summary from linear model fit')
Table 10: Summary from linear model fit
term estimate std.error statistic p.value
(Intercept) -36.4297072 14.8747312 -2.4491002 0.0189181
sexwomen -1.4146024 25.7220917 -0.0549956 0.9564227
year_n 0.0233345 0.0073783 3.1625710 0.0030250
bs(eduyears, knots = c(14))1 -52.0255138 45.6462798 -1.1397536 0.2613408
bs(eduyears, knots = c(14))2 93.3207084 91.1108278 1.0242549 0.3120264
bs(eduyears, knots = c(14))3 -61.4602190 110.1124840 -0.5581585 0.5799266
bs(eduyears, knots = c(14))4 7.8004982 21.0576228 0.3704358 0.7130621
sexwomen:year_n 0.0006670 0.0127569 0.0522889 0.9585654
sexwomen:bs(eduyears, knots = c(14))1 35.6845382 68.0014005 0.5247618 0.6027192
sexwomen:bs(eduyears, knots = c(14))2 -81.1592876 129.0648894 -0.6288255 0.5331293
sexwomen:bs(eduyears, knots = c(14))3 69.2953946 157.1561131 0.4409335 0.6616959
sexwomen:bs(eduyears, knots = c(14))4 0.0407412 33.2552425 0.0012251 0.9990288
year_n:bs(eduyears, knots = c(14))1 0.0258343 0.0226420 1.1409884 0.2608328
year_n:bs(eduyears, knots = c(14))2 -0.0463124 0.0451939 -1.0247509 0.3117952
year_n:bs(eduyears, knots = c(14))3 0.0306293 0.0546193 0.5607783 0.5781565
year_n:bs(eduyears, knots = c(14))4 -0.0037577 0.0104452 -0.3597567 0.7209699
sexwomen:year_n:bs(eduyears, knots = c(14))1 -0.0177678 0.0337292 -0.5267776 0.6013316
sexwomen:year_n:bs(eduyears, knots = c(14))2 0.0403738 0.0640202 0.6306418 0.5319531
sexwomen:year_n:bs(eduyears, knots = c(14))3 -0.0344753 0.0779537 -0.4422531 0.6607490
sexwomen:year_n:bs(eduyears, knots = c(14))4 -0.0000238 0.0164940 -0.0014428 0.9988562
summary(model)$adj.r.squared  
## [1] 0.9364598
Anova(model, type = 2)
## Anova Table (Type II tests)
## 
## Response: log(salary)
##                                         Sum Sq Df  F value    Pr(>F)    
## sex                                    0.08817  5  32.2521 7.295e-13 ***
## year_n                                 0.05891  1 107.7412 8.809e-13 ***
## bs(eduyears, knots = c(14))            0.35011  8  80.0434 < 2.2e-16 ***
## sex:year_n                             0.00008  1   0.1517   0.69908    
## sex:bs(eduyears, knots = c(14))        0.00706  4   3.2268   0.02218 *  
## year_n:bs(eduyears, knots = c(14))     0.00179  4   0.8168   0.52231    
## sex:year_n:bs(eduyears, knots = c(14)) 0.00032  4   0.1468   0.96335    
## Residuals                              0.02132 39                       
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
plot_model(model, type = "pred", terms = c("eduyears", "year_n","sex"))
## Model has log-transformed response. Back-transforming predictions to original response scale. Standard errors are still on the log-scale.

SSYK 214, Architects, engineers and related professionals, Year 2014 - 2018

Figure 33: SSYK 214, Architects, engineers and related professionals, Year 2014 – 2018

plot(model, which = 1)

SSYK 214, Architects, engineers and related professionals, Year 2014 - 2018

Figure 34: SSYK 214, Architects, engineers and related professionals, Year 2014 – 2018

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