Stepping_Stone_3
Ian_Cheung
2023-12-01
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summary(cars)## speed dist
## Min. : 4.0 Min. : 2.00
## 1st Qu.:12.0 1st Qu.: 26.00
## Median :15.0 Median : 36.00
## Mean :15.4 Mean : 42.98
## 3rd Qu.:19.0 3rd Qu.: 56.00
## Max. :25.0 Max. :120.00Description of Data
Results
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## [31] "methods" "base"france_data <- ess france_data <- ess %>% filter(cntry == "FR")france_data <- ess %>% filter(cntry == "FR") %>% mutate(trstplc = ifelse(trstplc %in% c(77, 88, 99), NA, trstplc))france_data <- france_data %>% filter(cntry == "FR") %>%
mutate(
# Recoding age variable, setting 999 to NA
age = ifelse(agea == 999, NA, agea),
# Recoding cohort variable, setting years before 1900 and after 2000 to NA
cohort = ifelse(yrbrn < 1930 | yrbrn > 2000, NA, yrbrn),
# Recoding generational cohorts based on year of birth
gen = case_when(
yrbrn %in% 1900:1964 ~ "1",
yrbrn %in% 1965:1996 ~ "2",
TRUE ~ as.character(cohort) # Keeping other values as character if they do not fit the ranges
),
# Converting cohort to a factor with labels
gen = factor(gen,
levels = c("1", "2"),
labels = c("youth", "adult"))
)france_data <- france_data %>% filter(cntry == "FR") %>%
# Recoding question of belonging to ethnic minority
mutate(minority = case_when(
blgetmg %in% c(7, 8, 9) ~ NA_character_,
blgetmg == 1 ~ "Ethnic Minority",
blgetmg == 2 ~ "Not Ethnic Minority",
TRUE ~ as.character(blgetmg) # Convert other values to character if necessary
))# here's how to make sure it's really cleaned
france_data <- france_data %>% filter(!is.na(trstplc))
france_data <- france_data %>% filter(!is.na(minority))
france_data <- france_data %>% filter(!is.na(gen))
# double-checking + quick distribution
#unique(france_data$trstplc)
#table(france_data$trstplc)
#table(france_data$gen)#Plotting outcome and explanatory.
ggplot(france_data, mapping = aes(x = gen, fill = trstplc)) + geom_bar()## Warning: The following aesthetics were dropped during statistical transformation: fill
## ℹ This can happen when ggplot fails to infer the correct grouping structure in
## the data.
## ℹ Did you forget to specify a `group` aesthetic or to convert a numerical
## variable into a factor?
france_data_shuffled <- france_data %>%
group_by(gen, trstplc) %>%
tally()
ggplot(france_data_shuffled, mapping = aes(x = gen, fill = trstplc)) + geom_bar()## Warning: The following aesthetics were dropped during statistical transformation: fill
## ℹ This can happen when ggplot fails to infer the correct grouping structure in
## the data.
## ℹ Did you forget to specify a `group` aesthetic or to convert a numerical
## variable into a factor?
# data summary skim
datasummary_skim(france_data %>% select(trstplc, yrbrn, blgetmg))| Unique (#) | Missing (%) | Mean | SD | Min | Median | Max | ||
|---|---|---|---|---|---|---|---|---|
| trstplc | 11 | 0 | 6.0 | 2.2 | 0.0 | 6.0 | 10.0 | |
| yrbrn | 89 | 0 | 1960.1 | 18.3 | 1905.0 | 1960.0 | 1996.0 | |
| blgetmg | 2 | 0 | 2.0 | 0.2 | 1.0 | 2.0 | 2.0 |
#Cleaning average trust in police by summarizing averages, grouping by al countries, filtering answers with refusal, don't know, and No answer.
country_averages <- ess %>%
filter(!(trstplc %in% c(77, 88, 99))) %>%
group_by(cntry) %>%
summarize(avg_trstplc = mean(trstplc, na.rm = TRUE))
# Reorder the factor levels of 'cntry' based on 'avg_trstplc'
country_averages$cntry <- reorder(country_averages$cntry, country_averages$avg_trstplc)
# Plotting the factor levels of 'cntry' based on 'avg_trstplc.'
Main_Trend_of_Country_Feeling_Close_to_Trust_in_Police <- ggplot(country_averages, aes(x = cntry, y = avg_trstplc, label = cntry)) +
geom_point(aes(color = avg_trstplc), size = 3) +
geom_text(nudge_y = 0.2, size = 3) +
labs(
x = "Country",
y = "Average Trust in Police",
title = "Main Trend of Average Trust in Police by Country"
) +
scale_color_gradient(low = "green", high = "darkgreen") +
geom_line(aes(group = 1), color = "darkgreen", linetype = "dashed")
theme_minimal() +
theme(
axis.text.x = element_blank(),
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## - attr(*, "complete")= logi TRUE
## - attr(*, "validate")= logi TRUE print(Main_Trend_of_Country_Feeling_Close_to_Trust_in_Police)
#print("Bivariate statistics and visualizations")
table(france_data$trstplc, france_data$gen) %>%
cprop()##
## youth adult All
## 0 2.4 3.5 2.9
## 1 1.6 1.8 1.7
## 2 3.6 4.0 3.8
## 3 5.5 6.1 5.8
## 4 6.9 7.4 7.1
## 5 18.1 17.1 17.7
## 6 14.1 14.3 14.2
## 7 18.7 20.6 19.5
## 8 19.9 16.6 18.5
## 9 5.3 5.5 5.4
## 10 4.0 3.1 3.6
## Total 100.0 100.0 100.0filtered_data_cleaned <- france_data %>% filter(!is.na(trstplc), !is.na(gen))
# Compute percentages
percentages <- filtered_data_cleaned %>%
group_by(gen, trstplc) %>%
summarise(n = n()) %>%
mutate(percentage = n/sum(n)*100)## `summarise()` has grouped output by 'gen'. You can override using the `.groups`
## argument.## `summarise()` has grouped output by 'wrkorg_recode'. You can override using the
#Check#unique(filtered_data_cleaned$gen)
## `.groups` argument.
Percentage_of_Attitudes_Towards_Police_by_Generations <- ggplot(percentages, aes(x = as.factor(gen), y = percentage, fill = factor(trstplc))) +
geom_bar(stat = "identity", position = position_dodge(width = 0.9), width = 0.7) +
geom_text(aes(label = paste0(round(percentage, 1), "%"), group = trstplc),
position = position_dodge(width = 0.9), vjust = -0.5, size = 3) + # Add rounded percentage labels
labs(title = "Percentage of Attitudes Towards Police by Generations",
x = "Attitude towards Police",
y = "Percentage (%)") +
scale_x_discrete(breaks = c("youth", "adult"), labels = c("youth", "adult")) +
scale_fill_manual(values = c("10" = "lightgreen", "9" = "lightgreen", "8" = "lightgreen", "7" = "lightgreen", "6" = "lightgreen", "5" = "lightgreen", "4" = "lightgreen", "3" = "lightgreen", "2" = "lightgreen", "1" = "lightgreen", "0" = "lightgreen"),
name = "Trust in Police Levels") +
theme_minimal()
print(Percentage_of_Attitudes_Towards_Police_by_Generations)
# Step 1: Calculate the test statistic of your sample
test_stat <- france_data %>%
specify(explanatory = gen, # change variable name for explanatory variable
response = trstplc) %>% # change variable name for outcome of interest
hypothesize(null = "independence") %>%
calculate(stat = "t") # replace in between quotation marks appropriate test statistic## Warning: The statistic is based on a difference or ratio; by default, for
## difference-based statistics, the explanatory variable is subtracted in the
## order "youth" - "adult", or divided in the order "youth" / "adult" for
## ratio-based statistics. To specify this order yourself, supply `order =
## c("youth", "adult")` to the calculate() function.print(test_stat$stat)## t
## 5.407069# Step 2: Simulate the null distribution
null_distribution_gen<- france_data %>%
specify(explanatory = gen,
response = trstplc) %>%
hypothesize(null = "independence") %>%
generate(reps = 1000, type = "permute") %>% # only line we are adding, use reps = 1000 as standard
calculate( stat = "t", order = c("youth", "adult"))
null_distribution_gen## Response: trstplc (numeric)
## Explanatory: gen (factor)
## Null Hypothesis: independence
## # A tibble: 1,000 × 2
## replicate stat
## <int> <dbl>
## 1 1 1.57
## 2 2 0.756
## 3 3 0.371
## 4 4 0.0688
## 5 5 0.775
## 6 6 -0.485
## 7 7 0.223
## 8 8 0.329
## 9 9 0.678
## 10 10 -2.05
## # ℹ 990 more rows# Step 3: Calculate the p-value of your sample
p_val_gen <- null_distribution_gen %>% # replace name here if you assigned something other than null_distribution above
get_pvalue(obs_stat = test_stat, direction = "two-sided") # would only replace test_stat if assigned another name in Step 1## Warning: Please be cautious in reporting a p-value of 0. This result is an
## approximation based on the number of `reps` chosen in the `generate()` step.
## See `?get_p_value()` for more information.p_val_gen## # A tibble: 1 × 1
## p_value
## <dbl>
## 1 0# Step 4: Visualize
null_distribution_gen %>%
visualize() +
shade_p_value(obs_stat = test_stat, direction = "two-sided")
null_distribution_gen## Response: trstplc (numeric)
## Explanatory: gen (factor)
## Null Hypothesis: independence
## # A tibble: 1,000 × 2
## replicate stat
## <int> <dbl>
## 1 1 1.57
## 2 2 0.756
## 3 3 0.371
## 4 4 0.0688
## 5 5 0.775
## 6 6 -0.485
## 7 7 0.223
## 8 8 0.329
## 9 9 0.678
## 10 10 -2.05
## # ℹ 990 more rows#We can also visualize alongside confidence intervals
conf_int <- null_distribution_gen %>%
get_confidence_interval(level = 0.95, type = "percentile")
null_distribution_gen %>%
visualize() +
shade_p_value(obs_stat = test_stat, direction = "two-sided") +
shade_confidence_interval(endpoints = conf_int)
null_distribution_gen## Response: trstplc (numeric)
## Explanatory: gen (factor)
## Null Hypothesis: independence
## # A tibble: 1,000 × 2
## replicate stat
## <int> <dbl>
## 1 1 1.57
## 2 2 0.756
## 3 3 0.371
## 4 4 0.0688
## 5 5 0.775
## 6 6 -0.485
## 7 7 0.223
## 8 8 0.329
## 9 9 0.678
## 10 10 -2.05
## # ℹ 990 more rows## Three models
# List of packages
packages <- c("tidyverse", "infer", "fst", "modelsummary", "effects", "survey", "MASS") # add any you need here
# Install packages if they aren't installed already
new_packages <- packages[!(packages %in% installed.packages()[,"Package"])]
if(length(new_packages)) install.packages(new_packages)
# Load the packages
lapply(packages, library, character.only = TRUE)## Loading required package: grid## Loading required package: Matrix##
## Attaching package: 'Matrix'## The following objects are masked from 'package:tidyr':
##
## expand, pack, unpack## Loading required package: survival##
## Attaching package: 'survey'## The following object is masked from 'package:graphics':
##
## dotchart##
## Attaching package: 'MASS'## The following object is masked from 'package:dplyr':
##
## select## [[1]]
## [1] "fstcore" "questionr" "ggridges" "rmarkdown" "kableExtra"
## [6] "knitr" "viridis" "viridisLite" "RColorBrewer" "effects"
## [11] "carData" "modelsummary" "fst" "infer" "lubridate"
## [16] "forcats" "stringr" "dplyr" "purrr" "readr"
## [21] "tidyr" "tibble" "ggplot2" "tidyverse" "broom"
## [26] "flextable" "stats" "graphics" "grDevices" "utils"
## [31] "datasets" "methods" "base"
##
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## [16] "forcats" "stringr" "dplyr" "purrr" "readr"
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## [11] "carData" "modelsummary" "fst" "infer" "lubridate"
## [16] "forcats" "stringr" "dplyr" "purrr" "readr"
## [21] "tidyr" "tibble" "ggplot2" "tidyverse" "broom"
## [26] "flextable" "stats" "graphics" "grDevices" "utils"
## [31] "datasets" "methods" "base"
##
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## [16] "forcats" "stringr" "dplyr" "purrr" "readr"
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## [26] "flextable" "stats" "graphics" "grDevices" "utils"
## [31] "datasets" "methods" "base"
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## [21] "stringr" "dplyr" "purrr" "readr" "tidyr"
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##
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## [1] "MASS" "survey" "survival" "Matrix" "grid"
## [6] "fstcore" "questionr" "ggridges" "rmarkdown" "kableExtra"
## [11] "knitr" "viridis" "viridisLite" "RColorBrewer" "effects"
## [16] "carData" "modelsummary" "fst" "infer" "lubridate"
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## [26] "tidyr" "tibble" "ggplot2" "tidyverse" "broom"
## [31] "flextable" "stats" "graphics" "grDevices" "utils"
## [36] "datasets" "methods" "base"model1 <- lm(trstplc ~ gen, data = france_data)
model2 <- lm(trstplc ~ gen + minority, data = france_data)
model3 <- lm(trstplc ~ gen + minority + gen*minority, data = france_data)
modelsummary(
list(model1, model2, model3))| (1) | (2) | (3) | |
|---|---|---|---|
| (Intercept) | 6.055 | 5.652 | 5.570 |
| (0.023) | (0.089) | (0.139) | |
| genadult | −0.192 | −0.178 | −0.044 |
| (0.035) | (0.035) | (0.177) | |
| minorityNot Ethnic Minority | 0.413 | 0.498 | |
| (0.088) | (0.141) | ||
| genadult × minorityNot Ethnic Minority | −0.140 | ||
| (0.181) | |||
| Num.Obs. | 16511 | 16511 | 16511 |
| R2 | 0.002 | 0.003 | 0.003 |
| R2 Adj. | 0.002 | 0.003 | 0.003 |
| AIC | 73493.6 | 73473.8 | 73475.2 |
| BIC | 73516.8 | 73504.6 | 73513.7 |
| Log.Lik. | −36743.817 | −36732.881 | −36732.584 |
| RMSE | 2.24 | 2.24 | 2.24 |
model4 <- lm(trstplc ~ minority, data = france_data)
model5 <- lm(trstplc ~ minority + gen, data = france_data)
model6 <- lm(trstplc ~ minority + gen + minority*gen, data = france_data)
modelsummary(
list(model4, model5, model6))| (1) | (2) | (3) | |
|---|---|---|---|
| (Intercept) | 5.542 | 5.652 | 5.570 |
| (0.086) | (0.089) | (0.139) | |
| minorityNot Ethnic Minority | 0.449 | 0.413 | 0.498 |
| (0.088) | (0.088) | (0.141) | |
| genadult | −0.178 | −0.044 | |
| (0.035) | (0.177) | ||
| minorityNot Ethnic Minority × genadult | −0.140 | ||
| (0.181) | |||
| Num.Obs. | 16511 | 16511 | 16511 |
| R2 | 0.002 | 0.003 | 0.003 |
| R2 Adj. | 0.002 | 0.003 | 0.003 |
| AIC | 73497.3 | 73473.8 | 73475.2 |
| BIC | 73520.4 | 73504.6 | 73513.7 |
| Log.Lik. | −36745.632 | −36732.881 | −36732.584 |
| RMSE | 2.24 | 2.24 | 2.24 |
modelsummary(
list(model1, model2, model3),
fmt = 1,
estimate = c( "{estimate} ({std.error}){stars}",
"{estimate} ({std.error}){stars}",
"{estimate} ({std.error}){stars}"),
statistic = NULL,
coef_omit = "Intercept")| (1) | (2) | (3) | |
|---|---|---|---|
| genadult | −0.2 (0.0)*** | −0.2 (0.0)*** | 0.0 (0.2) |
| minorityNot Ethnic Minority | 0.4 (0.1)*** | 0.5 (0.1)*** | |
| genadult × minorityNot Ethnic Minority | −0.1 (0.2) | ||
| Num.Obs. | 16511 | 16511 | 16511 |
| R2 | 0.002 | 0.003 | 0.003 |
| R2 Adj. | 0.002 | 0.003 | 0.003 |
| AIC | 73493.6 | 73473.8 | 73475.2 |
| BIC | 73516.8 | 73504.6 | 73513.7 |
| Log.Lik. | −36743.817 | −36732.881 | −36732.584 |
| RMSE | 2.24 | 2.24 | 2.24 |
### Seperate here
# We use the "effect" function to call the interaction term from model 1. We assign the results to "effect_plot"
interaction_plot_1 <- effect("gen", model1, na.rm=TRUE)
#We plot here the interaction term
plot(interaction_plot_1,
main="Interaction effect the youth and adult x minority status",
xlab="the youth and adult",
ylab="Trust in Police")
# We use the "effect" function to call the interaction term from model 2. We assign the results to "effect_plot"
interaction_plot_2 <- effect("gen*minority", model2, na.rm=TRUE)## NOTE: gen:minority does not appear in the model#We plot here the interaction term
plot(interaction_plot_2,
main="Interaction effect the youth and adult x minority status",
xlab="the youth and adult",
ylab="Trust in Police")
# We use the "effect" function to call the interaction term from model 3. We assign the results to "effect_plot"
interaction_plot_3 <- effect("gen*minority", model3, na.rm=TRUE)
#We plot here the interaction term
plot(interaction_plot_3,
main="Interaction effect the youth and adult x minority status",
xlab="the youth and adult",
ylab="Trust in Police")
# Now, let's extract just the coefficients
coefficients1 <- coef(model1)
print(coefficients1)## (Intercept) genadult
## 6.0546223 -0.1915794coefficients2 <- coef(model2)
print(coefficients2)## (Intercept) genadult
## 5.6524164 -0.1784969
## minorityNot Ethnic Minority
## 0.4134766coefficients3 <- coef(model3)
print(coefficients3)## (Intercept) genadult
## 5.56976744 -0.04446624
## minorityNot Ethnic Minority genadult:minorityNot Ethnic Minority
## 0.49844153 -0.13956237#For example, for my own interpretation
#(intercept of education level)
#if a person has a BA= 8.257593
#If a person has no BA= 8.257593
#if a person is a male= 8.1828554
#If a person is a female= 8.1828554 -0.1502479
#If a person has paid work= 8.0712298
#If a person has no paid work= 8.0712298 + 0.0721098
# A first crack at a table output
tidy(model1)## # A tibble: 2 × 5
## term estimate std.error statistic p.value
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 (Intercept) 6.05 0.0230 263. 0
## 2 genadult -0.192 0.0352 -5.44 0.0000000555tidy(model2)## # A tibble: 3 × 5
## term estimate std.error statistic p.value
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 (Intercept) 5.65 0.0890 63.5 0
## 2 genadult -0.178 0.0353 -5.05 0.000000443
## 3 minorityNot Ethnic Minority 0.413 0.0884 4.68 0.00000292tidy(model3)## # A tibble: 4 × 5
## term estimate std.error statistic p.value
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 (Intercept) 5.57 0.139 40.0 0
## 2 genadult -0.0445 0.177 -0.251 0.802
## 3 minorityNot Ethnic Minority 0.498 0.141 3.53 0.000421
## 4 genadult:minorityNot Ethnic Minority -0.140 0.181 -0.771 0.441# Striving to improve table presentation
tidy(model1) |>
knitr::kable (digits = 3)| term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|
| (Intercept) | 6.055 | 0.023 | 262.950 | 0 |
| genadult | -0.192 | 0.035 | -5.435 | 0 |
tidy(model2) |>
knitr::kable(digits = 3)| term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|
| (Intercept) | 5.652 | 0.089 | 63.507 | 0 |
| genadult | -0.178 | 0.035 | -5.051 | 0 |
| minorityNot Ethnic Minority | 0.413 | 0.088 | 4.678 | 0 |
tidy(model3) |>
knitr::kable(digits = 3)| term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|
| (Intercept) | 5.570 | 0.139 | 39.961 | 0.000 |
| genadult | -0.044 | 0.177 | -0.251 | 0.802 |
| minorityNot Ethnic Minority | 0.498 | 0.141 | 3.527 | 0.000 |
| genadult:minorityNot Ethnic Minority | -0.140 | 0.181 | -0.771 | 0.441 |
# The full summary output
summary(model1)##
## Call:
## lm(formula = trstplc ~ gen, data = france_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.055 -1.055 0.137 1.945 4.137
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.05462 0.02303 262.950 < 2e-16 ***
## genadult -0.19158 0.03525 -5.435 5.55e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.24 on 16509 degrees of freedom
## Multiple R-squared: 0.001786, Adjusted R-squared: 0.001726
## F-statistic: 29.54 on 1 and 16509 DF, p-value: 5.55e-08summary(model2)##
## Call:
## lm(formula = trstplc ~ gen + minority, data = france_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.0659 -1.0659 0.1126 1.9341 4.5261
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.65242 0.08900 63.507 < 2e-16 ***
## genadult -0.17850 0.03534 -5.051 4.43e-07 ***
## minorityNot Ethnic Minority 0.41348 0.08839 4.678 2.92e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.239 on 16508 degrees of freedom
## Multiple R-squared: 0.003108, Adjusted R-squared: 0.002987
## F-statistic: 25.73 on 2 and 16508 DF, p-value: 6.956e-12summary(model3)##
## Call:
## lm(formula = trstplc ~ gen + minority + gen * minority, data = france_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.0682 -1.0682 0.1158 1.9318 4.4747
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.56977 0.13938 39.961 < 2e-16 ***
## genadult -0.04447 0.17749 -0.251 0.802184
## minorityNot Ethnic Minority 0.49844 0.14132 3.527 0.000421 ***
## genadult:minorityNot Ethnic Minority -0.13956 0.18112 -0.771 0.440978
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.239 on 16507 degrees of freedom
## Multiple R-squared: 0.003144, Adjusted R-squared: 0.002962
## F-statistic: 17.35 on 3 and 16507 DF, p-value: 3.032e-11# Using modelsummary for prettier table, focusing here on just R squared and adj.
modelsummary::modelsummary(
list(model1),
gof_map = c("nobs", "r.squared", "adj.r.squared"))| (1) | |
|---|---|
| (Intercept) | 6.055 |
| (0.023) | |
| genadult | −0.192 |
| (0.035) | |
| Num.Obs. | 16511 |
| R2 | 0.002 |
| R2 Adj. | 0.002 |
modelsummary::modelsummary(
list(model2),
gof_map = c("nobs", "r.squared", "adj.r.squared"))| (1) | |
|---|---|
| (Intercept) | 5.652 |
| (0.089) | |
| genadult | −0.178 |
| (0.035) | |
| minorityNot Ethnic Minority | 0.413 |
| (0.088) | |
| Num.Obs. | 16511 |
| R2 | 0.003 |
| R2 Adj. | 0.003 |
modelsummary::modelsummary(
list(model3),
gof_map = c("nobs", "r.squared", "adj.r.squared"))| (1) | |
|---|---|
| (Intercept) | 5.570 |
| (0.139) | |
| genadult | −0.044 |
| (0.177) | |
| minorityNot Ethnic Minority | 0.498 |
| (0.141) | |
| genadult × minorityNot Ethnic Minority | −0.140 |
| (0.181) | |
| Num.Obs. | 16511 |
| R2 | 0.003 |
| R2 Adj. | 0.003 |
## Finally, Getting equation output with equatiomatic
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## ## Installing package into 'C:/Users/Owner/AppData/Local/R/win-library/4.3'
## (as 'lib' is unspecified)equatiomatic::extract_eq(model1, use_coefs = TRUE)\[ \operatorname{\widehat{trstplc}} = 6.05 - 0.19(\operatorname{gen}_{\operatorname{adult}}) \]
equatiomatic::extract_eq(model2, use_coefs = TRUE)\[ \operatorname{\widehat{trstplc}} = 5.65 - 0.18(\operatorname{gen}_{\operatorname{adult}}) + 0.41(\operatorname{minority}_{\operatorname{Not\ Ethnic\ Minority}}) \]
equatiomatic::extract_eq(model3, use_coefs = TRUE)\[ \operatorname{\widehat{trstplc}} = 5.57 - 0.04(\operatorname{gen}_{\operatorname{adult}}) + 0.5(\operatorname{minority}_{\operatorname{Not\ Ethnic\ Minority}}) - 0.14(\operatorname{gen}_{\operatorname{adult}} \times \operatorname{minority}_{\operatorname{Not\ Ethnic\ Minority}}) \]