707_Proposal.Rmd

---
title: "Project Code"
author: "Costa Stavrianidis"
date: "2022-10-13"
output: html_document
---

```{r setup, include=FALSE}
library(tidyverse)
library(reshape2)
```

# Reading in the dataset
```{r, warning=FALSE}
survey <- read_csv("C:/Users/kelvi/Downloads/archive/2015.csv", show_col_types = FALSE)
```

# Cleaning the data for variables of interest
```{r}
survey1 <- survey %>% select(`_MICHD`, ADDEPEV2, MENTHLTH, EMTSUPRT, ADDOWN, `_RFHLTH`, PHYSHLTH,
                             `_HCVU651`, MEDCOST, `_RFHYPE5`, `_RFCHOL`, CVDSTRK3, DIABETE3, SEX,
                             `_EDUCAG`, INCOME2, `_BMI5`, `_SMOKER3`, AVEDRNK2, `_TOTINDA`, DRADVISE,
                             RDUCHART, SCNTMEL1, `_AGE65YR`, `_FRTLT1`, `_VEGLT1`) %>% 
  rename(Gen_Health = `_RFHLTH`, Phys_Health = PHYSHLTH, Ment_Health = MENTHLTH, Med_Cost = MEDCOST,
         Stroke = CVDSTRK3, Diabetes = DIABETE3, Sex = SEX, Income = INCOME2, Avg_Drinks = AVEDRNK2,
         Sodium_Intake = DRADVISE, Aspirin = RDUCHART, Meal_Money = SCNTMEL1, Health_Cov = `_HCVU651`,
         BP = `_RFHYPE5`, Chol = `_RFCHOL`, Heart_Disease = `_MICHD`, Age_65 = `_AGE65YR`, 
         BMI = `_BMI5`, Education = `_EDUCAG`, Smoking = `_SMOKER3`, Fruit = `_FRTLT1`, 
         Veggies = `_VEGLT1`, Exercise = `_TOTINDA`, Depression = ADDEPEV2, Support = EMTSUPRT,
         Down = ADDOWN) %>% 
  mutate(Heart_Disease = recode(Heart_Disease, '2' = 0), 
         Depression = recode(Depression, '2' = 0, '7' = as.numeric(NA), '9' = as.numeric(NA)),
         Ment_Health = recode(Ment_Health, '88' = 0, '77' = as.numeric(NA), '99' = as.numeric(NA)),
         Support = recode(Support, '5' = 1, '4' = 2, '2' = 4, '1' = 5, '7' = as.numeric(NA),
                          '9' = as.numeric(NA)), 
         Down = recode(Down, '88' = 0, '77' = as.numeric(NA), '99' = as.numeric(NA)),
         Gen_Health = recode(Gen_Health, '2' = 0, '3' = as.numeric(NA)),
         Phys_Health = recode(Phys_Health, '88' = 0, '77' = as.numeric(NA), '99' = as.numeric(NA)),
         Health_Cov = recode(Health_Cov, '2' = 0, '9' = as.numeric(NA)),
         Med_Cost = recode(Med_Cost, '2' = 0, '7' = as.numeric(NA), '9' = as.numeric(NA)),
         BP = recode(BP, '1' = 0, '2' = 1, '9' = as.numeric(NA)),
         Chol = recode(Chol, '1' = 0, '2' = 1, '9' = as.numeric(NA)),
         Stroke = recode(Stroke, '1' = 0, '2' = 1, '7' = as.numeric(NA), '9' = as.numeric(NA)),
         Diabetes = recode(Diabetes, '2' = 1, '3' = 1, '4' = 2, '1' = 3, '7' = as.numeric(NA), 
                           '9' = as.numeric(NA)),
         Education = recode(Education, '9' = as.numeric(NA)),
         Income = recode(Income, '77' = as.numeric(NA), '99' = as.numeric(NA)),
         BMI = BMI/100,
         Smoking = recode(Smoking, '4' = 1, '3' = 2, '2' = 3, '1' = 4, '9' = as.numeric(NA)),
         Avg_Drinks = recode(Avg_Drinks, '77' = as.numeric(NA), '99' = as.numeric(NA)),
         Exercise = recode(Exercise, '2' = 0, '9' = as.numeric(NA)),
         Sodium_Intake = recode(Sodium_Intake, '2' = 0, '7' = as.numeric(NA), '9' = as.numeric(NA)),
         Aspirin = recode(Aspirin, '2' = 0, '7' = as.numeric(NA), '9' = as.numeric(NA)),
         Meal_Money = recode(Meal_Money, '5' = 1, '4' = 2, '2' = 4, '1' = 5, '7' = as.numeric(NA),
                             '8' = as.numeric(NA), '9' = as.numeric(NA)),
         Age_65 = recode(Age_65, '3' = as.numeric(NA)),
         Fruit = recode(Fruit, '2' = 0, '9' = as.numeric(NA)),
         Veggies = recode(Veggies, '2' = 0, '9' = as.numeric(NA)))
glimpse(survey1)
```

# Variable descriptions

Heart_Disease: Respondents that have ever reported having coronary heart disease (CHD) or myocardial infarction (MI)
0 - did not report
1 - reported
NA - not asked or missing

Depression: (Ever told) you that you have a depressive disorder, including depression, major depression, dysthymia, or minor depression?
0 - no
1 - yes
NA - don't know, refused

Ment_Health: Now thinking about your mental health, which includes stress, depression, and problems with emotions, for how many days during the past 30 days was your mental health not good?
0:30 - # of days
NA - don't know, refused

Support: how often do you get the social and emotional support you need?
1 - never
2 - rarely
3 - sometimes
4 - usually
5 - always
NA - don't know, refused, missing

Down: Over the last 2 weeks, how many days have you felt down, depressed or hopeless?
0:14 - # of days
NA - don't know, refused, missing

Gen_Health: Adults with good or better general health
0 - fair or poor health
1 - good or better health
NA - don't know, not sure or refused/missing

Phys_Health: Now thinking about your physical health, which includes physical illness and injury, for how many days during the past 30 days was your physical health not good?
0:30 - # days
NA - don't know, refused, missing

Health_Cov: Respondents aged 18-64 who have any form of health care coverage
0 - do not have
1 - have
NA - don't know, refused, missing

Med_Cost: Was there a time in the past 12 months when you needed to see a doctor but could not because of cost?
0 - no 
1 - yes
NA - don't know, refused, missing

BP: Adults who have been told they have high blood pressure by a doctor, nurse, or other health professional
0 - no
1 - yes
NA - don't know, refused, missing

Chol: Adults who have had their cholesterol checked and have been told by a doctor, nurse, or other health professional that it was high
0 - no
1 - yes
NA - don't know, refused, missing

Stroke: (Ever told) you had a stroke.
0 - no
1 - yes
NA - don't know, refused

Diabetes: (Ever told) you have diabetes (If "Yes" and respondent is female, ask "Was this only when you were pregnant?". If Respondent says pre-diabetes or borderline diabetes, use response code 4.)
1 - no or yes, but female told only during pregnancy
2 - no, pre-diabetes or borderline
3 - yes
NA - don't know, refused, missing

Sex: Indicate sex of respondent.
1 - male
2 - female

Education: Level of education completed
1 - did not graduate highschool
2 - graduated highschool
3 - attended college or technical school
4 - graduated from college or technical school
NA - don't know, refused, missing

Income: Is your annual household income from all sources: (If respondent refuses at any income level, code "Refused.")
1 - <$10,000
2 - $10,000:$14,999
3 - $15,000:$19,999
4 - $20,000:$24,999
5 - $25,000:$34,999
6 - $35,000:$49,999
7 - $50,000:$74,999
8 - >=$75,000
NA - don't know, refused, missing

BMI: Body Mass Index (BMI)
1:99.99 - bmi
NA - don't know, refused, missing

Smoking: Four-level smoker status: Everyday smoker, Someday smoker, Former smoker, Non-smoker
1 - never smoked
2 - former smoker
3 - now smokes some days
4 - now smokes every day
NA - don't know, refused, missing

Avg_Drinks: One drink is equivalent to a 12-ounce beer, a 5-ounce glass of wine, or a drink with one shot of liquor. During the past 30 days, on the days when you drank, about how many drinks did you drink on the average? (A 40 ounce beer would count as 3 drinks, or a cocktail drink with 2 shots would count as 2 drinks.)
1:76 - # of drinks
NA - don't know, refused, missing

Exercise: Adults who reported doing physical activity or exercise during the past 30 days other than their regular job
0 - did not have physical activity or exercise
1 - had physical activity or exercise
NA - don't know, refused, missing

Sodium_Intake: Has a doctor or other health professional ever advised you to reduce sodium or salt intake?
0 - no
1 - yes
NA - don't know, refused, missing

Aspirin: Do you take aspirin to reduce the chance of a heart attack?
0 - no
1 - yes
NA - don't know, refused, missing

Meal_Money: How often in the past 12 months would you say you were worried or stressed about having enough money to buy nutritious meals?
1 - never
2 - rarely
3 - sometimes
4 - usually
5 - always
NA - don't know, not applicable, refused, missing

Age_65: Two-level age category
1 - age 18:64
2 - age 65 or older
NA - don't know, refused, missing

Fruit: Consume Fruit 1 or more times per day
0 - less than one time per day
1 - one or more times per day
NA - don't know, refused, missing

Veggies: Consume Vegetables 1 or more times per day
0 - less than one time per day
1 - one or more times per day
NA - don't know, refused, missing

# Exploratory data analysis
```{r}
colSums(is.na(survey1))/length(survey1$Heart_Disease)
# Many features have a large amount of missing values

survey1 <- survey1 %>% select(-c(Support, Down, Sodium_Intake, Aspirin, Meal_Money))
```


```{r}
 
# creating correlation matrix
corr_mat1 <- round(cor(survey1, use = "pairwise.complete.obs"),2)

# reduce the size of correlation matrix
melted_corr_mat1 <- melt(corr_mat1)
head(melted_corr_mat1)

# plotting the correlation heatmap
library(ggplot2)

covarian<- ggplot(data = melted_corr_mat1, aes(x=Var1, y=Var2,
                                   fill=value)) +
geom_tile() + theme(axis.text.x = element_text(angle = 90, vjust = 0.5, hjust=1))

covarian
ggheatmap <- ggplot(melted_corr_mat1, aes(Var2, Var1, fill = value))+
 geom_tile(color = "white")+
 scale_fill_gradient2(low = "blue", high = "red", mid = "white", 
   midpoint = 0, limit = c(-1,1), space = "Lab", 
    name="Pearson\nCorrelation") +
  theme_minimal()+ # minimal theme
 theme(axis.text.x = element_text(angle = 90, vjust = 1, 
    size = 9, hjust = 1))+
 coord_fixed() + ggtitle("Figure 1: Heatmap of Covariance Matrix") + xlab("Variables") + ylab("Variables")

ggheatmap
```

Explore dataset

```{r}
head(survey1,10)
```

```{r}
row.names(survey1)
```

```{r}
names(survey1)
```

```{r}
apply(survey1, 2, mean, na.rm = TRUE)
```

Note: rows = 1, columns = 2

```{r}
apply(survey1, 2, var, na.rm = TRUE)
```

2. It is important to standardize the variables to have mean zero and standard deviation one before performing PCA. 

```{r}
pr.out=prcomp(survey1, scale=TRUE, na.action = na.fail)
```

prcomp() function centers the variables to have mean zero. By using the option scale=TRUE, we scale the variables to have standard deviation one. 

```{r}
names(pr.out)
```

```{r}
pr.out$center
```


```{r}
pr.out$scale^2
```

3. The rotation matrix provides the principal component loadings; each col- umn of pr.out$rotation contains the corresponding principal component loading vector.

```{r}
pr.out$rotation
```

Why are there 4 principal components?

4. The 50 × 4 matrix x has as its columns the principal component score vectors. That is, the kth column is the kth principal component score vector.

```{r}
dim(pr.out$x)
```

```{r}
pr.out$x
```


4. Plot the first 2 principal components.

```{r}
biplot(pr.out, scale=0)
```

score 0 is to ensure that the arrows are scaled to represent the loadings.

5. The prcomp() function also outputs the standard deviation of each prin- cipal component. For instance, on the survey1 data set, we can access these standard deviations as follows:

```{r}
pr.var=pr.out$sdev^2
pr.var
```

Proportion of variance explained.

```{r}
pve=pr.var/sum(pr.var)
```

# Plots
```{r}
plot(pve, xlab="Principal Component", ylab="Proportion of Variance Explained ", ylim=c(0,1),type='b')
```

```{r}
plot(cumsum(pve), xlab="Principal Component ", ylab=" Cumulative Proportion of Variance Explained ", ylim=c(0,1), type='b')
```

```