HW 1
2025-05-05
library(foreign)
library(ltm)## Loading required package: MASS## Loading required package: msm## Loading required package: polycorknitr::opts_chunk$set(echo = TRUE, message = FALSE, warning = FALSE)
df = read.spss("C:/Users/majam/Downloads/ESS11(1).sav", to.data.frame = T)Introduction
Depression is a prevalent mental health condition influenced by a complex interplay of social, economic, and environmental factors (Ali & Kassem, 2021). Understanding these determinants is essential to design effective interventions and policies. This analysis employs the CES-D8 Depression Scale to operationalize depressive symptoms and examines the effects of three social determinants: income perception, social meeting frequency, and childhood household conflicts (European Social Survey, 2022).
df$d20 = as.numeric(df$fltdpr)
df$d21 = as.numeric(df$flteeff)
df$d22 = as.numeric(df$slprl)
df$d23 = as.numeric(df$wrhpp)
df$d24 = as.numeric(df$fltlnl)
df$d25 = as.numeric(df$enjlf)
df$d26 = as.numeric(df$fltsd)
df$d27 = as.numeric(df$cldgng)
df$d23 = 5 - df$d23
df$d25 = 5 - df$d25
df_austria <- df[df$cntry == "Austria", ]
df_austria <- df_austria[, order(names(df_austria))]Variables related to depression were standardized for consistency (e.g., reversing scales for “happy” and “enjoyed life” items).
cronbach.alpha(df_austria[,c("d20", "d21", "d22", "d23", "d24", "d25", "d26", "d27")], na.rm=T)##
## Cronbach's alpha for the 'df_austria[, c("d20", "d21", "d22", "d23", "d24", "d25", "d26", ' ' "d27")]' data-set
##
## Items: 8
## Sample units: 2354
## alpha: 0.801Cronbach’s alpha 0.8009065 was calculated, demonstrating good internal consistency for the depression items. The dataset was subset for Austria, and variables were recoded into numeric formats for analysis.
df_austria$depression = rowSums(df_austria[,c("d20", "d21", "d22", "d23", "d24", "d25", "d26", "d27")]) / 8
summary(df_austria$depression)## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 1.000 1.250 1.500 1.609 1.875 4.000 33#Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
#1.000 1.250 1.500 1.609 1.875 4.000 33
hist(df_austria$depression, breaks=8)
Hypothesis 1:
Individuals with negative feelings about income levels are more likely to experience higher levels of depression. Levels 1 - 4 1: Living comfortable, 2: Coping, 3: Difficult 4: Very difficult
df_austria$hincfel_num <- as.numeric(factor(df_austria$hincfel, levels = c(
"Living comfortably on present income",
"Coping on present income",
"Difficult on present income",
"Very difficult on present income")))
t1 = table(df_austria$depression, df_austria$hincfel_num)
model <- lm(depression ~ hincfel_num, data = df_austria)
summary(model)##
## Call:
## lm(formula = depression ~ hincfel_num, data = df_austria)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.98512 -0.31000 -0.08478 0.24011 2.36511
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.28466 0.02457 52.29 <2e-16 ***
## hincfel_num 0.17511 0.01244 14.08 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4257 on 2305 degrees of freedom
## (47 observations deleted due to missingness)
## Multiple R-squared: 0.07921, Adjusted R-squared: 0.07881
## F-statistic: 198.3 on 1 and 2305 DF, p-value: < 2.2e-16Results Hypothesis 1:
Statistically significant positive relationship between perceived income difficulty and depression. As people perceive their income situation as more difficult, their depression scores tend to increase. The average depression score is 1.6087355. A linear regression predicting depression from perceived income difficulty yielded an intercept of 1.28 and a slope of 0.175. This indicates that each one-step increase in perceived income difficulty increases depression score by 0.175 units. The model is statistically significant (p < <2e-16) with an R² of 0.079, explaining about 7.9% of the variance in depression.
Hypothesis 2
Social Meeting: Lower social activities are associated with higher levels of depression.
df_austria$sclmeet_num <- as.numeric(factor(df_austria$sclmeet, levels = c(
"Never",
"Less than once a month",
"Once a month",
"Several times a month",
"Once a week",
"Several times a week"
)))
df_austria$sclmeet_num = 7 - df_austria$sclmeet_num
plot(df_austria$sclmeet_num, df_austria$depression,
xlab = "Social Meetings (sclmeet_num)",
ylab = "Depression",
main = "Scatterplot of Depression vs. Social Meetings")
abline(lm(depression ~ sclmeet_num, data = df_austria), col = "blue")
model2 <- lm(depression ~ sclmeet_num, data = df_austria)
summary(model2)##
## Call:
## lm(formula = depression ~ sclmeet_num, data = df_austria)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.73724 -0.30439 -0.06653 0.22919 2.44561
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.508672 0.020176 74.777 < 2e-16 ***
## sclmeet_num 0.045713 0.008107 5.639 1.93e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4356 on 2207 degrees of freedom
## (145 observations deleted due to missingness)
## Multiple R-squared: 0.0142, Adjusted R-squared: 0.01375
## F-statistic: 31.79 on 1 and 2207 DF, p-value: 1.933e-08Results Hypothesis 2
A linear regression showed that lower frequency of social meetings
was significantly associated with higher levels of depression.
Specifically, for each unit increase in social isolation
(sclmeet_num), the depression score increased by 0.046
units (t = 5.64, p = <0.001). The model explained
1.4% of the variance in depression.
Hypothesis 3
More frequent serious conflicts in the household during childhood are associated with higher levels of depression in adulthood.
df_austria$cnfpplh_num <- as.numeric(factor(df_austria$cnfpplh, levels = c(
"Always",
"Often",
"Sometimes",
"Hardly ever",
"Never"
)))
df_austria$cnfpplh_num = 6 - df_austria$cnfpplh_num
model3 <- lm(depression ~ cnfpplh_num, data = df_austria)
summary(model3)##
## Call:
## lm(formula = depression ~ cnfpplh_num, data = df_austria)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.9601 -0.3401 -0.1003 0.2697 2.3947
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.360368 0.020537 66.24 <2e-16 ***
## cnfpplh_num 0.119944 0.008948 13.40 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4283 on 2305 degrees of freedom
## (47 observations deleted due to missingness)
## Multiple R-squared: 0.07232, Adjusted R-squared: 0.07192
## F-statistic: 179.7 on 1 and 2305 DF, p-value: < 2.2e-16Results Hypothesis 3
The linear regression revealed that each unit increase in income
difficulty is associated with an average increase in depression score of
0.175, which was statistically significant (p <
2.92^{-43}).
model_multi <- lm(depression ~ hincfel_num + sclmeet_num + cnfpplh_num, data = df_austria)
summary_model <- summary(model_multi)
summary_model##
## Call:
## lm(formula = depression ~ hincfel_num + sclmeet_num + cnfpplh_num,
## data = df_austria)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.92345 -0.28921 -0.07481 0.21690 2.31523
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.012703 0.032125 31.524 < 2e-16 ***
## hincfel_num 0.151676 0.012329 12.302 < 2e-16 ***
## sclmeet_num 0.038815 0.007587 5.116 3.39e-07 ***
## cnfpplh_num 0.109968 0.008812 12.479 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4033 on 2180 degrees of freedom
## (170 observations deleted due to missingness)
## Multiple R-squared: 0.1542, Adjusted R-squared: 0.153
## F-statistic: 132.4 on 3 and 2180 DF, p-value: < 2.2e-16In the multivariate regression model, depression increased by 0.15
points per unit increase in income difficulty,
0.04 per unit less frequent social meetings,
and 0.11 per unit less trust in people.
The model explained 15.4% of the variance in depression scores.