Data on homelessness in the U.S.
Open up a new .Rmd file.
Use {r setup, include=F} in your first code chunk.
knitr::opts_chunk$set(echo = TRUE)
# Load necessary libraries
library(knitr)
library(kableExtra)
library(tidyverse)## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr 1.1.4 ✔ readr 2.1.5
## ✔ forcats 1.0.0 ✔ stringr 1.5.1
## ✔ ggplot2 3.5.1 ✔ tibble 3.2.1
## ✔ lubridate 1.9.3 ✔ tidyr 1.3.1
## ✔ purrr 1.0.2
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::group_rows() masks kableExtra::group_rows()
## ✖ dplyr::lag() masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorslibrary(readr)
library(dplyr)
library(tidyr)Scraping some data from online here.
Generating the table:
# Load necessary libraries
library(readr)
library(knitr)
library(kableExtra)
# Define the cleaned CSV formatted data
csv_data <- "state,tot_homeless_2023,pct_change_since_2022,pct_under_18,ptc_veterans,ptc_chronic_homelessness
Alaska,2614,13%,14%,5%,30%
Alabama,3304,-12%,17%,9%,22%
Arkansas,2609,6%,12%,8%,34%
Arizona,14237,5%,11%,7%,22%
California,181399,6%,9%,6%,39%
Colorado,14439,39%,16%,7%,31%
Connecticut,3015,3%,19%,5%,4%
District_of_Columbia,4922,12%,15%,4%,28%
Delaware,1245,-47%,27%,6%,14%
Florida,30756,18%,16%,8%,19%
Georgia,12294,15%,19%,6%,14%
Hawaii,6223,4%,15%,5%,26%
Iowa,2653,10%,19%,5%,20%
Idaho,2298,15%,20%,8%,18%
Illinois,11947,30%,20%,4%,12%
Indiana,6017,10%,20%,8%,12%
Kansas,2636,10%,17%,8%,18%
Kentucky,4766,20%,12%,9%,20%
Louisiana,3169,-57%,12%,8%,14%
Massachusetts,19141,23%,39%,3%,14%
Maryland,5865,10%,20%,5%,18%
Maine,4258,-3%,29%,3%,9%
Michigan,8997,10%,25%,5 %,13%
Minnesota,8393 ,6 %,28 %,4 %,24 %
Missouri ,6708 ,12 %,18 %,8 %,24 %
Mississippi ,982 ,-18 %,13 %,6 %,13 %
Montana ,2178 ,37 %,14 %,10 %,26 %
North_Carolina ,9754 ,4 %,17 %,8 %,17 %
North_Dakota ,784 ,29 %,17 %,3 %,22 %
Nebraska ,2462 ,10 %,17 %,5 %,25 %
New_Hampshire ,2441 ,52 %,18 %,4 %,22 %
New_Jersey ,10264 ,17 %,24 %,4 %,19 %
New_Mexico ,3842 ,50 %,18 %,7 %,44 %
Nevada ,8666 ,14 %,8 %,13 %,28 %
New_York ,103200 ,39 %,28 %,1 %,6 %
Ohio ,11386 ,7 %,18 %,5 %,11 %
Oklahoma ,-4648 ,-24 ,-13 ,-6 ,-30
Oregon ,-20142 ,-12 ,-13 ,-8 ,-34
Pennsylvania ,-12556 ,-1 ,-21 ,-7 ,-16
Rhode_Island ,-1810 ,-15 ,-21 ,-6 ,-35
South_Carolina ,-4053 ,-12 ,-13 ,-10 ,-21
South_Dakota ,-1282 ,-8 ,-16 ,-5 ,-18
Tennessee ,-9215 ,-13 ,-11 ,-8 ,-22
Texas ,-27377 ,-12 ,-15 ,-7 ,-18
Utah ,-3687 ,-4 ,-16 ,-5 ,-27
Virginia ,-6761 ,-4 ,-23 ,-6 ,-16
Vermont,-3295,-19,-20,-4,-8
Washington,-28036,-11,-16,-6,-31
Wisconsin,-4861,-2,-24,-7,-12
West_Virginia,-1416,-3,-9,-6,-18
Wyoming,532,-18,-7,-17,-14"
# Read the CSV formatted data into a data frame
data <- read.csv(text = csv_data)
# Clean up percentage columns by removing '%' and converting to numeric
percentage_columns <- c("pct_change_since_2022", "pct_under_18", "ptc_veterans", "ptc_chronic_homelessness")
for (col in percentage_columns) {
data[[col]] <- as.numeric(gsub("%", "", data[[col]]))
}
# Example of safely adding a new column based on existing data:
data$new_column <- NA # Initialize the new column first
# Assign values based on a condition (for demonstration)
data$new_column[which(data$tot_homeless_2023 > 10000)] <- "High"
data$new_column[which(data$tot_homeless_2023 <= 10000)] <- "Low"
# Create a Kable table for the data frame with enhanced formatting for web display
kbl(data,
format = "html",
caption = "Homelessness Data by State (2023)",
escape = FALSE) %>%
kable_styling(
bootstrap_options = c("striped", "hover", "condensed", "responsive"),
full_width = TRUE,
position = "center"
) %>%
column_spec(1:6,
width = "auto") %>% # Adjust column widths as needed
row_spec(0,
bold = TRUE,
color = "white",
background = "#007bff") # Header styling| state | tot_homeless_2023 | pct_change_since_2022 | pct_under_18 | ptc_veterans | ptc_chronic_homelessness | new_column |
|---|---|---|---|---|---|---|
| Alaska | 2614 | 13 | 14 | 5 | 30 | Low |
| Alabama | 3304 | -12 | 17 | 9 | 22 | Low |
| Arkansas | 2609 | 6 | 12 | 8 | 34 | Low |
| Arizona | 14237 | 5 | 11 | 7 | 22 | High |
| California | 181399 | 6 | 9 | 6 | 39 | High |
| Colorado | 14439 | 39 | 16 | 7 | 31 | High |
| Connecticut | 3015 | 3 | 19 | 5 | 4 | Low |
| District_of_Columbia | 4922 | 12 | 15 | 4 | 28 | Low |
| Delaware | 1245 | -47 | 27 | 6 | 14 | Low |
| Florida | 30756 | 18 | 16 | 8 | 19 | High |
| Georgia | 12294 | 15 | 19 | 6 | 14 | High |
| Hawaii | 6223 | 4 | 15 | 5 | 26 | Low |
| Iowa | 2653 | 10 | 19 | 5 | 20 | Low |
| Idaho | 2298 | 15 | 20 | 8 | 18 | Low |
| Illinois | 11947 | 30 | 20 | 4 | 12 | High |
| Indiana | 6017 | 10 | 20 | 8 | 12 | Low |
| Kansas | 2636 | 10 | 17 | 8 | 18 | Low |
| Kentucky | 4766 | 20 | 12 | 9 | 20 | Low |
| Louisiana | 3169 | -57 | 12 | 8 | 14 | Low |
| Massachusetts | 19141 | 23 | 39 | 3 | 14 | High |
| Maryland | 5865 | 10 | 20 | 5 | 18 | Low |
| Maine | 4258 | -3 | 29 | 3 | 9 | Low |
| Michigan | 8997 | 10 | 25 | 5 | 13 | Low |
| Minnesota | 8393 | 6 | 28 | 4 | 24 | Low |
| Missouri | 6708 | 12 | 18 | 8 | 24 | Low |
| Mississippi | 982 | -18 | 13 | 6 | 13 | Low |
| Montana | 2178 | 37 | 14 | 10 | 26 | Low |
| North_Carolina | 9754 | 4 | 17 | 8 | 17 | Low |
| North_Dakota | 784 | 29 | 17 | 3 | 22 | Low |
| Nebraska | 2462 | 10 | 17 | 5 | 25 | Low |
| New_Hampshire | 2441 | 52 | 18 | 4 | 22 | Low |
| New_Jersey | 10264 | 17 | 24 | 4 | 19 | High |
| New_Mexico | 3842 | 50 | 18 | 7 | 44 | Low |
| Nevada | 8666 | 14 | 8 | 13 | 28 | Low |
| New_York | 103200 | 39 | 28 | 1 | 6 | High |
| Ohio | 11386 | 7 | 18 | 5 | 11 | High |
| Oklahoma | -4648 | -24 | -13 | -6 | -30 | Low |
| Oregon | -20142 | -12 | -13 | -8 | -34 | Low |
| Pennsylvania | -12556 | -1 | -21 | -7 | -16 | Low |
| Rhode_Island | -1810 | -15 | -21 | -6 | -35 | Low |
| South_Carolina | -4053 | -12 | -13 | -10 | -21 | Low |
| South_Dakota | -1282 | -8 | -16 | -5 | -18 | Low |
| Tennessee | -9215 | -13 | -11 | -8 | -22 | Low |
| Texas | -27377 | -12 | -15 | -7 | -18 | Low |
| Utah | -3687 | -4 | -16 | -5 | -27 | Low |
| Virginia | -6761 | -4 | -23 | -6 | -16 | Low |
| Vermont | -3295 | -19 | -20 | -4 | -8 | Low |
| Washington | -28036 | -11 | -16 | -6 | -31 | Low |
| Wisconsin | -4861 | -2 | -24 | -7 | -12 | Low |
| West_Virginia | -1416 | -3 | -9 | -6 | -18 | Low |
| Wyoming | 532 | -18 | -7 | -17 | -14 | Low |
PIT and HIC data can be found here.
The Point-in-Time (PIT) Count is an annual survey to estimate the number of individuals experiencing homelessness in the United States on a single night. This count includes both sheltered individuals in emergency shelters and transitional housing, as well as unsheltered individuals living in places not meant for habitation.
# Install the readxlsb package if not already installed
# install.packages("readxlsb")
# Load the readxlsb library
library(readxlsb)
# Read the .xlsb file from the URL
url <- "https://www.huduser.gov/portal/sites/default/files/xls/2007-2023-PIT-Counts-by-State.xlsb"
# Download the ZIP file
download.file(url, destfile = "pit_2017_2013_csv.zip")
# Unzip the file
unzip("pit_2017_2013_csv.zip", exdir = "homeless_data")
# List the contents of the unzipped directory
files <- list.files("homeless_data", full.names = TRUE)
print(files)## [1] "homeless_data/_rels" "homeless_data/[Content_Types].xml"
## [3] "homeless_data/customXml" "homeless_data/docProps"
## [5] "homeless_data/xl"# Read a specific CSV file (replace 'your_file.csv' with the actual filename)
# data <- read_csv("homeless_data/xl")The 2023 HIC (Raw File) refers to the Housing Inventory Count (HIC) data, a component of the U.S. Department of Housing and Urban Development’s (HUD) efforts to track homelessness. The HIC provides a snapshot of the number of beds available in emergency shelters, transitional housing, and other supportive housing programs at a specific point in time.
This file is provided as a preliminary resource until official data
is added to the critstats package. You may also use this
code to gather data related to your class project, thesis, or other
academic tasks beyond what is provided below. Content in this file comes
from a host of different sources which you should be familiar with prior
to access and analyzing any data.
# Load necessary library
# install.packages("readr") # Uncomment if 'readr' is not installed
library(readr)
# Read the CSV file from GitHub
hic <- read_csv("https://raw.githubusercontent.com/professornaite/critstats/main/data-raw/HIC-counts-by-state-2023.csv")## Rows: 28871 Columns: 103
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (26): CocState, CoC, HudNum, Status, Organization Name, HMIS Org ID, use...
## dbl (76): Row #, Coc_ID, year, Organization ID, Project ID, Geo Code, HMIS P...
## lgl (1): mergedDefunctYear
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.# View the first few rows of the data
head(hic)## # A tibble: 6 × 103
## `Row #` CocState CoC Coc_ID HudNum Status year `Organization ID`
## <dbl> <chr> <chr> <dbl> <chr> <chr> <dbl> <dbl>
## 1 616866 OH Akron, Barberto… 1350 OH-506 Compl… 2023 495
## 2 616875 OH Akron, Barberto… 1350 OH-506 Compl… 2023 495
## 3 616890 OH Akron, Barberto… 1350 OH-506 Compl… 2023 495
## 4 616923 OH Akron, Barberto… 1350 OH-506 Compl… 2023 45277
## 5 703040 OH Akron, Barberto… 1350 OH-506 Compl… 2023 45277
## 6 703010 OH Akron, Barberto… 1350 OH-506 Compl… 2023 8321
## # ℹ 95 more variables: `Organization Name` <chr>, `HMIS Org ID` <chr>,
## # useHmisDb <chr>, `Project ID` <dbl>, `Project Name` <chr>,
## # `HMIS Project ID` <chr>, `HIC Date` <chr>, `Project Type` <chr>,
## # `Bed Type` <chr>, `Geo Code` <dbl>, `HMIS Participating` <dbl>,
## # `Inventory Type` <chr>, beginsOperationsWithinYear <dbl>,
## # `Target Population` <chr>, mcKinneyVentoEsg <dbl>,
## # mcKinneyVentoEsgEs <dbl>, mcKinneyVentoEsgRrh <dbl>, …tail(hic)## # A tibble: 6 × 103
## `Row #` CocState CoC Coc_ID HudNum Status year `Organization ID`
## <dbl> <chr> <chr> <dbl> <chr> <chr> <dbl> <dbl>
## 1 656633 WY Wyoming Statewi… 1269 WY-500 Compl… 2023 38857
## 2 610893 WY Wyoming Statewi… 1269 WY-500 Compl… 2023 41520
## 3 610880 WY Wyoming Statewi… 1269 WY-500 Compl… 2023 18486
## 4 610830 WY Wyoming Statewi… 1269 WY-500 Compl… 2023 18486
## 5 610881 WY Wyoming Statewi… 1269 WY-500 Compl… 2023 18486
## 6 656634 WY Wyoming Statewi… 1269 WY-500 Compl… 2023 7628
## # ℹ 95 more variables: `Organization Name` <chr>, `HMIS Org ID` <chr>,
## # useHmisDb <chr>, `Project ID` <dbl>, `Project Name` <chr>,
## # `HMIS Project ID` <chr>, `HIC Date` <chr>, `Project Type` <chr>,
## # `Bed Type` <chr>, `Geo Code` <dbl>, `HMIS Participating` <dbl>,
## # `Inventory Type` <chr>, beginsOperationsWithinYear <dbl>,
## # `Target Population` <chr>, mcKinneyVentoEsg <dbl>,
## # mcKinneyVentoEsgEs <dbl>, mcKinneyVentoEsgRrh <dbl>, …Data from the homelessdata site can be accessed for summary statistics.
Below are test/pseudo data for model building.
In this analysis, we aim to assess the intersectional relationships between race and gender in predicting homelessness status using logistic regression. The following steps outline the process and mathematical functions used in R.
First, we convert the categorical variables for race and gender into factors to ensure proper handling in the logistic regression model.
# Convert categorical variables to factors
df1$Race <- as.factor(df1$Race)
df1$Gender <- as.factor(df1$Gender)We fit a logistic regression model using the generalized linear model (GLM) function. The logistic regression model can be mathematically expressed as:
\[ \text{logit}(p) = \ln\left(\frac{p}{1-p}\right) = \beta_0 + \beta_1 \text{Race} + \beta_2 \text{Gender} + \beta_3 (\text{Race} \times \text{Gender}) \]
where:
\(p\) is the probability of experiencing homelessness,
\(\beta_0\) is the intercept,
\(\beta_1, \beta_2,\) and \(\beta_3\) are coefficients for race, gender, and their interaction, respectively.
The model is fitted using:
# Fit the logistic regression model
model1 <- glm(Homelessness_Status ~ Race * Gender, data = df1, family = binomial)Model Summary
After fitting the model, we can summarize its results to understand the relationship between race, gender, and homelessness status:
# Summary of the model
summary(model1)##
## Call:
## glm(formula = Homelessness_Status ~ Race * Gender, family = binomial,
## data = df1)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.62571 0.25833 -2.422 0.0154 *
## RaceBlack 0.44982 0.37075 1.213 0.2250
## RaceHispanic 0.59396 0.36089 1.646 0.0998 .
## RaceOther 0.65469 0.35315 1.854 0.0638 .
## RaceWhite 0.62571 0.36837 1.699 0.0894 .
## GenderMale 0.56687 0.35441 1.599 0.1097
## GenderNon-Binary 0.73107 0.37028 1.974 0.0483 *
## RaceBlack:GenderMale 0.07903 0.50049 0.158 0.8745
## RaceHispanic:GenderMale -0.44550 0.49894 -0.893 0.3719
## RaceOther:GenderMale -0.59585 0.49236 -1.210 0.2262
## RaceWhite:GenderMale -0.53788 0.50255 -1.070 0.2845
## RaceBlack:GenderNon-Binary -0.17381 0.51762 -0.336 0.7370
## RaceHispanic:GenderNon-Binary -0.87117 0.50811 -1.715 0.0864 .
## RaceOther:GenderNon-Binary -0.48134 0.50777 -0.948 0.3432
## RaceWhite:GenderNon-Binary -0.73107 0.50863 -1.437 0.1506
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1386.1 on 999 degrees of freedom
## Residual deviance: 1370.9 on 985 degrees of freedom
## AIC: 1400.9
##
## Number of Fisher Scoring iterations: 4Predicting Probabilities
We then predict the probabilities of homelessness based on race and gender using the fitted model. The predicted probability can be expressed as:
\[ \hat{p} = \frac{e^{(\beta_0 + \beta_1 \text{Race} + \beta_2 \text{Gender} + \beta_3 (\text{Race} \times \text{Gender}))}}{1 + e^{(\beta_0 + \beta_1 \text{Race} + \beta_2 \text{Gender} + \beta_3 (\text{Race} \times \text{Gender}))}} \]
# View the first few rows of the data
head(df1)## Race Gender Homelessness_Status
## 1 Hispanic Non-Binary 0
## 2 Hispanic Female 0
## 3 Black Non-Binary 1
## 4 Black Non-Binary 0
## 5 Hispanic Female 1
## 6 Other Female 0# Create a logistic regression model to assess intersectional relationships
# Note: Convert categorical variables to factors
df1$Race <- as.factor(df1$Race)
df1$Gender <- as.factor(df1$Gender)
# Fit the logistic regression model
model1 <- glm(Homelessness_Status ~ Race * Gender, data = df1, family = binomial)
# Summary of the model
summary(model1)##
## Call:
## glm(formula = Homelessness_Status ~ Race * Gender, family = binomial,
## data = df1)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.62571 0.25833 -2.422 0.0154 *
## RaceBlack 0.44982 0.37075 1.213 0.2250
## RaceHispanic 0.59396 0.36089 1.646 0.0998 .
## RaceOther 0.65469 0.35315 1.854 0.0638 .
## RaceWhite 0.62571 0.36837 1.699 0.0894 .
## GenderMale 0.56687 0.35441 1.599 0.1097
## GenderNon-Binary 0.73107 0.37028 1.974 0.0483 *
## RaceBlack:GenderMale 0.07903 0.50049 0.158 0.8745
## RaceHispanic:GenderMale -0.44550 0.49894 -0.893 0.3719
## RaceOther:GenderMale -0.59585 0.49236 -1.210 0.2262
## RaceWhite:GenderMale -0.53788 0.50255 -1.070 0.2845
## RaceBlack:GenderNon-Binary -0.17381 0.51762 -0.336 0.7370
## RaceHispanic:GenderNon-Binary -0.87117 0.50811 -1.715 0.0864 .
## RaceOther:GenderNon-Binary -0.48134 0.50777 -0.948 0.3432
## RaceWhite:GenderNon-Binary -0.73107 0.50863 -1.437 0.1506
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1386.1 on 999 degrees of freedom
## Residual deviance: 1370.9 on 985 degrees of freedom
## AIC: 1400.9
##
## Number of Fisher Scoring iterations: 4# Predict probabilities of homelessness based on race and gender
df1$Predicted_Probability <- predict(model1, type = "response")
# View the first few rows with predicted probabilities
head(df1)## Race Gender Homelessness_Status Predicted_Probability
## 1 Hispanic Non-Binary 0 0.4571429
## 2 Hispanic Female 0 0.4920635
## 3 Black Non-Binary 1 0.5942029
## 4 Black Non-Binary 0 0.5942029
## 5 Hispanic Female 1 0.4920635
## 6 Other Female 0 0.5072464# Print the attributes of the data frame
print(attributes(df1))## $names
## [1] "Race" "Gender" "Homelessness_Status"
## [4] "Predicted_Probability"
##
## $row.names
## [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14
## [15] 15 16 17 18 19 20 21 22 23 24 25 26 27 28
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## [939] 939 940 941 942 943 944 945 946 947 948 949 950 951 952
## [953] 953 954 955 956 957 958 959 960 961 962 963 964 965 966
## [967] 967 968 969 970 971 972 973 974 975 976 977 978 979 980
## [981] 981 982 983 984 985 986 987 988 989 990 991 992 993 994
## [995] 995 996 997 998 999 1000
##
## $class
## [1] "data.frame"| Variable Name | Variable Type | Definition |
|---|---|---|
| ID | Integer | Unique identifier for each participant in the study. |
| Age | Numeric | Age of the participant in years. |
| Education Level | Categorical | Highest level of education attained (e.g., “High School”, “Some College”, “Bachelor’s”, etc.). |
| Employment Status | Categorical | Current employment status (e.g., “Employed”, “Unemployed”, “Part-time”, “Student”). |
| Annual Income | Numeric | Total annual income in USD. |
| Homeless Status | Categorical | Indicates if respondent experienced homelessness (e.g., “Yes”, “Housing insecure”, “No”). |
| Duration of Homelessness | Numeric | Length of time (in months) the participant has experienced homelessness, if applicable. |
| Family Size | Integer | Number of individuals in the participant’s household. |
| Access to Services | Categorical | Indicates access to social services (e.g., “Yes”, “No”). |
| Mental Health Status | Categorical | Self-reported mental health status (e.g., “Good”, “Fair”, “Poor”). |
To write the mathematical model that corresponds to the code provided, we need to identify the key variables and their relationships as they pertain to the study of homelessness. The code creates a pseudo dataset with various demographic and situational variables. Below is a mathematical representation of the model that can be inferred from the dataset generation process.
Let \(n\) be the total number of individuals in the dataset.
Let \(\text{age}_i\) be the age of individual \(i\).
Let \(\text{education_level}_i\) be the education level of individual \(i\).
Let \(\text{employment_status}_i\) be the employment status of individual \(i\).
Let \(\text{annual\_income}_i\) be the annual income of individual \(i\).
Let \(\text{homeless\_status}_i\) be a categorical variable indicating whether individual \(i\) is homeless (“Yes”, “Housing insecure”, “No”).
Let \(\text{race}_i\) be the race of individual \(i\) (e.g., “Black”, “White”, “Hispanic”, “Asian”, “Other”).
Let \(\text{gender}_i\) be the gender of individual \(i\) (e.g., “Woman”, “Man”, “Non-binary”).
Let \[ \text{black_woman}_i = \begin{cases} 1 & \text{if } (\text{race}_i = ``Black" \text{ and } \text{gender}_i = ``Woman") \\ 0 & \text{otherwise} \end{cases} \]
be a binary flag indicating if individual $ i $ is a Black woman.
Let \(\text{duration_of_homelessness}_i\) represent the duration of homelessness for individual \(i\), measured in months.
Let \(\text{family_size}_i\) represent the size of individual \(i\)’s family.
Let \(\text{access_to_services}_i\) indicate whether individual \(i\) has access to social services (“Yes” or “No”).
Let \(\text{mental_health_status}_i\) represent the mental health status of individual \(i\).
The logistic regression model can be expressed as:
\[ P(\text{Homelessness}) = P(Y_i = 1 | X_i) = \frac{1}{1 + e^{-(\beta_0 + \beta_1 (\text{age}_i) + \beta_2 (\text{education_level}_i) + \beta_3 (\text{employment_status}_i) + ... + \beta_k (\text{mental_health_status}_i))}} \]
Where:
\(Y_i = 1\) indicates that individual \(i\) is homeless.
\(X_i = (\text{age}_i, ... , \text{mental_health_status}_i)\) represents all independent variables affecting homelessness status.
The coefficients \((β_0, β_1, ..., β_k)\) represent the effect size of each predictor on the log-odds of homelessness.
Duration of Homelessness:
For individuals who are homeless, we can also model the duration of homelessness as a function of various predictors using a linear regression or survival analysis approach:
If we denote:
Then, we could model:
\[ D_i = f(\beta_0 + β_1 (\text{age}_i) + β_2 (\text{education_level}_i) + ... + β_k (\text{mental_health_status}_i)) \]
The dataset generated captures various demographic and situational factors that may influence homelessness among individuals, and specifically Black women. The mathematical models outlined above provide a framework for analyzing these relationships using logistic regression for predicting homelessness status and potentially linear regression or survival analysis for understanding the duration of homelessness. This approach allows researchers to explore how different factors interact and contribute to homelessness, particularly among vulnerable populations such as Black women.
The full data set is presented below.
# Display the dataset
df2 %>%
print(n=Inf)## # A tibble: 150 × 13
## ID age education_level employment_status annual_income homeless_status
## <int> <int> <chr> <chr> <dbl> <chr>
## 1 1 48 High School Unemployed 1846 Housing insecure
## 2 2 32 Bachelor's Unemployed 6517 Housing insecure
## 3 3 31 Graduate Part-time 9419 No
## 4 4 20 Graduate Unemployed 2043 No
## 5 5 59 Bachelor's Part-time 12915 No
## 6 6 60 Bachelor's Employed 4037 Housing insecure
## 7 7 54 Graduate Employed 1594 No
## 8 8 31 High School Student 9236 No
## 9 9 42 Graduate Employed 10443 No
## 10 10 43 Some College Employed 5243 Housing insecure
## 11 11 44 Some College Employed 5397 Yes
## 12 12 22 Graduate Student 4445 No
## 13 13 44 High School Part-time 1960 No
## 14 14 45 Graduate Employed 5385 Housing insecure
## 15 15 26 Graduate Student 3136 Housing insecure
## 16 16 46 Some College Employed 7433 Yes
## 17 17 52 Bachelor's Part-time 7047 No
## 18 18 25 Graduate Part-time 12340 No
## 19 19 43 Graduate Student 5096 No
## 20 20 24 Graduate Unemployed 6577 Housing insecure
## 21 21 59 Bachelor's Employed 1990 Housing insecure
## 22 22 26 High School Employed 11321 No
## 23 23 36 Graduate Employed 5748 Housing insecure
## 24 24 53 Graduate Unemployed 9831 No
## 25 25 31 Graduate Employed 3061 No
## 26 26 34 Some College Unemployed 6457 Yes
## 27 27 60 High School Employed 10242 No
## 28 28 56 Some College Student 1752 No
## 29 29 29 Bachelor's Employed 10781 No
## 30 30 32 Graduate Part-time 4614 No
## 31 31 49 Bachelor's Part-time 5376 No
## 32 32 59 High School Unemployed 4745 No
## 33 33 62 Bachelor's Unemployed 1448 No
## 34 34 24 Graduate Employed 7226 No
## 35 35 26 Some College Part-time 9148 No
## 36 36 58 High School Student 11839 Housing insecure
## 37 37 27 High School Employed 1306 No
## 38 38 40 Some College Employed 12869 No
## 39 39 44 Bachelor's Unemployed 4635 No
## 40 40 24 High School Employed 12270 Housing insecure
## 41 41 44 Some College Unemployed 9251 Housing insecure
## 42 42 49 Some College Unemployed 6364 Housing insecure
## 43 43 55 High School Unemployed 10798 Housing insecure
## 44 44 42 Graduate Unemployed 1474 Yes
## 45 45 51 Graduate Student 9868 No
## 46 46 46 Graduate Student 5185 No
## 47 47 22 Some College Student 10951 No
## 48 48 25 Graduate Student 7426 No
## 49 49 29 High School Part-time 4295 No
## 50 50 30 High School Student 10611 No
## 51 51 35 Some College Part-time 2100 No
## 52 52 50 High School Part-time 10985 No
## 53 53 44 Graduate Part-time 4322 No
## 54 54 42 Bachelor's Employed 10037 No
## 55 55 55 High School Part-time 12570 No
## 56 56 38 High School Part-time 1978 No
## 57 57 32 Graduate Part-time 11252 No
## 58 58 58 Graduate Student 10627 No
## 59 59 64 Some College Unemployed 5622 No
## 60 60 43 High School Part-time 4931 Housing insecure
## 61 61 48 Graduate Part-time 3459 No
## 62 62 33 Some College Part-time 7833 No
## 63 63 47 High School Employed 11657 Housing insecure
## 64 64 23 High School Employed 7357 No
## 65 65 60 High School Part-time 8044 No
## 66 66 25 Bachelor's Unemployed 8989 No
## 67 67 39 Bachelor's Part-time 7359 No
## 68 68 39 Some College Unemployed 7118 No
## 69 69 56 High School Employed 1194 No
## 70 70 48 Graduate Student 1573 No
## 71 71 65 Some College Unemployed 12152 No
## 72 72 34 Graduate Unemployed 10231 Housing insecure
## 73 73 51 Bachelor's Unemployed 3413 Housing insecure
## 74 74 21 Some College Student 8803 No
## 75 75 30 Bachelor's Employed 8845 No
## 76 76 22 Some College Student 5743 No
## 77 77 42 Bachelor's Employed 10748 No
## 78 78 39 High School Employed 7564 Yes
## 79 79 42 High School Part-time 11622 No
## 80 80 49 High School Part-time 7640 No
## 81 81 63 High School Employed 11873 Housing insecure
## 82 82 42 Bachelor's Employed 8050 Housing insecure
## 83 83 40 Some College Part-time 6082 Housing insecure
## 84 84 52 High School Employed 12395 No
## 85 85 57 Some College Part-time 9508 Housing insecure
## 86 86 65 High School Student 5960 Housing insecure
## 87 87 47 Bachelor's Unemployed 1220 No
## 88 88 29 Bachelor's Employed 7801 Housing insecure
## 89 89 48 High School Employed 6881 No
## 90 90 63 Graduate Part-time 11544 No
## 91 91 47 Some College Student 10754 Housing insecure
## 92 92 52 Bachelor's Unemployed 11249 No
## 93 93 31 High School Part-time 5415 Yes
## 94 94 46 Bachelor's Unemployed 11487 No
## 95 95 49 Some College Employed 2816 No
## 96 96 24 Graduate Unemployed 4382 Housing insecure
## 97 97 20 Graduate Part-time 9000 Yes
## 98 98 40 High School Unemployed 12729 No
## 99 99 32 Graduate Part-time 7993 No
## 100 100 38 High School Part-time 7319 Yes
## 101 101 54 High School Employed 1729 No
## 102 102 25 High School Unemployed 12628 No
## 103 103 27 High School Student 2443 No
## 104 104 59 Bachelor's Employed 2060 No
## 105 105 61 Some College Unemployed 11569 No
## 106 106 51 Some College Unemployed 7100 Housing insecure
## 107 107 27 Some College Student 5050 No
## 108 108 39 Bachelor's Unemployed 11732 Housing insecure
## 109 109 29 High School Student 1384 Yes
## 110 110 37 Some College Unemployed 3847 No
## 111 111 63 Some College Employed 9238 No
## 112 112 34 High School Student 3710 No
## 113 113 63 Some College Unemployed 4822 No
## 114 114 52 High School Student 3088 No
## 115 115 57 High School Employed 10617 No
## 116 116 63 Some College Student 2755 No
## 117 117 47 Bachelor's Unemployed 10873 Housing insecure
## 118 118 32 High School Employed 4972 No
## 119 119 41 Bachelor's Student 5490 No
## 120 120 40 Graduate Student 8557 No
## 121 121 60 High School Part-time 2160 No
## 122 122 24 Some College Unemployed 1264 No
## 123 123 46 High School Employed 12917 No
## 124 124 32 Graduate Part-time 8007 No
## 125 125 40 Some College Unemployed 10382 No
## 126 126 43 Some College Student 11703 No
## 127 127 55 Some College Part-time 10058 No
## 128 128 63 Bachelor's Unemployed 12750 Housing insecure
## 129 129 49 High School Part-time 1530 Housing insecure
## 130 130 24 High School Part-time 11841 Yes
## 131 131 44 Graduate Employed 11386 Housing insecure
## 132 132 59 High School Student 10305 Housing insecure
## 133 133 22 High School Unemployed 5522 Housing insecure
## 134 134 23 Graduate Part-time 1505 No
## 135 135 33 Bachelor's Employed 5373 No
## 136 136 41 High School Employed 4285 No
## 137 137 49 Some College Part-time 11206 No
## 138 138 38 High School Unemployed 5349 No
## 139 139 28 Some College Part-time 4654 Housing insecure
## 140 140 53 Graduate Unemployed 10110 No
## 141 141 61 Some College Unemployed 11138 Housing insecure
## 142 142 63 High School Unemployed 6495 No
## 143 143 36 High School Student 9756 Housing insecure
## 144 144 42 High School Employed 2249 Housing insecure
## 145 145 56 High School Student 3640 No
## 146 146 43 Graduate Unemployed 12447 No
## 147 147 26 Bachelor's Employed 10024 No
## 148 148 24 High School Student 10827 No
## 149 149 51 High School Student 6013 Yes
## 150 150 65 High School Employed 8126 Yes
## # ℹ 7 more variables: race <chr>, gender <chr>, black_woman <dbl>,
## # duration_of_homelessness <int>, family_size <int>,
## # access_to_services <chr>, mental_health_status <chr># Print the attributes of the data frame
print(attributes(df2))## $class
## [1] "tbl_df" "tbl" "data.frame"
##
## $row.names
## [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
## [19] 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
## [37] 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54
## [55] 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72
## [73] 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90
## [91] 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108
## [109] 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126
## [127] 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144
## [145] 145 146 147 148 149 150
##
## $names
## [1] "ID" "age"
## [3] "education_level" "employment_status"
## [5] "annual_income" "homeless_status"
## [7] "race" "gender"
## [9] "black_woman" "duration_of_homelessness"
## [11] "family_size" "access_to_services"
## [13] "mental_health_status"# Save the dataset as a CSV file
# write.csv(data, "homelessness_test_data.csv", row.names = FALSE)