Data622 - Group2 - Homework4
Zachary Palmore, Kevin Potter, Amit Kapoor, Adam Gersowitz, Paul Perez
10/21/2021
Overview
In this project, we analyze a real-life mental health dataset to provide context around suicide prediction given a variety of unidentifiable demographic data. Our goals are to understand the variables relationships, identify those variables that influence our target, and develop models that can predict a patient’s risk of suicide.
Approach
We will first perform exploratory data analysis (EDA) on the dataset to inform our analysis and build better models. Methods include Clustering, Principal Component Analysis, Gradient Boosting, and Support Vector Machines. This EDA step is crucial to understanding variables’ relationships and identifying which variables influence our target.
Once we understand the data, we prepare it for modeling. This includes partitioning the data with a 75-25 train-test split, performing necessary imputations, relevant centering and scaling, and more as outlined in our data exploration and preparation sections. When building our models we focus on using methods that produce real-world accuracy. For this reason, we attempt to select the best generalizable model with accuracy as our primary indicator during model evaluation.
Data Exploration
The dataset with its column IDs, variable names, and variables descriptions are provided below for reference.
| Columns | Variable | Description |
|---|---|---|
| C | Sex | Male-1, Female-2 |
| D | Race | White-1, African American-2, Hispanic-3, Asian-4, Native American-5, Other or missing data -6 |
| E - W | ADHD self-report scale | Never-0, rarely-1, sometimes-2, often-3, very often-4 |
| X - AM | Mood disorder questions | No-0, yes-1; question 3: no problem-0, minor-1, moderate-2, serious-3 |
| AN - AS | Individual substances misuse | no use-0, use-1, abuse-2, dependence-3 |
| AT | Court Order | No-0, Yes-1 |
| AU | Education | 1-12 grade, 13+ college |
| AV | History of Violence | No-0, Yes-1 |
| AW | Disorderly Conduct | No-0, Yes-1 |
| AX | Suicide attempt | No-0, Yes-1 |
| AY | Abuse Hx | No-0, Physical (P)-1, Sexual (S)-2, Emotional (E)-3, P&S-4, P&E-5, S&E-6, P&S&E-7 |
| AZ | Non-substance-related Dx | 0 - none; 1 - one; 2 - More than one |
| BA | Substance-related Dx | 0 - none; 1 - one Substance-related; 2 - two; 3 - three or more |
| BB | Psychiatric Meds | 0 - none; 1 - one psychotropic med; 2 - more than one psychotropic med |
Notice how the data is grouped with ADHD, Mood disorders, and Individual Substance misuse present across a range of columns. These groups are reviewed throughout the exploration process and new features are generated to attempt to improve model performance.
Data Characteristics
## [1] 53The data contains 175 observations of 53 variables. We import the data from a remote repository and find that 51 of the variables should be of the factor data type given clear levels in their distributions. As is, these variables are interpreted as character strings. This will need to be converted for realistic results. The remaining variables can be numeric for our purposes.
We review one grouped variable set, known as mood disorders (MD), to show what we’re working with. These contain a series of associated questions (Q1-Q3) with Q1 containing parts ‘a’ through ‘m.’
## # A tibble: 175 x 15
## `MD Q1a` `MD Q1b` `MD Q1c` `MD Q1d` `MD Q1e` `MD Q1f` `MD Q1g` `MD Q1h`
## <fct> <fct> <fct> <fct> <fct> <fct> <fct> <fct>
## 1 1 1 1 1 0 1 1 1
## 2 1 1 1 1 1 1 1 1
## 3 0 0 0 0 1 1 1 0
## 4 1 1 0 0 1 1 1 1
## 5 0 1 0 1 0 1 1 0
## 6 0 1 0 1 1 1 1 1
## 7 1 1 0 0 1 1 0 0
## 8 0 0 0 0 0 1 1 0
## 9 1 1 0 1 1 1 1 0
## 10 1 1 0 0 1 0 1 0
## # … with 165 more rows, and 7 more variables: MD Q1i <fct>, MD Q1j <fct>,
## # MD Q1k <fct>, MD Q1L <fct>, MD Q1m <fct>, MD Q2 <fct>, MD Q3 <fct>Each part of Q1 ‘a’ through ‘m’ corresponds with a specific question related to mood disorders for a single patient. In our feature engineering, it may be useful to tally these responses for a more holistic perspective of the patient’s overall mood. We repeat this for the other groups to get an sense of the patient well-being which should provide insight into their risk of suicide.
Data summary
## Data Frame Summary
## adhd_data
## Dimensions: 175 x 53
## Duplicates: 0
##
## +----+---------------------+--------------------------+--------------------+----------+---------+
## | No | Variable | Stats / Values | Freqs (% of Valid) | Valid | Missing |
## +====+=====================+==========================+====================+==========+=========+
## | 1 | Age | Mean (sd) : 39.5 (11.2) | 42 distinct values | 175 | 0 |
## | | [numeric] | min < med < max: | | (100.0%) | (0.0%) |
## | | | 18 < 42 < 69 | | | |
## | | | IQR (CV) : 18.5 (0.3) | | | |
## +----+---------------------+--------------------------+--------------------+----------+---------+
## | 2 | Sex | 1. 1 | 99 (56.6%) | 175 | 0 |
## | | [factor] | 2. 2 | 76 (43.4%) | (100.0%) | (0.0%) |
## +----+---------------------+--------------------------+--------------------+----------+---------+
## | 3 | Race | 1. 1 | 72 (41.1%) | 175 | 0 |
## | | [factor] | 2. 2 | 100 (57.1%) | (100.0%) | (0.0%) |
## | | | 3. 3 | 1 ( 0.6%) | | |
## | | | 4. 6 | 2 ( 1.1%) | | |
## +----+---------------------+--------------------------+--------------------+----------+---------+
## | 4 | ADHD Q1 | 1. 0 | 39 (22.3%) | 175 | 0 |
## | | [factor] | 2. 1 | 43 (24.6%) | (100.0%) | (0.0%) |
## | | | 3. 2 | 44 (25.1%) | | |
## | | | 4. 3 | 30 (17.1%) | | |
## | | | 5. 4 | 19 (10.9%) | | |
## +----+---------------------+--------------------------+--------------------+----------+---------+
## | 5 | ADHD Q2 | 1. 0 | 25 (14.3%) | 175 | 0 |
## | | [factor] | 2. 1 | 46 (26.3%) | (100.0%) | (0.0%) |
## | | | 3. 2 | 47 (26.9%) | | |
## | | | 4. 3 | 33 (18.9%) | | |
## | | | 5. 4 | 24 (13.7%) | | |
## +----+---------------------+--------------------------+--------------------+----------+---------+
## | 6 | ADHD Q3 | 1. 0 | 26 (14.9%) | 175 | 0 |
## | | [factor] | 2. 1 | 46 (26.3%) | (100.0%) | (0.0%) |
## | | | 3. 2 | 46 (26.3%) | | |
## | | | 4. 3 | 32 (18.3%) | | |
## | | | 5. 4 | 25 (14.3%) | | |
## +----+---------------------+--------------------------+--------------------+----------+---------+
## | 7 | ADHD Q4 | 1. 0 | 27 (15.4%) | 175 | 0 |
## | | [factor] | 2. 1 | 31 (17.7%) | (100.0%) | (0.0%) |
## | | | 3. 2 | 50 (28.6%) | | |
## | | | 4. 3 | 31 (17.7%) | | |
## | | | 5. 4 | 36 (20.6%) | | |
## +----+---------------------+--------------------------+--------------------+----------+---------+
## | 8 | ADHD Q5 | 1. 0 | 33 (18.9%) | 175 | 0 |
## | | [factor] | 2. 1 | 21 (12.0%) | (100.0%) | (0.0%) |
## | | | 3. 2 | 32 (18.3%) | | |
## | | | 4. 3 | 47 (26.9%) | | |
## | | | 5. 4 | 41 (23.4%) | | |
## | | | 6. 5 | 1 ( 0.6%) | | |
## +----+---------------------+--------------------------+--------------------+----------+---------+
## | 9 | ADHD Q6 | 1. 0 | 36 (20.6%) | 175 | 0 |
## | | [factor] | 2. 1 | 29 (16.6%) | (100.0%) | (0.0%) |
## | | | 3. 2 | 45 (25.7%) | | |
## | | | 4. 3 | 45 (25.7%) | | |
## | | | 5. 4 | 20 (11.4%) | | |
## +----+---------------------+--------------------------+--------------------+----------+---------+
## | 10 | ADHD Q7 | 1. 0 | 22 (12.6%) | 175 | 0 |
## | | [factor] | 2. 1 | 53 (30.3%) | (100.0%) | (0.0%) |
## | | | 3. 2 | 54 (30.9%) | | |
## | | | 4. 3 | 25 (14.3%) | | |
## | | | 5. 4 | 21 (12.0%) | | |
## +----+---------------------+--------------------------+--------------------+----------+---------+
## | 11 | ADHD Q8 | 1. 0 | 21 (12.0%) | 175 | 0 |
## | | [factor] | 2. 1 | 40 (22.9%) | (100.0%) | (0.0%) |
## | | | 3. 2 | 40 (22.9%) | | |
## | | | 4. 3 | 42 (24.0%) | | |
## | | | 5. 4 | 32 (18.3%) | | |
## +----+---------------------+--------------------------+--------------------+----------+---------+
## | 12 | ADHD Q9 | 1. 0 | 31 (17.7%) | 175 | 0 |
## | | [factor] | 2. 1 | 43 (24.6%) | (100.0%) | (0.0%) |
## | | | 3. 2 | 36 (20.6%) | | |
## | | | 4. 3 | 41 (23.4%) | | |
## | | | 5. 4 | 24 (13.7%) | | |
## +----+---------------------+--------------------------+--------------------+----------+---------+
## | 13 | ADHD Q10 | 1. 0 | 15 ( 8.6%) | 175 | 0 |
## | | [factor] | 2. 1 | 46 (26.3%) | (100.0%) | (0.0%) |
## | | | 3. 2 | 49 (28.0%) | | |
## | | | 4. 3 | 33 (18.9%) | | |
## | | | 5. 4 | 32 (18.3%) | | |
## +----+---------------------+--------------------------+--------------------+----------+---------+
## | 14 | ADHD Q11 | 1. 0 | 16 ( 9.1%) | 175 | 0 |
## | | [factor] | 2. 1 | 33 (18.9%) | (100.0%) | (0.0%) |
## | | | 3. 2 | 48 (27.4%) | | |
## | | | 4. 3 | 43 (24.6%) | | |
## | | | 5. 4 | 35 (20.0%) | | |
## +----+---------------------+--------------------------+--------------------+----------+---------+
## | 15 | ADHD Q12 | 1. 0 | 55 (31.4%) | 175 | 0 |
## | | [factor] | 2. 1 | 55 (31.4%) | (100.0%) | (0.0%) |
## | | | 3. 2 | 37 (21.1%) | | |
## | | | 4. 3 | 15 ( 8.6%) | | |
## | | | 5. 4 | 13 ( 7.4%) | | |
## +----+---------------------+--------------------------+--------------------+----------+---------+
## | 16 | ADHD Q13 | 1. 0 | 15 ( 8.6%) | 175 | 0 |
## | | [factor] | 2. 1 | 29 (16.6%) | (100.0%) | (0.0%) |
## | | | 3. 2 | 46 (26.3%) | | |
## | | | 4. 3 | 47 (26.9%) | | |
## | | | 5. 4 | 38 (21.7%) | | |
## +----+---------------------+--------------------------+--------------------+----------+---------+
## | 17 | ADHD Q14 | 1. 0 | 27 (15.4%) | 175 | 0 |
## | | [factor] | 2. 1 | 24 (13.7%) | (100.0%) | (0.0%) |
## | | | 3. 2 | 40 (22.9%) | | |
## | | | 4. 3 | 47 (26.9%) | | |
## | | | 5. 4 | 37 (21.1%) | | |
## +----+---------------------+--------------------------+--------------------+----------+---------+
## | 18 | ADHD Q15 | 1. 0 | 50 (28.6%) | 175 | 0 |
## | | [factor] | 2. 1 | 39 (22.3%) | (100.0%) | (0.0%) |
## | | | 3. 2 | 35 (20.0%) | | |
## | | | 4. 3 | 27 (15.4%) | | |
## | | | 5. 4 | 24 (13.7%) | | |
## +----+---------------------+--------------------------+--------------------+----------+---------+
## | 19 | ADHD Q16 | 1. 0 | 40 (22.9%) | 175 | 0 |
## | | [factor] | 2. 1 | 49 (28.0%) | (100.0%) | (0.0%) |
## | | | 3. 2 | 39 (22.3%) | | |
## | | | 4. 3 | 17 ( 9.7%) | | |
## | | | 5. 4 | 30 (17.1%) | | |
## +----+---------------------+--------------------------+--------------------+----------+---------+
## | 20 | ADHD Q17 | 1. 0 | 49 (28.0%) | 175 | 0 |
## | | [factor] | 2. 1 | 41 (23.4%) | (100.0%) | (0.0%) |
## | | | 3. 2 | 46 (26.3%) | | |
## | | | 4. 3 | 22 (12.6%) | | |
## | | | 5. 4 | 17 ( 9.7%) | | |
## +----+---------------------+--------------------------+--------------------+----------+---------+
## | 21 | ADHD Q18 | 1. 0 | 49 (28.0%) | 175 | 0 |
## | | [factor] | 2. 1 | 52 (29.7%) | (100.0%) | (0.0%) |
## | | | 3. 2 | 35 (20.0%) | | |
## | | | 4. 3 | 20 (11.4%) | | |
## | | | 5. 4 | 19 (10.9%) | | |
## +----+---------------------+--------------------------+--------------------+----------+---------+
## | 22 | ADHD Total | 1. 0 | 1 ( 0.6%) | 175 | 0 |
## | | [factor] | 2. 1 | 2 ( 1.1%) | (100.0%) | (0.0%) |
## | | | 3. 3 | 1 ( 0.6%) | | |
## | | | 4. 5 | 1 ( 0.6%) | | |
## | | | 5. 6 | 3 ( 1.7%) | | |
## | | | 6. 7 | 2 ( 1.1%) | | |
## | | | 7. 8 | 1 ( 0.6%) | | |
## | | | 8. 9 | 2 ( 1.1%) | | |
## | | | 9. 10 | 2 ( 1.1%) | | |
## | | | 10. 11 | 1 ( 0.6%) | | |
## | | | [ 52 others ] | 159 (90.9%) | | |
## +----+---------------------+--------------------------+--------------------+----------+---------+
## | 23 | MD Q1a | 1. 0 | 79 (45.1%) | 175 | 0 |
## | | [factor] | 2. 1 | 96 (54.9%) | (100.0%) | (0.0%) |
## +----+---------------------+--------------------------+--------------------+----------+---------+
## | 24 | MD Q1b | 1. 0 | 75 (42.9%) | 175 | 0 |
## | | [factor] | 2. 1 | 100 (57.1%) | (100.0%) | (0.0%) |
## +----+---------------------+--------------------------+--------------------+----------+---------+
## | 25 | MD Q1c | 1. 0 | 80 (45.7%) | 175 | 0 |
## | | [factor] | 2. 1 | 95 (54.3%) | (100.0%) | (0.0%) |
## +----+---------------------+--------------------------+--------------------+----------+---------+
## | 26 | MD Q1d | 1. 0 | 73 (41.7%) | 175 | 0 |
## | | [factor] | 2. 1 | 102 (58.3%) | (100.0%) | (0.0%) |
## +----+---------------------+--------------------------+--------------------+----------+---------+
## | 27 | MD Q1e | 1. 0 | 78 (44.6%) | 175 | 0 |
## | | [factor] | 2. 1 | 97 (55.4%) | (100.0%) | (0.0%) |
## +----+---------------------+--------------------------+--------------------+----------+---------+
## | 28 | MD Q1f | 1. 0 | 53 (30.3%) | 175 | 0 |
## | | [factor] | 2. 1 | 122 (69.7%) | (100.0%) | (0.0%) |
## +----+---------------------+--------------------------+--------------------+----------+---------+
## | 29 | MD Q1g | 1. 0 | 49 (28.0%) | 175 | 0 |
## | | [factor] | 2. 1 | 126 (72.0%) | (100.0%) | (0.0%) |
## +----+---------------------+--------------------------+--------------------+----------+---------+
## | 30 | MD Q1h | 1. 0 | 77 (44.0%) | 175 | 0 |
## | | [factor] | 2. 1 | 98 (56.0%) | (100.0%) | (0.0%) |
## +----+---------------------+--------------------------+--------------------+----------+---------+
## | 31 | MD Q1i | 1. 0 | 72 (41.1%) | 175 | 0 |
## | | [factor] | 2. 1 | 103 (58.9%) | (100.0%) | (0.0%) |
## +----+---------------------+--------------------------+--------------------+----------+---------+
## | 32 | MD Q1j | 1. 0 | 107 (61.1%) | 175 | 0 |
## | | [factor] | 2. 1 | 68 (38.9%) | (100.0%) | (0.0%) |
## +----+---------------------+--------------------------+--------------------+----------+---------+
## | 33 | MD Q1k | 1. 0 | 90 (51.4%) | 175 | 0 |
## | | [factor] | 2. 1 | 85 (48.6%) | (100.0%) | (0.0%) |
## +----+---------------------+--------------------------+--------------------+----------+---------+
## | 34 | MD Q1L | 1. 0 | 73 (41.7%) | 175 | 0 |
## | | [factor] | 2. 1 | 102 (58.3%) | (100.0%) | (0.0%) |
## +----+---------------------+--------------------------+--------------------+----------+---------+
## | 35 | MD Q1m | 1. 0 | 89 (50.9%) | 175 | 0 |
## | | [factor] | 2. 1 | 86 (49.1%) | (100.0%) | (0.0%) |
## +----+---------------------+--------------------------+--------------------+----------+---------+
## | 36 | MD Q2 | 1. 0 | 49 (28.0%) | 175 | 0 |
## | | [factor] | 2. 1 | 126 (72.0%) | (100.0%) | (0.0%) |
## +----+---------------------+--------------------------+--------------------+----------+---------+
## | 37 | MD Q3 | 1. 0 | 25 (14.3%) | 175 | 0 |
## | | [factor] | 2. 1 | 25 (14.3%) | (100.0%) | (0.0%) |
## | | | 3. 2 | 49 (28.0%) | | |
## | | | 4. 3 | 76 (43.4%) | | |
## +----+---------------------+--------------------------+--------------------+----------+---------+
## | 38 | MD TOTAL | 1. 0 | 9 ( 5.1%) | 175 | 0 |
## | | [factor] | 2. 1 | 3 ( 1.7%) | (100.0%) | (0.0%) |
## | | | 3. 2 | 5 ( 2.9%) | | |
## | | | 4. 3 | 6 ( 3.4%) | | |
## | | | 5. 4 | 4 ( 2.3%) | | |
## | | | 6. 5 | 7 ( 4.0%) | | |
## | | | 7. 6 | 10 ( 5.7%) | | |
## | | | 8. 7 | 6 ( 3.4%) | | |
## | | | 9. 8 | 8 ( 4.6%) | | |
## | | | 10. 9 | 12 ( 6.9%) | | |
## | | | [ 8 others ] | 105 (60.0%) | | |
## +----+---------------------+--------------------------+--------------------+----------+---------+
## | 39 | Alcohol | 1. 0 | 80 (46.8%) | 171 | 4 |
## | | [factor] | 2. 1 | 18 (10.5%) | (97.7%) | (2.3%) |
## | | | 3. 2 | 7 ( 4.1%) | | |
## | | | 4. 3 | 66 (38.6%) | | |
## +----+---------------------+--------------------------+--------------------+----------+---------+
## | 40 | THC | 1. 0 | 116 (67.8%) | 171 | 4 |
## | | [factor] | 2. 1 | 12 ( 7.0%) | (97.7%) | (2.3%) |
## | | | 3. 2 | 3 ( 1.8%) | | |
## | | | 4. 3 | 40 (23.4%) | | |
## +----+---------------------+--------------------------+--------------------+----------+---------+
## | 41 | Cocaine | 1. 0 | 101 (59.1%) | 171 | 4 |
## | | [factor] | 2. 1 | 9 ( 5.3%) | (97.7%) | (2.3%) |
## | | | 3. 2 | 5 ( 2.9%) | | |
## | | | 4. 3 | 56 (32.7%) | | |
## +----+---------------------+--------------------------+--------------------+----------+---------+
## | 42 | Stimulants | 1. 0 | 160 (93.6%) | 171 | 4 |
## | | [factor] | 2. 1 | 6 ( 3.5%) | (97.7%) | (2.3%) |
## | | | 3. 3 | 5 ( 2.9%) | | |
## +----+---------------------+--------------------------+--------------------+----------+---------+
## | 43 | Sedative-hypnotics | 1. 0 | 161 (94.2%) | 171 | 4 |
## | | [factor] | 2. 1 | 4 ( 2.3%) | (97.7%) | (2.3%) |
## | | | 3. 2 | 1 ( 0.6%) | | |
## | | | 4. 3 | 5 ( 2.9%) | | |
## +----+---------------------+--------------------------+--------------------+----------+---------+
## | 44 | Opioids | 1. 0 | 146 (85.4%) | 171 | 4 |
## | | [factor] | 2. 1 | 4 ( 2.3%) | (97.7%) | (2.3%) |
## | | | 3. 3 | 21 (12.3%) | | |
## +----+---------------------+--------------------------+--------------------+----------+---------+
## | 45 | Court order | 1. 0 | 155 (91.2%) | 170 | 5 |
## | | [factor] | 2. 1 | 15 ( 8.8%) | (97.1%) | (2.9%) |
## +----+---------------------+--------------------------+--------------------+----------+---------+
## | 46 | Education | 1. 6 | 2 ( 1.2%) | 166 | 9 |
## | | [factor] | 2. 7 | 2 ( 1.2%) | (94.9%) | (5.1%) |
## | | | 3. 8 | 5 ( 3.0%) | | |
## | | | 4. 9 | 12 ( 7.2%) | | |
## | | | 5. 10 | 12 ( 7.2%) | | |
## | | | 6. 11 | 23 (13.9%) | | |
## | | | 7. 12 | 67 (40.4%) | | |
## | | | 8. 13 | 15 ( 9.0%) | | |
## | | | 9. 14 | 14 ( 8.4%) | | |
## | | | 10. 15 | 1 ( 0.6%) | | |
## | | | [ 4 others ] | 13 ( 7.8%) | | |
## +----+---------------------+--------------------------+--------------------+----------+---------+
## | 47 | Hx of Violence | 1. 0 | 124 (75.6%) | 164 | 11 |
## | | [factor] | 2. 1 | 40 (24.4%) | (93.7%) | (6.3%) |
## +----+---------------------+--------------------------+--------------------+----------+---------+
## | 48 | Disorderly Conduct | 1. 0 | 45 (27.4%) | 164 | 11 |
## | | [factor] | 2. 1 | 119 (72.6%) | (93.7%) | (6.3%) |
## +----+---------------------+--------------------------+--------------------+----------+---------+
## | 49 | Suicide | 1. 0 | 113 (69.8%) | 162 | 13 |
## | | [factor] | 2. 1 | 49 (30.2%) | (92.6%) | (7.4%) |
## +----+---------------------+--------------------------+--------------------+----------+---------+
## | 50 | Abuse | 1. 0 | 101 (62.7%) | 161 | 14 |
## | | [factor] | 2. 1 | 8 ( 5.0%) | (92.0%) | (8.0%) |
## | | | 3. 2 | 20 (12.4%) | | |
## | | | 4. 3 | 4 ( 2.5%) | | |
## | | | 5. 4 | 6 ( 3.7%) | | |
## | | | 6. 5 | 10 ( 6.2%) | | |
## | | | 7. 6 | 4 ( 2.5%) | | |
## | | | 8. 7 | 8 ( 5.0%) | | |
## +----+---------------------+--------------------------+--------------------+----------+---------+
## | 51 | Non-subst Dx | 1. 0 | 102 (66.7%) | 153 | 22 |
## | | [factor] | 2. 1 | 35 (22.9%) | (87.4%) | (12.6%) |
## | | | 3. 2 | 16 (10.5%) | | |
## +----+---------------------+--------------------------+--------------------+----------+---------+
## | 52 | Subst Dx | 1. 0 | 42 (27.6%) | 152 | 23 |
## | | [factor] | 2. 1 | 61 (40.1%) | (86.9%) | (13.1%) |
## | | | 3. 2 | 35 (23.0%) | | |
## | | | 4. 3 | 14 ( 9.2%) | | |
## +----+---------------------+--------------------------+--------------------+----------+---------+
## | 53 | Psych meds. | 1. 0 | 19 (33.3%) | 57 | 118 |
## | | [factor] | 2. 1 | 21 (36.8%) | (32.6%) | (67.4%) |
## | | | 3. 2 | 17 (29.8%) | | |
## +----+---------------------+--------------------------+--------------------+----------+---------+Coorelation
Next we will see the correlation among ADHD questions and MD questions. As we can deduce from below 2 correlation plots, ADHD questions are highly correlated and MD questions comparatively shows moderate correlation.
Data Preparation
Factor Analysis
Like PCA, Factor Analysis too, reduces larger number of variables into smaller number of variables, called latent variables.It is used to identify underlying factors that explain the correlation among set of variables. Factor analysis is a great tool for treating multivariate questionnaire studies.
For ADHD questions, test of the hypothesis that 3 factors are sufficient. The chi square statistic is 197.3 on 102 degrees of freedom. The p-value is 0.0000000476. We have used regression factor scores here as they predict the location of each individual on the factor.
##
## Call:
## factanal(x = sapply(adhd_data[, c(4:21)], as.numeric), factors = 3, scores = "regression", rotation = "promax")
##
## Uniquenesses:
## ADHD Q1 ADHD Q2 ADHD Q3 ADHD Q4 ADHD Q5 ADHD Q6 ADHD Q7 ADHD Q8
## 0.493 0.470 0.447 0.360 0.454 0.605 0.457 0.344
## ADHD Q9 ADHD Q10 ADHD Q11 ADHD Q12 ADHD Q13 ADHD Q14 ADHD Q15 ADHD Q16
## 0.378 0.372 0.444 0.516 0.008 0.460 0.538 0.266
## ADHD Q17 ADHD Q18
## 0.496 0.360
##
## Loadings:
## Factor1 Factor2 Factor3
## ADHD Q1 0.738 0.102 -0.142
## ADHD Q2 0.743
## ADHD Q3 0.972 -0.186 -0.144
## ADHD Q4 0.967 -0.164
## ADHD Q5 0.379 0.447
## ADHD Q6 0.173 0.185 0.332
## ADHD Q7 0.675
## ADHD Q8 0.731 0.110
## ADHD Q9 0.500 0.194 0.159
## ADHD Q10 0.687 0.237 -0.113
## ADHD Q11 0.480 0.327
## ADHD Q12 0.302 0.511
## ADHD Q13 -0.163 1.142
## ADHD Q14 0.158 0.122 0.512
## ADHD Q15 0.638
## ADHD Q16 -0.241 1.014
## ADHD Q17 0.682
## ADHD Q18 0.823 -0.116
##
## Factor1 Factor2 Factor3
## SS loadings 5.298 3.079 2.095
## Proportion Var 0.294 0.171 0.116
## Cumulative Var 0.294 0.465 0.582
##
## Factor Correlations:
## Factor1 Factor2 Factor3
## Factor1 1.000 0.765 -0.685
## Factor2 0.765 1.000 -0.748
## Factor3 -0.685 -0.748 1.000
##
## Test of the hypothesis that 3 factors are sufficient.
## The chi square statistic is 197.3 on 102 degrees of freedom.
## The p-value is 4.76e-08
For MD questions we could see that 1st MD question has multiple sub questions as compared to 2nd and 3rd question. Now for these set of MD questions too, we will apply similar factor analysis as of ADHD questions. Test of the hypothesis that 3 factors are sufficient. The chi square statistic is 88.82 on 63 degrees of freedom. The p-value is 0.0178.
##
## Call:
## factanal(x = sapply(adhd_data[, c(23:37)], as.numeric), factors = 3, scores = "regression", rotation = "promax")
##
## Uniquenesses:
## MD Q1a MD Q1b MD Q1c MD Q1d MD Q1e MD Q1f MD Q1g MD Q1h MD Q1i MD Q1j MD Q1k
## 0.562 0.506 0.736 0.735 0.564 0.536 0.446 0.388 0.507 0.567 0.638
## MD Q1L MD Q1m MD Q2 MD Q3
## 0.005 0.719 0.394 0.601
##
## Loadings:
## Factor1 Factor2 Factor3
## MD Q1a 0.345 0.117 0.308
## MD Q1b 0.732
## MD Q1c 0.565
## MD Q1d 0.342 0.257
## MD Q1e 0.283 0.568 -0.194
## MD Q1f 0.632
## MD Q1g 0.735
## MD Q1h 0.856
## MD Q1i 0.738
## MD Q1j 0.662
## MD Q1k -0.172 0.515 0.265
## MD Q1L 0.133 -0.124 0.981
## MD Q1m 0.228 0.158 0.240
## MD Q2 0.738
## MD Q3 0.751 -0.184
##
## Factor1 Factor2 Factor3
## SS loadings 3.009 2.790 1.241
## Proportion Var 0.201 0.186 0.083
## Cumulative Var 0.201 0.387 0.469
##
## Factor Correlations:
## Factor1 Factor2 Factor3
## Factor1 1.000 0.550 -0.587
## Factor2 0.550 1.000 -0.563
## Factor3 -0.587 -0.563 1.000
##
## Test of the hypothesis that 3 factors are sufficient.
## The chi square statistic is 88.82 on 63 degrees of freedom.
## The p-value is 0.0178
In the next step we will remove all ADHD Question columns, ADHD Total, MD questions columns and MD TOTAL columns. Then we will add the new factors found above for ADHD and MD questions.
Here is glimpse of new set of data.
## Age Sex Race ADHD Total MD TOTAL Alcohol THC Cocaine Stimulants
## 1 24 1 1 40 15 1 1 1 0
## 2 48 2 1 55 14 0 0 0 0
## 3 51 2 1 31 5 0 0 0 0
## 4 43 1 1 45 13 1 1 1 1
## 5 34 1 1 48 7 1 1 0 0
## 6 39 2 1 55 14 1 0 0 0
## Sedative-hypnotics Opioids Court order Education Hx of Violence
## 1 0 0 1 11 0
## 2 0 0 0 14 0
## 3 0 0 0 12 0
## 4 0 0 0 12 0
## 5 0 0 1 9 1
## 6 0 0 0 11 0
## Disorderly Conduct Suicide Abuse Non-subst Dx Subst Dx Psych meds. ADHD_FACT1
## 1 1 1 0 2 0 2 1.6922046
## 2 0 1 4 1 0 1 2.0799334
## 3 0 0 6 2 0 1 -0.5301540
## 4 0 1 7 2 0 2 0.9321586
## 5 1 1 0 2 0 0 2.5823393
## 6 1 1 2 0 0 0 -0.8422991
## ADHD_FACT2 ADHD_FACT3 MD_FACT1 MD_FACT2 MD_FACT3
## 1 1.6740898 -3.3243648 1.3855809 1.59853502 -2.8509956
## 2 1.5195976 -2.6626233 0.7973360 -0.08361024 0.3704740
## 3 0.3261461 -0.1297720 0.4673052 -0.80624391 -1.0898824
## 4 -0.5385242 0.2275811 0.8725442 -0.45310917 0.5084134
## 5 -1.6535142 -0.2129593 2.1105464 -1.37884110 -1.8594994
## 6 1.3342893 1.0827141 0.2816620 0.44486489 0.4402313Handling missing values
We can see from this chart that Psych meds. contributes to 67.43% of missing data which is maximum among all missing data in other columns. We will remove this column before imputation. We then impute values using MICE (Multivariate Imputation by Chained Equations) for columns having missing values.
## Alcohol THC Cocaine Stimulants Sedative_hypnotics Opioids Court_order
## 0:80 0:118 0:102 0:163 0:162 0:147 0:158
## 1:21 1: 13 1: 10 1: 7 1: 5 1: 6 1: 17
## 2: 8 2: 4 2: 7 3: 5 2: 1 3: 22
## 3:66 3: 40 3: 56 3: 7
##
##
##
## Education Hx_of_Violence Disorderly_Conduct Suicide Abuse
## 12 :68 0:132 0: 47 0:124 0 :108
## 11 :25 1: 43 1:128 1: 51 2 : 21
## 13 :16 5 : 12
## 14 :14 7 : 11
## 9 :13 1 : 8
## 10 :13 4 : 6
## (Other):26 (Other): 9
## Non_subst_Dx Subst_Dx
## 0:114 0:51
## 1: 39 1:66
## 2: 22 2:38
## 3:20
##
##
## ## Alcohol THC Cocaine Stimulants Sedative_hypnotics Opioids Court_order
## 1 1 1 1 0 0 0 1
## 2 0 0 0 0 0 0 0
## 3 0 0 0 0 0 0 0
## 4 1 1 1 1 0 0 0
## 5 1 1 0 0 0 0 1
## 6 1 0 0 0 0 0 0
## Education Hx_of_Violence Disorderly_Conduct Suicide Abuse Non_subst_Dx
## 1 11 0 1 1 0 2
## 2 14 0 0 1 4 1
## 3 12 0 0 0 6 2
## 4 12 0 0 1 7 2
## 5 9 1 1 1 0 2
## 6 11 0 1 1 2 0
## Subst_Dx ADHD_Total ADHD_FACT1 ADHD_FACT2 ADHD_FACT3 MD_Total MD_FACT1
## 1 0 40 1.6922046 1.6740898 -3.3243648 15 1.3855809
## 2 0 55 2.0799334 1.5195976 -2.6626233 14 0.7973360
## 3 0 31 -0.5301540 0.3261461 -0.1297720 5 0.4673052
## 4 0 45 0.9321586 -0.5385242 0.2275811 13 0.8725442
## 5 0 48 2.5823393 -1.6535142 -0.2129593 7 2.1105464
## 6 0 55 -0.8422991 1.3342893 1.0827141 14 0.2816620
## MD_FACT2 MD_FACT3 Race Sex Age
## 1 1.59853502 -2.8509956 1 1 24
## 2 -0.08361024 0.3704740 1 2 48
## 3 -0.80624391 -1.0898824 1 2 51
## 4 -0.45310917 0.5084134 1 1 43
## 5 -1.37884110 -1.8594994 1 1 34
## 6 0.44486489 0.4402313 1 2 39Preprocess using transformation
In this transformation, we would first use dummyVars to create dummy variables for categorical features. Next we use center and scaling transformation.
## Alcohol.0 Alcohol.1 Alcohol.2 Alcohol.3 THC.0 THC.1 THC.2
## 1 -0.9150373 2.7002645 -0.218244 -0.7759153 -1.434694 3.5199900 -0.1525062
## 2 1.0866068 -0.3682179 -0.218244 -0.7759153 0.693030 -0.2824683 -0.1525062
## 3 1.0866068 -0.3682179 -0.218244 -0.7759153 0.693030 -0.2824683 -0.1525062
## 4 -0.9150373 2.7002645 -0.218244 -0.7759153 -1.434694 3.5199900 -0.1525062
## 5 -0.9150373 2.7002645 -0.218244 -0.7759153 -1.434694 3.5199900 -0.1525062
## 6 -0.9150373 2.7002645 -0.218244 -0.7759153 0.693030 -0.2824683 -0.1525062
## THC.3 Cocaine.0 Cocaine.1 Cocaine.2 Cocaine.3 Stimulants.0
## 1 -0.5427736 -1.1786755 4.0503968 -0.2035401 -0.6840315 0.270553
## 2 -0.5427736 0.8435619 -0.2454786 -0.2035401 -0.6840315 0.270553
## 3 -0.5427736 0.8435619 -0.2454786 -0.2035401 -0.6840315 0.270553
## 4 -0.5427736 -1.1786755 4.0503968 -0.2035401 -0.6840315 -3.675012
## 5 -0.5427736 0.8435619 -0.2454786 -0.2035401 -0.6840315 0.270553
## 6 -0.5427736 0.8435619 -0.2454786 -0.2035401 -0.6840315 0.270553
## Stimulants.1 Stimulants.3 Sedative_hypnotics.0 Sedative_hypnotics.1
## 1 -0.2035401 -0.1710079 0.2824683 -0.1710079
## 2 -0.2035401 -0.1710079 0.2824683 -0.1710079
## 3 -0.2035401 -0.1710079 0.2824683 -0.1710079
## 4 4.8849623 -0.1710079 0.2824683 -0.1710079
## 5 -0.2035401 -0.1710079 0.2824683 -0.1710079
## 6 -0.2035401 -0.1710079 0.2824683 -0.1710079
## Sedative_hypnotics.2 Sedative_hypnotics.3 Opioids.0 Opioids.1 Opioids.3
## 1 -0.07559289 -0.2035401 0.435187 -0.1878832 -0.3781127
## 2 -0.07559289 -0.2035401 0.435187 -0.1878832 -0.3781127
## 3 -0.07559289 -0.2035401 0.435187 -0.1878832 -0.3781127
## 4 -0.07559289 -0.2035401 0.435187 -0.1878832 -0.3781127
## 5 -0.07559289 -0.2035401 0.435187 -0.1878832 -0.3781127
## 6 -0.07559289 -0.2035401 0.435187 -0.1878832 -0.3781127
## Court_order.0 Court_order.1 Education.6 Education.7 Education.8 Education.9
## 1 -3.0399027 3.0399027 -0.1316898 -0.107213 -0.1878832 -0.2824683
## 2 0.3270781 -0.3270781 -0.1316898 -0.107213 -0.1878832 -0.2824683
## 3 0.3270781 -0.3270781 -0.1316898 -0.107213 -0.1878832 -0.2824683
## 4 0.3270781 -0.3270781 -0.1316898 -0.107213 -0.1878832 -0.2824683
## 5 -3.0399027 3.0399027 -0.1316898 -0.107213 -0.1878832 3.5199900
## 6 0.3270781 -0.3270781 -0.1316898 -0.107213 -0.1878832 -0.2824683
## Education.10 Education.11 Education.12 Education.13 Education.14 Education.15
## 1 -0.2824683 2.4424812 -0.7949104 -0.316313 -0.2940402 -0.07559289
## 2 -0.2824683 -0.4070802 -0.7949104 -0.316313 3.3814621 -0.07559289
## 3 -0.2824683 -0.4070802 1.2508149 -0.316313 -0.2940402 -0.07559289
## 4 -0.2824683 -0.4070802 1.2508149 -0.316313 -0.2940402 -0.07559289
## 5 -0.2824683 -0.4070802 -0.7949104 -0.316313 -0.2940402 -0.07559289
## 6 -0.2824683 2.4424812 -0.7949104 -0.316313 -0.2940402 -0.07559289
## Education.16 Education.17 Education.18 Education.19 Hx_of_Violence.0
## 1 -0.218244 -0.107213 -0.1316898 -0.07559289 0.5691187
## 2 -0.218244 -0.107213 -0.1316898 -0.07559289 0.5691187
## 3 -0.218244 -0.107213 -0.1316898 -0.07559289 0.5691187
## 4 -0.218244 -0.107213 -0.1316898 -0.07559289 0.5691187
## 5 -0.218244 -0.107213 -0.1316898 -0.07559289 -1.7470621
## 6 -0.218244 -0.107213 -0.1316898 -0.07559289 0.5691187
## Hx_of_Violence.1 Disorderly_Conduct.0 Disorderly_Conduct.1 Abuse.0
## 1 -0.5691187 -0.6042262 0.6042262 0.7853823
## 2 -0.5691187 1.6455522 -1.6455522 -1.2659894
## 3 -0.5691187 1.6455522 -1.6455522 -1.2659894
## 4 -0.5691187 1.6455522 -1.6455522 -1.2659894
## 5 1.7470621 -0.6042262 0.6042262 0.7853823
## 6 -0.5691187 -0.6042262 0.6042262 -1.2659894
## Abuse.1 Abuse.2 Abuse.3 Abuse.4 Abuse.5 Abuse.6 Abuse.7
## 1 -0.218244 -0.3682179 -0.1710079 -0.1878832 -0.270553 -0.1525062 -0.2582439
## 2 -0.218244 -0.3682179 -0.1710079 5.2920425 -0.270553 -0.1525062 -0.2582439
## 3 -0.218244 -0.3682179 -0.1710079 -0.1878832 -0.270553 6.5196407 -0.2582439
## 4 -0.218244 -0.3682179 -0.1710079 -0.1878832 -0.270553 -0.1525062 3.8501813
## 5 -0.218244 -0.3682179 -0.1710079 -0.1878832 -0.270553 -0.1525062 -0.2582439
## 6 -0.218244 2.7002645 -0.1710079 -0.1878832 -0.270553 -0.1525062 -0.2582439
## Non_subst_Dx.0 Non_subst_Dx.1 Non_subst_Dx.2 Subst_Dx.0 Subst_Dx.1 Subst_Dx.2
## 1 -1.3631483 -0.533972 2.6296017 1.554824 -0.7759153 -0.5251545
## 2 -1.3631483 1.862056 -0.3781127 1.554824 -0.7759153 -0.5251545
## 3 -1.3631483 -0.533972 2.6296017 1.554824 -0.7759153 -0.5251545
## 4 -1.3631483 -0.533972 2.6296017 1.554824 -0.7759153 -0.5251545
## 5 -1.3631483 -0.533972 2.6296017 1.554824 -0.7759153 -0.5251545
## 6 0.7294039 -0.533972 -0.3781127 1.554824 -0.7759153 -0.5251545
## Subst_Dx.3 ADHD_Total.0 ADHD_Total.1 ADHD_Total.3 ADHD_Total.5 ADHD_Total.6
## 1 -0.3581828 -0.07559289 -0.107213 -0.07559289 -0.07559289 -0.1316898
## 2 -0.3581828 -0.07559289 -0.107213 -0.07559289 -0.07559289 -0.1316898
## 3 -0.3581828 -0.07559289 -0.107213 -0.07559289 -0.07559289 -0.1316898
## 4 -0.3581828 -0.07559289 -0.107213 -0.07559289 -0.07559289 -0.1316898
## 5 -0.3581828 -0.07559289 -0.107213 -0.07559289 -0.07559289 -0.1316898
## 6 -0.3581828 -0.07559289 -0.107213 -0.07559289 -0.07559289 -0.1316898
## ADHD_Total.7 ADHD_Total.8 ADHD_Total.9 ADHD_Total.10 ADHD_Total.11
## 1 -0.107213 -0.07559289 -0.107213 -0.107213 -0.07559289
## 2 -0.107213 -0.07559289 -0.107213 -0.107213 -0.07559289
## 3 -0.107213 -0.07559289 -0.107213 -0.107213 -0.07559289
## 4 -0.107213 -0.07559289 -0.107213 -0.107213 -0.07559289
## 5 -0.107213 -0.07559289 -0.107213 -0.107213 -0.07559289
## 6 -0.107213 -0.07559289 -0.107213 -0.107213 -0.07559289
## ADHD_Total.12 ADHD_Total.13 ADHD_Total.14 ADHD_Total.16 ADHD_Total.17
## 1 -0.1525062 -0.07559289 -0.1525062 -0.07559289 -0.218244
## 2 -0.1525062 -0.07559289 -0.1525062 -0.07559289 -0.218244
## 3 -0.1525062 -0.07559289 -0.1525062 -0.07559289 -0.218244
## 4 -0.1525062 -0.07559289 -0.1525062 -0.07559289 -0.218244
## 5 -0.1525062 -0.07559289 -0.1525062 -0.07559289 -0.218244
## 6 -0.1525062 -0.07559289 -0.1525062 -0.07559289 -0.218244
## ADHD_Total.18 ADHD_Total.19 ADHD_Total.20 ADHD_Total.21 ADHD_Total.23
## 1 -0.07559289 -0.1710079 -0.1316898 -0.1316898 -0.07559289
## 2 -0.07559289 -0.1710079 -0.1316898 -0.1316898 -0.07559289
## 3 -0.07559289 -0.1710079 -0.1316898 -0.1316898 -0.07559289
## 4 -0.07559289 -0.1710079 -0.1316898 -0.1316898 -0.07559289
## 5 -0.07559289 -0.1710079 -0.1316898 -0.1316898 -0.07559289
## 6 -0.07559289 -0.1710079 -0.1316898 -0.1316898 -0.07559289
## ADHD_Total.24 ADHD_Total.25 ADHD_Total.26 ADHD_Total.27 ADHD_Total.28
## 1 -0.1878832 -0.1525062 -0.07559289 -0.107213 -0.1878832
## 2 -0.1878832 -0.1525062 -0.07559289 -0.107213 -0.1878832
## 3 -0.1878832 -0.1525062 -0.07559289 -0.107213 -0.1878832
## 4 -0.1878832 -0.1525062 -0.07559289 -0.107213 -0.1878832
## 5 -0.1878832 -0.1525062 -0.07559289 -0.107213 -0.1878832
## 6 -0.1878832 -0.1525062 -0.07559289 -0.107213 -0.1878832
## ADHD_Total.29 ADHD_Total.30 ADHD_Total.31 ADHD_Total.32 ADHD_Total.33
## 1 -0.107213 -0.1316898 -0.2035401 -0.2035401 -0.1316898
## 2 -0.107213 -0.1316898 -0.2035401 -0.2035401 -0.1316898
## 3 -0.107213 -0.1316898 4.8849623 -0.2035401 -0.1316898
## 4 -0.107213 -0.1316898 -0.2035401 -0.2035401 -0.1316898
## 5 -0.107213 -0.1316898 -0.2035401 -0.2035401 -0.1316898
## 6 -0.107213 -0.1316898 -0.2035401 -0.2035401 -0.1316898
## ADHD_Total.34 ADHD_Total.35 ADHD_Total.36 ADHD_Total.37 ADHD_Total.38
## 1 -0.07559289 -0.1316898 -0.1316898 -0.107213 -0.1316898
## 2 -0.07559289 -0.1316898 -0.1316898 -0.107213 -0.1316898
## 3 -0.07559289 -0.1316898 -0.1316898 -0.107213 -0.1316898
## 4 -0.07559289 -0.1316898 -0.1316898 -0.107213 -0.1316898
## 5 -0.07559289 -0.1316898 -0.1316898 -0.107213 -0.1316898
## 6 -0.07559289 -0.1316898 -0.1316898 -0.107213 -0.1316898
## ADHD_Total.39 ADHD_Total.40 ADHD_Total.41 ADHD_Total.42 ADHD_Total.43
## 1 -0.1316898 5.2920425 -0.1316898 -0.1710079 -0.1316898
## 2 -0.1316898 -0.1878832 -0.1316898 -0.1710079 -0.1316898
## 3 -0.1316898 -0.1878832 -0.1316898 -0.1710079 -0.1316898
## 4 -0.1316898 -0.1878832 -0.1316898 -0.1710079 -0.1316898
## 5 -0.1316898 -0.1878832 -0.1316898 -0.1710079 -0.1316898
## 6 -0.1316898 -0.1878832 -0.1316898 -0.1710079 -0.1316898
## ADHD_Total.44 ADHD_Total.45 ADHD_Total.46 ADHD_Total.47 ADHD_Total.48
## 1 -0.107213 -0.1316898 -0.1316898 -0.1316898 -0.1878832
## 2 -0.107213 -0.1316898 -0.1316898 -0.1316898 -0.1878832
## 3 -0.107213 -0.1316898 -0.1316898 -0.1316898 -0.1878832
## 4 -0.107213 7.5502129 -0.1316898 -0.1316898 -0.1878832
## 5 -0.107213 -0.1316898 -0.1316898 -0.1316898 5.2920425
## 6 -0.107213 -0.1316898 -0.1316898 -0.1316898 -0.1878832
## ADHD_Total.49 ADHD_Total.50 ADHD_Total.51 ADHD_Total.52 ADHD_Total.53
## 1 -0.1878832 -0.1316898 -0.107213 -0.1316898 -0.07559289
## 2 -0.1878832 -0.1316898 -0.107213 -0.1316898 -0.07559289
## 3 -0.1878832 -0.1316898 -0.107213 -0.1316898 -0.07559289
## 4 -0.1878832 -0.1316898 -0.107213 -0.1316898 -0.07559289
## 5 -0.1878832 -0.1316898 -0.107213 -0.1316898 -0.07559289
## 6 -0.1878832 -0.1316898 -0.107213 -0.1316898 -0.07559289
## ADHD_Total.54 ADHD_Total.55 ADHD_Total.56 ADHD_Total.57 ADHD_Total.58
## 1 -0.1316898 -0.1316898 -0.1316898 -0.107213 -0.07559289
## 2 -0.1316898 7.5502129 -0.1316898 -0.107213 -0.07559289
## 3 -0.1316898 -0.1316898 -0.1316898 -0.107213 -0.07559289
## 4 -0.1316898 -0.1316898 -0.1316898 -0.107213 -0.07559289
## 5 -0.1316898 -0.1316898 -0.1316898 -0.107213 -0.07559289
## 6 -0.1316898 7.5502129 -0.1316898 -0.107213 -0.07559289
## ADHD_Total.62 ADHD_Total.63 ADHD_Total.65 ADHD_Total.67 ADHD_Total.69
## 1 -0.107213 -0.07559289 -0.1316898 -0.07559289 -0.07559289
## 2 -0.107213 -0.07559289 -0.1316898 -0.07559289 -0.07559289
## 3 -0.107213 -0.07559289 -0.1316898 -0.07559289 -0.07559289
## 4 -0.107213 -0.07559289 -0.1316898 -0.07559289 -0.07559289
## 5 -0.107213 -0.07559289 -0.1316898 -0.07559289 -0.07559289
## 6 -0.107213 -0.07559289 -0.1316898 -0.07559289 -0.07559289
## ADHD_Total.71 ADHD_Total.72 ADHD_FACT1 ADHD_FACT2 ADHD_FACT3 MD_Total.0
## 1 -0.07559289 -0.107213 1.0783202 1.2371956 -2.13013067 -0.2321789
## 2 -0.07559289 -0.107213 1.3253918 1.1230219 -1.70611102 -0.2321789
## 3 -0.07559289 -0.107213 -0.3378290 0.2410304 -0.08315315 -0.2321789
## 4 -0.07559289 -0.107213 0.5939976 -0.3979833 0.14582561 -0.2321789
## 5 -0.07559289 -0.107213 1.6455389 -1.2219897 -0.13645646 -0.2321789
## 6 -0.07559289 -0.107213 -0.5367366 0.9860743 0.69376338 -0.2321789
## MD_Total.1 MD_Total.2 MD_Total.3 MD_Total.4 MD_Total.5 MD_Total.6 MD_Total.7
## 1 -0.1316898 -0.1710079 -0.1878832 -0.1525062 -0.2035401 -0.2454786 -0.1878832
## 2 -0.1316898 -0.1710079 -0.1878832 -0.1525062 -0.2035401 -0.2454786 -0.1878832
## 3 -0.1316898 -0.1710079 -0.1878832 -0.1525062 4.8849623 -0.2454786 -0.1878832
## 4 -0.1316898 -0.1710079 -0.1878832 -0.1525062 -0.2035401 -0.2454786 -0.1878832
## 5 -0.1316898 -0.1710079 -0.1878832 -0.1525062 -0.2035401 -0.2454786 5.2920425
## 6 -0.1316898 -0.1710079 -0.1878832 -0.1525062 -0.2035401 -0.2454786 -0.1878832
## MD_Total.8 MD_Total.9 MD_Total.10 MD_Total.11 MD_Total.12 MD_Total.13
## 1 -0.218244 -0.270553 -0.2824683 -0.3376308 -0.270553 -0.2824683
## 2 -0.218244 -0.270553 -0.2824683 -0.3376308 -0.270553 -0.2824683
## 3 -0.218244 -0.270553 -0.2824683 -0.3376308 -0.270553 -0.2824683
## 4 -0.218244 -0.270553 -0.2824683 -0.3376308 -0.270553 3.5199900
## 5 -0.218244 -0.270553 -0.2824683 -0.3376308 -0.270553 -0.2824683
## 6 -0.218244 -0.270553 -0.2824683 -0.3376308 -0.270553 -0.2824683
## MD_Total.14 MD_Total.15 MD_Total.16 MD_Total.17 MD_FACT1 MD_FACT2
## 1 -0.270553 3.3814621 -0.270553 -0.2582439 1.2270551 1.42214452
## 2 3.675012 -0.2940402 -0.270553 -0.2582439 0.7061119 -0.07438426
## 3 -0.270553 -0.2940402 -0.270553 -0.2582439 0.4138403 -0.71727885
## 4 -0.270553 -0.2940402 -0.270553 -0.2582439 0.7727155 -0.40311079
## 5 -0.270553 -0.2940402 -0.270553 -0.2582439 1.8690765 -1.22669275
## 6 3.675012 -0.2940402 -0.270553 -0.2582439 0.2494367 0.39577623
## MD_FACT3 Race.1 Race.2 Race.3 Race.6 Sex.1 Sex.2
## 1 -2.2790099 1.192636 -1.151397 -0.07559289 -0.107213 0.8736647 -0.8736647
## 2 0.2961471 1.192636 -1.151397 -0.07559289 -0.107213 -1.1380633 1.1380633
## 3 -0.8712229 1.192636 -1.151397 -0.07559289 -0.107213 -1.1380633 1.1380633
## 4 0.4064121 1.192636 -1.151397 -0.07559289 -0.107213 0.8736647 -0.8736647
## 5 -1.4864343 1.192636 -1.151397 -0.07559289 -0.107213 0.8736647 -0.8736647
## 6 0.3519091 1.192636 -1.151397 -0.07559289 -0.107213 -1.1380633 1.1380633
## Age Suicide
## 1 -1.38522071 1
## 2 0.76320137 1
## 3 1.03175413 0
## 4 0.31561343 1
## 5 -0.49004485 1
## 6 -0.04245691 1Training and Test Partition
In this step for data preparation we will partition the training dataset in training and validation sets using createDataPartition method from caret package. We will reserve 75% for training and rest 25% for validation purpose.
Principal Component Analysis
Principal Compenent Analysis (PCA) is one way for which we can reduce the dimensionality of a data set which would help increase the interpretability of the data while minimizing information loss. We’re going to perform PCA for ADHD and MD response questions below while using scree plots to determine the numberof PCA’s to keep. The Scree plot will display the eigenvalues in a downward curve, and order them from largest to smallest.
Groups: - All ADHD Questions - All MD Questions
ADHD
First we will use the prcomp function to perform a prinicpal component analysis on the adhd response questions. We will also center and scale this dataset to ensure normality.
We will use the factoextra library to display the results of our PCA. this library specializes in extracting and visualizing the out put of exploratory multivariate analysis. Through this and a correlation table we can see the relationship between each ADHD response score and the Prinicple Components. The list of PC’s (sorted by descending impact on the variance of score) whos us the components that are the most impactful in grouping the respondents. By viewing the associated plots and correlations we can see the ADHd response questions 4,8,9,10,16,17,18 are the most impactful on plot of PC1 and PC2 which indicates they should be used in initial modeling of this dataset. We can also see the factors that are most impactful for other principal components below.
| PC1 | PC2 | PC3 | PC4 | PC5 | PC6 | PC7 | PC8 | PC9 | PC10 | |
|---|---|---|---|---|---|---|---|---|---|---|
| ADHD Q1 | 0.6985307 | -0.2193486 | 0.3373110 | -0.3701134 | 0.1620365 | -0.0553265 | -0.1155856 | 0.0634832 | -0.1094866 | -0.0377477 |
| ADHD Q2 | 0.7094961 | -0.3217329 | 0.2195271 | -0.2415871 | 0.3149977 | -0.1249863 | -0.0479395 | 0.0317923 | -0.0122129 | -0.0999910 |
| ADHD Q3 | 0.6729396 | -0.3603530 | 0.1289838 | 0.0346323 | -0.4064821 | -0.2440550 | 0.2269925 | 0.0498093 | -0.1499112 | 0.0857626 |
| ADHD Q4 | 0.7369016 | -0.3570819 | 0.1752141 | -0.0289810 | 0.0048257 | 0.1540025 | 0.2389656 | 0.0989201 | 0.0467233 | 0.0867524 |
| ADHD Q5 | 0.7270038 | -0.1316262 | -0.4393256 | 0.0626412 | -0.2317282 | -0.1653866 | 0.0161188 | -0.0428040 | 0.0762013 | -0.1024186 |
| ADHD Q6 | 0.6478223 | 0.0330650 | -0.3661242 | -0.4081271 | -0.2010428 | -0.1415404 | -0.2965562 | 0.1158451 | -0.0211615 | 0.1254054 |
| ADHD Q7 | 0.7397991 | -0.1570714 | 0.0745633 | -0.0177672 | -0.2719875 | 0.3665232 | -0.2695678 | 0.0441089 | 0.1778132 | -0.1383997 |
| ADHD Q8 | 0.8036604 | -0.1261053 | 0.1172968 | 0.2398635 | -0.1092407 | 0.2986436 | -0.0941213 | -0.0499510 | 0.1101020 | -0.0180454 |
| ADHD Q9 | 0.7964059 | -0.0211553 | 0.0758966 | 0.2369039 | 0.0344579 | 0.1119800 | -0.0114321 | -0.1023371 | -0.2126006 | 0.3686080 |
| ADHD Q10 | 0.7928193 | -0.0575642 | 0.1026147 | 0.0988034 | 0.0887157 | -0.2189485 | 0.1349158 | -0.0761935 | 0.3242706 | -0.0426716 |
| ADHD Q11 | 0.7417771 | -0.1597164 | -0.1426989 | 0.2224023 | 0.2630911 | -0.0408302 | -0.1102323 | -0.2676399 | -0.1642994 | -0.0785017 |
| ADHD Q12 | 0.6870249 | 0.2504992 | 0.1759628 | 0.3410893 | -0.0587711 | -0.2751124 | -0.2002291 | 0.0034243 | -0.1083341 | -0.2645647 |
| ADHD Q13 | 0.7625738 | -0.0172434 | -0.4488216 | 0.0218549 | 0.1970229 | 0.1218555 | -0.0469157 | 0.0246575 | -0.1670974 | 0.0501835 |
| ADHD Q14 | 0.7182484 | 0.0234819 | -0.3752626 | 0.0082586 | 0.2726111 | 0.0471124 | 0.2687958 | 0.1484807 | 0.1890430 | -0.0475068 |
| ADHD Q15 | 0.6366225 | 0.3890284 | -0.0003455 | -0.2716084 | -0.1802961 | 0.1957894 | 0.3451969 | -0.1635894 | -0.2382264 | -0.2557042 |
| ADHD Q16 | 0.6730194 | 0.5370634 | 0.1543455 | -0.1542437 | 0.1306438 | 0.0783525 | -0.0724010 | -0.0541541 | 0.0570699 | 0.0511255 |
| ADHD Q17 | 0.6545364 | 0.4299515 | 0.1096686 | 0.2022074 | 0.0183908 | -0.0287934 | 0.0308355 | 0.5043290 | -0.0651618 | 0.0409995 |
| ADHD Q18 | 0.7097528 | 0.4135904 | 0.1118259 | -0.1089439 | -0.0884321 | -0.1447675 | 0.0202057 | -0.2629143 | 0.2056367 | 0.2302737 |
## Importance of components:
## PC1 PC2 PC3 PC4 PC5 PC6 PC7
## Standard deviation 3.0498 1.16471 1.00693 0.8990 0.85050 0.7707 0.75154
## Proportion of Variance 0.5168 0.07536 0.05633 0.0449 0.04019 0.0330 0.03138
## Cumulative Proportion 0.5168 0.59211 0.64844 0.6933 0.73353 0.7665 0.79791
## PC8 PC9 PC10 PC11 PC12 PC13 PC14
## Standard deviation 0.70763 0.66788 0.64291 0.63647 0.60782 0.59495 0.53747
## Proportion of Variance 0.02782 0.02478 0.02296 0.02251 0.02052 0.01966 0.01605
## Cumulative Proportion 0.82573 0.85051 0.87347 0.89598 0.91650 0.93617 0.95222
## PC15 PC16 PC17 PC18
## Standard deviation 0.52569 0.46267 0.4529 0.40566
## Proportion of Variance 0.01535 0.01189 0.0114 0.00914
## Cumulative Proportion 0.96757 0.97946 0.9909 1.00000
We will repeat the process above on MD response questions to get a better understanding of which of these questions are the most impactful. we can see for PC1 and PC2 MD Q1h, 1j, 1g and Q2 have the greatest impact.
MD
| PC1 | PC2 | PC3 | PC4 | PC5 | PC6 | PC7 | PC8 | PC9 | PC10 | |
|---|---|---|---|---|---|---|---|---|---|---|
| MD Q1a | -0.6888686 | -0.1322144 | 0.0229725 | -0.3776545 | 0.1155431 | -0.0404785 | 0.0388949 | -0.1162723 | 0.4468442 | 0.1964300 |
| MD Q1b | -0.6421749 | -0.3857186 | 0.1381774 | 0.1459230 | -0.0448104 | 0.3624483 | -0.0835332 | -0.0859054 | -0.1659170 | 0.2404834 |
| MD Q1c | -0.4439895 | 0.4544153 | -0.4763749 | -0.0977568 | 0.2182164 | 0.2983609 | -0.0077300 | 0.4015333 | 0.0420701 | 0.1271287 |
| MD Q1d | -0.5655577 | 0.0049581 | 0.0644164 | -0.0442116 | 0.6697469 | 0.0871900 | 0.2433963 | -0.1694837 | -0.1157862 | -0.3292808 |
| MD Q1e | -0.6391312 | 0.2391336 | -0.1887304 | 0.1745264 | 0.2662259 | -0.3369547 | -0.4017349 | -0.0905138 | 0.0118533 | 0.1715816 |
| MD Q1f | -0.6668512 | -0.2825469 | 0.1009022 | 0.2032375 | 0.0540147 | -0.3484816 | 0.1227297 | 0.0355070 | 0.1087798 | 0.0646588 |
| MD Q1g | -0.6818994 | -0.3687898 | 0.0536512 | 0.1911240 | -0.0795600 | -0.1339641 | -0.0784985 | 0.2639884 | 0.0297445 | -0.2777134 |
| MD Q1h | -0.6193596 | 0.4973240 | 0.0584859 | 0.2126773 | -0.1071923 | -0.1494907 | 0.2548126 | -0.1564241 | -0.1695906 | 0.2257054 |
| MD Q1i | -0.5873223 | 0.4451927 | -0.1405849 | 0.2802170 | -0.3060325 | 0.0937060 | 0.3489444 | -0.0655044 | 0.1712265 | -0.1236134 |
| MD Q1j | -0.5954591 | 0.4356557 | 0.1328873 | 0.0517699 | -0.1947518 | 0.1288149 | -0.3882469 | -0.0806025 | 0.1669153 | -0.3275386 |
| MD Q1k | -0.5118310 | 0.4082574 | 0.5106816 | -0.2784104 | -0.0101545 | 0.1258235 | -0.1131692 | -0.0723359 | -0.1783703 | 0.0726037 |
| MD Q1L | -0.7087339 | -0.1724858 | 0.1944088 | -0.4085494 | -0.1796511 | -0.0457976 | 0.1524746 | 0.2247044 | 0.0686013 | -0.0053545 |
| MD Q1m | -0.5682204 | -0.0522540 | -0.4267685 | -0.4284171 | -0.2416706 | -0.2261652 | -0.0162980 | -0.0879603 | -0.3723061 | -0.1253928 |
| MD Q2 | -0.7328573 | -0.2802758 | 0.0969890 | 0.2440009 | 0.0151007 | 0.0994268 | -0.0339440 | 0.2755074 | -0.1765543 | 0.0622319 |
| MD Q3 | -0.5118573 | -0.5064956 | -0.3385010 | 0.0527350 | -0.1123956 | 0.2676439 | -0.0517879 | -0.3591049 | 0.0661023 | -0.0063493 |
## Importance of components:
## PC1 PC2 PC3 PC4 PC5 PC6 PC7
## Standard deviation 2.3857 1.3474 0.9721 0.94891 0.91563 0.82515 0.79246
## Proportion of Variance 0.3794 0.1210 0.0630 0.06003 0.05589 0.04539 0.04187
## Cumulative Proportion 0.3794 0.5004 0.5635 0.62348 0.67937 0.72476 0.76663
## PC8 PC9 PC10 PC11 PC12 PC13 PC14
## Standard deviation 0.77044 0.74286 0.72814 0.70302 0.65162 0.5835 0.55685
## Proportion of Variance 0.03957 0.03679 0.03535 0.03295 0.02831 0.0227 0.02067
## Cumulative Proportion 0.80620 0.84299 0.87834 0.91128 0.93959 0.9623 0.98296
## PC15
## Standard deviation 0.50553
## Proportion of Variance 0.01704
## Cumulative Proportion 1.00000
Gradient Boosting: Suicide
Assume you are modeling whether a patient attempted suicide (column AX). This is a binary target variable. Please use Gradient Boosting to predict whether a patient attempts suicides. Please use whatever boosting approach you deem appropriate. But please be sure to walk us through your steps.
We remove the rows null values in the target column and drop the Non-subset Dx column because it had a lot of nulls as well. XGBoost needs data to be in a matrix so we convert the dataframes to numeric matricies.
CV Split
We split the data into three folds for cross validation to imrove the ability of the model to generailze and help with overfitting. We create a function to help with parameter tunning and make use of the bayesOpt package.
https://cran.r-project.org/web/packages/ParBayesianOptimization/vignettes/tuningHyperparameters.html
## Epoch Iteration max_depth min_child_weight subsample gpUtility acqOptimum
## 1: 0 1 4 16.900949 0.3980034 NA FALSE
## 2: 0 2 9 22.465545 0.4598973 NA FALSE
## 3: 0 3 4 2.543344 0.3380428 NA FALSE
## 4: 0 4 7 8.946161 0.2773560 NA FALSE
## 5: 1 5 2 1.601433 0.4039243 0.5941911 TRUE
## 6: 2 6 10 1.000000 0.5000000 0.5294463 TRUE
## 7: 3 7 10 1.000000 0.2500000 0.3537376 TRUE
## inBounds Elapsed Score nrounds errorMessage
## 1: TRUE 0.042 0.500000 1 NA
## 2: TRUE 0.024 0.500000 1 NA
## 3: TRUE 0.041 0.722162 24 NA
## 4: TRUE 0.013 0.500000 1 NA
## 5: TRUE 0.050 0.732463 22 NA
## 6: TRUE 0.062 0.762502 16 NA
## 7: TRUE 0.030 0.646280 2 NA## $max_depth
## [1] 10
##
## $min_child_weight
## [1] 1
##
## $subsample
## [1] 0.5Build Models
Clustering Method
We use K-nearest neighbor (KNN) to identify clusters of patients that share similar patterns that could help us predict our target variable. KNN works by identifying the “k” closest neighbors in the dataset. This works particularly well for classification.
## [1] <NA>
## Levels: 0 1 2## [1] 0## [1] <NA>
## Levels: 0 1 2## [1] 0## k-Nearest Neighbors
##
## 132 samples
## 50 predictor
## 2 classes: '0', '1'
##
## Pre-processing: centered (157), scaled (157)
## Resampling: Cross-Validated (10 fold, repeated 5 times)
## Summary of sample sizes: 119, 119, 119, 118, 119, 118, ...
## Resampling results across tuning parameters:
##
## k Accuracy Kappa
## 5 0.7109158 0.0329247345
## 7 0.7169597 0.0002244742
## 9 0.7218315 0.0085714286
## 11 0.7201648 0.0000000000
## 13 0.7219414 0.0123065729
## 15 0.7201648 0.0000000000
## 17 0.7201648 0.0000000000
## 19 0.7201648 0.0000000000
## 21 0.7201648 0.0000000000
## 23 0.7201648 0.0000000000
## 25 0.7201648 0.0000000000
## 27 0.7201648 0.0000000000
## 29 0.7201648 0.0000000000
## 31 0.7201648 0.0000000000
## 33 0.7201648 0.0000000000
## 35 0.7201648 0.0000000000
## 37 0.7201648 0.0000000000
## 39 0.7201648 0.0000000000
## 41 0.7201648 0.0000000000
## 43 0.7201648 0.0000000000
##
## Accuracy was used to select the optimal model using the largest value.
## The final value used for the model was k = 13.
## [1] 0.7209302## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 31 12
## 1 0 0
##
## Accuracy : 0.7209
## 95% CI : (0.5633, 0.8467)
## No Information Rate : 0.7209
## P-Value [Acc > NIR] : 0.576988
##
## Kappa : 0
##
## Mcnemar's Test P-Value : 0.001496
##
## Sensitivity : 1.0000
## Specificity : 0.0000
## Pos Pred Value : 0.7209
## Neg Pred Value : NaN
## Prevalence : 0.7209
## Detection Rate : 0.7209
## Detection Prevalence : 1.0000
## Balanced Accuracy : 0.5000
##
## 'Positive' Class : 0
## Our KNN model accuracy comes out to 72.1%
Support Vector Machine
The objective of the support vector machine algorithm is to find a hyperplane in an N-dimensional space (N being the number of features) that classifies the data points. Hyperplanes are decision boundaries to classify the data points. Data points that falls on either side of the hyperplane can be qualified for different classes. Support vectors are data points that are closer to the hyperplane and effect the position and orientation of the hyperplane. Using these support vectors, we do maximize the margin of the classifier.
There are number of R packages available to implement SVM. The train function can be used for SVM using methods as svmRadial, svmLinear and svmPoly that fit different kernels.
##
## Call:
## summary.resamples(object = svm_resamps)
##
## Models: Linear, Radial, Poly
## Number of resamples: 10
##
## Accuracy
## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## Linear 0.5714286 0.6282051 0.6923077 0.6902930 0.6923077 0.9230769 0
## Radial 0.5384615 0.6428571 0.7321429 0.7057692 0.7692308 0.8461538 0
## Poly 0.5384615 0.6282051 0.7307692 0.7463370 0.8887363 0.9285714 0
##
## Kappa
## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## Linear -0.0500000 0.157205698 0.2752525 0.2649674 0.3438347 0.8059701 0
## Radial -0.2580645 0.007462687 0.1698842 0.1639568 0.3157895 0.5806452 0
## Poly -0.2580645 -0.066302119 0.2419355 0.2943945 0.7089552 0.8108108 0We can see out Support Vector Machine Linear, Radial, and Poly fit had median accuracy rates of .631, .769 and .769 respectively indicating of radial or poly SVM should be chosen for future modeling.
Gradient Boosted
We use the information from the above function to fit our final model, make predictions, and evaluate results.
## Confusion Matrix and Statistics
##
## y_label_test
## xgbpred 0 1
## 0 27 8
## 1 1 4
##
## Accuracy : 0.775
## 95% CI : (0.6155, 0.8916)
## No Information Rate : 0.7
## P-Value [Acc > NIR] : 0.1959
##
## Kappa : 0.3571
##
## Mcnemar's Test P-Value : 0.0455
##
## Sensitivity : 0.9643
## Specificity : 0.3333
## Pos Pred Value : 0.7714
## Neg Pred Value : 0.8000
## Prevalence : 0.7000
## Detection Rate : 0.6750
## Detection Prevalence : 0.8750
## Balanced Accuracy : 0.6488
##
## 'Positive' Class : 0
## This produced an accuracy rate of 77.5%
Model Performance
We can see that model SVM models has the best accuracy at 77.5% when applied to the test dataset. We could improve these models through more through feature selection via PCA or other methods and by focusing on feature engineering by using what was identified by these methods.
Conclusion
Through the use of feature engineering and different models we can see that there are numerous ways to approach a dataset such as this. Both models were better at predicting when a patient would not attempt to commit suicide, and not nearly as good at predicting when a patient would. Going forward it would be best to modify the model to focus on predicting when someone would attempt suicide. It is much more beneficial given the problem at hand to be over cautious and less accurate then to be more accurate but less cautious. Potentially using principle components could improve the model and focusing on feature engineering in regards to “positive” cases where the patient atttempted suicide.
References
https://towardsdatascience.com/what-is-the-difference-between-pca-and-factor-analysis-5362ef6fa6f9
https://scholarworks.umass.edu/cgi/viewcontent.cgi?article=1226&context=pare
Code Appendix
knitr::opts_chunk$set(echo=FALSE, error=FALSE, warning=FALSE, message=FALSE, fig.align="center", fig.width = 10)
# Libraries
library(summarytools)
library(tidyverse)
library(DataExplorer)
library(reshape2)
library(mice)
library(caret)
library(MASS)
library(e1071)
library(tree)
library(corrplot)
library(kableExtra)
library(htmltools)
library(readxl)
library(psych)
library(xgboost)
library(ParBayesianOptimization)
library(factoextra)
set.seed(622)
# read data
adhd_data <- read_excel("ADHD_data.xlsx", sheet = "Data") %>% na_if("") %>% dplyr::select(-1)
#columns <- list(dimnames(adhd_data)[2])
#df <- adhd_data[,2:53]
adhd_data[,2:53] <- lapply(adhd_data[,2:53], factor)
adhd_data.dims <- dim(adhd_data)
adhd_data.dims[[2]]
adhd_data[,c(23:37)]
# select categorical columns
cat_cols <- dimnames(adhd_data[,2:53])[[2]]
adhd_fact <- adhd_data[cat_cols]
# long format
adhd_factm <- melt(adhd_fact, measure.vars = cat_cols, variable.name = 'metric', value.name = 'value')
# plot categorical columns
ggplot(adhd_factm, aes(x = value)) +
geom_bar(aes(fill = metric)) +
facet_wrap( ~ metric, nrow = 5L, scales = 'free') + coord_flip() +
theme(legend.position = "none")
dfSummary(adhd_data, style = 'grid', graph.col = FALSE)
adhds <- sapply(adhd_data[,c(4:21)], as.numeric) %>% cor()
corrplot::corrplot(adhds, method="number")
mds <- sapply(adhd_data[,c(23:37)], as.numeric) %>% cor()
corrplot::corrplot(mds, method="number")
adhd_ques_fa <- factanal(sapply(adhd_data[,c(4:21)], as.numeric),
factors = 3,
rotation = "promax",
scores = "regression")
adhd_ques_fa
fa.diagram(adhd_ques_fa$loadings)
md_ques_fa <- factanal(sapply(adhd_data[,c(23:37)], as.numeric),
factors = 3,
rotation = "promax",
scores = "regression")
md_ques_fa
fa.diagram(md_ques_fa$loadings)
# ADHD question scores dataframe
adhd_ques_fa <- as.data.frame(adhd_ques_fa$scores)
names(adhd_ques_fa) <- c('ADHD_FACT1','ADHD_FACT2','ADHD_FACT3')
# MD questions scores dataframe
md_ques_fa <- as.data.frame(md_ques_fa$scores)
names(md_ques_fa) <- c('MD_FACT1','MD_FACT2','MD_FACT3')
# remove ADHD and MD columns
adhd_newdata <- adhd_data %>% dplyr::select(-c(starts_with('ADHD Q'), starts_with('MD Q')))
# Add new factor columns created
adhd_newdata <- cbind(adhd_newdata, adhd_ques_fa, md_ques_fa)
head(adhd_newdata)
# plot missing values
plot_missing(adhd_newdata)
# rename columns to apply mice
adhd_newdata <- adhd_newdata %>%
rename('ADHD_Total'='ADHD Total',
'MD_Total'='MD TOTAL',
'Sedative_hypnotics'='Sedative-hypnotics',
'Court_order' = 'Court order',
'Hx_of_Violence'='Hx of Violence',
'Disorderly_Conduct'='Disorderly Conduct',
'Non_subst_Dx'='Non-subst Dx',
'Subst_Dx'='Subst Dx',
'Psych_meds'='Psych meds.') %>%
dplyr::select(-Psych_meds)
# select columns with non missing values
temp <- adhd_newdata %>% dplyr::select(c(starts_with('ADHD_'), starts_with('MD_'), 'Race', 'Sex', 'Age'))
# impute predictors using mice
adhd_impute <- adhd_newdata %>% dplyr::select(-c(starts_with('ADHD_'), starts_with('MD_'), 'Race', 'Sex', 'Age'))
adhd_impute <- complete(mice(data=adhd_impute, print=FALSE))
summary(adhd_impute)
# Merged the imputed dataframe with temp
adhd_newdata <- cbind(adhd_impute, temp)
head(adhd_newdata)
# Filter out
#adhd_data <- adhd_data %>% filter(!is.na(Alcohol) &
# !is.na(THC) &
# !is.na(Cocaine) &
# !is.na(Stimulants) &
# !is.na(`Sedative-hypnotics`) &
# !is.na(Opioids) &
# !is.na(`Court order`) &
# !is.na(Education) &
# !is.na(`Hx of Violence`) &
# !is.na(`Disorderly Conduct`) &
# !is.na(Suicide) &
# !is.na(Abuse) &
# !is.na(`Non-subst Dx`) &
# !is.na(`Subst Dx`) &
# !is.na(`Psych meds.`))
# impute numeric predictors using mice
#adhd_data <- complete(mice(data=adhd_data[,:53], method="pmm", print=FALSE))
set.seed(622)
# create dummy variables for categorical features
adhd_dummy <- dummyVars(Suicide ~ ., data = adhd_newdata)
adhd_dummy <- predict(adhd_dummy, newdata=adhd_newdata)
# center and scaling
adhd_transformed <- adhd_dummy %>%
preProcess(c("center", "scale")) %>%
predict(adhd_dummy) %>%
as.data.frame()
# add Suicide column
adhd_transformed$Suicide <- adhd_newdata$Suicide
head(adhd_transformed)
set.seed(622)
partition <- createDataPartition(adhd_data$Suicide, p=0.75, list = FALSE)
training <- adhd_data[partition,]
testing <- adhd_data[-partition,]
# training/validation partition for independent variables
#X.train <- ld.clean[partition, ] %>% dplyr::select(-Loan_Status)
#X.test <- ld.clean[-partition, ] %>% dplyr::select(-Loan_Status)
# training/validation partition for dependent variable Loan_Status
#y.train <- ld.clean$Loan_Status[partition]
#y.test <- ld.clean$Loan_Status[-partition]
# create subset of ADHD Questions for PCA
adhd_ques_pca <- sapply(adhd_data[,c(4:21)], as.numeric)
# create subset of MD Questions for PCA
md_ques_pca <- sapply(adhd_data[,c(23:37)], as.numeric)
pca_adhd <- prcomp(adhd_ques_pca, scale. = TRUE, center=TRUE)
cor(adhd_ques_pca, pca_adhd$x[,1:10]) %>%
kableExtra::kbl(booktabs = T, caption ="ADHD Correlations") %>%
kable_styling(latex_options = c("striped"), full_width = F)
summary(pca_adhd)
fviz_eig(pca_adhd)
#top 10 contributors to the dimension of PC1 and PC2
fviz_contrib(pca_adhd, choice = "var", axes = c(1,2), top = 15)
fviz_pca_var(pca_adhd,
col.var ="contrib", # Color by contributions to the PC
gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
repel = TRUE # Avoid text overlapping
,axes=c(1,2)
)
#top 10 contributors to the dimension of PC1 and PC3
fviz_contrib(pca_adhd, choice = "var", axes = c(1,3), top = 15)
fviz_pca_var(pca_adhd,
col.var = "contrib", # Color by contributions to the PC
gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
repel = TRUE # Avoid text overlapping
,axes=c(1,3)
)
#top 10 contributors to the dimension of PC2 and PC3
fviz_contrib(pca_adhd, choice = "var", axes = c(2,3), top = 15)
fviz_pca_var(pca_adhd,
col.var = "contrib", # Color by contributions to the PC
gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
repel = TRUE # Avoid text overlapping
,axes=c(2,3)
)
pca_md <- prcomp(md_ques_pca, scale. = TRUE, center=TRUE)
cor(md_ques_pca, pca_md$x[,1:10]) %>%
kableExtra::kbl(booktabs = T, caption ="md Correlations") %>%
kable_styling(latex_options = c("striped"), full_width = F)
summary(pca_md)
fviz_eig(pca_md)
#top 10 contributors to the dimension of PC1 and PC2
fviz_contrib(pca_md, choice = "var", axes = c(1,2), top = 15)
fviz_pca_var(pca_md,
col.var ="contrib", # Color by contributions to the PC
gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
repel = TRUE # Avoid text overlapping
,axes=c(1,2)
)
#top 10 contributors to the dimension of PC1 and PC3
fviz_contrib(pca_md, choice = "var", axes = c(1,3), top = 15)
fviz_pca_var(pca_md,
col.var = "contrib", # Color by contributions to the PC
gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
repel = TRUE # Avoid text overlapping
,axes=c(1,3)
)
#top 10 contributors to the dimension of PC2 and PC3
fviz_contrib(pca_md, choice = "var", axes = c(2,3), top = 15)
fviz_pca_var(pca_md,
col.var = "contrib", # Color by contributions to the PC
gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
repel = TRUE # Avoid text overlapping
,axes=c(2,3)
)
gb__train <-subset(training[complete.cases(training$Suicide), ], select= -`Non-subst Dx`)
gb__test <-subset(testing[complete.cases(testing$Suicide), ], select= -`Non-subst Dx`)
y_label_tr <- as.matrix(gb__train$Suicide)
y_label_test <- as.matrix(gb__test$Suicide)
gb__train <- sapply(subset(gb__train, select = -Suicide), as.numeric)
gb_test <- sapply(subset(gb__test, select = -Suicide), as.numeric)
Folds <- list(
Fold1 = as.integer(seq(1,nrow(gb__train),by = 3))
, Fold2 = as.integer(seq(2,nrow(gb__train),by = 3))
, Fold3 = as.integer(seq(3,nrow(gb__train),by = 3))
)
scoringFunction <- function(max_depth, min_child_weight, subsample) {
dtrain <- xgb.DMatrix(gb__train, label=y_label_tr)
Pars <- list(
booster = "gbtree"
, eta = 0.01
, max_depth = max_depth
, min_child_weight = min_child_weight
, subsample = subsample
, objective = "binary:logistic"
, eval_metric = "auc"
)
xgbcv <- xgb.cv(
params = Pars
, data = dtrain
, nround = 100
, folds = Folds
, prediction = TRUE
, showsd = TRUE
, early_stopping_rounds = 5
, maximize = TRUE
, verbose = 0)
return(
list(
Score = max(xgbcv$evaluation_log$test_auc_mean)
, nrounds = xgbcv$best_iteration
)
)
}
set.seed(50)
bounds <- list(
max_depth = c(2L, 10L)
, min_child_weight = c(1, 25)
, subsample = c(0.25, .5)
)
optObj <- bayesOpt(
FUN = scoringFunction
, bounds = bounds
, initPoints = 4
, iters.n = 3
)
optObj$scoreSummary
print(getBestPars(optObj))
set.seed(622)
mode <- function(x){
levels <- unique(x)
indicies <- tabulate(match(x, levels))
levels[which.max(indicies)]
}
# Clean up training data
training_factors <- training %>%
dplyr::select(-Age, -`ADHD Total`, `MD TOTAL`)
training_factors <- data.frame(lapply(training_factors, as.factor))
train_knn <- training_factors %>%
mutate(across(everything(), ~replace_na(., mode(.))))
mode(train_knn$Psych.meds.)
train_knn$Psych.meds.[which(is.na(train_knn$Psych.meds.))] <- 0
sum(is.na(train_knn$Psych.meds.))
# Clean up testing data
testing_factors <- testing %>%
dplyr::select(-Age, -`ADHD Total`, `MD TOTAL`)
testing_factors <- data.frame(lapply(testing_factors, as.factor))
test_knn <- testing_factors %>%
mutate(across(everything(), ~replace_na(., mode(.))))
mode(test_knn$Psych.meds.)
test_knn$Psych.meds.[which(is.na(test_knn$Psych.meds.))] <- 0
sum(is.na(test_knn$Psych.meds.))
# Train KNN model
train.knn <- (train_knn[, names(train_knn) != "Suicide"])
prep <- preProcess(x = train.knn, method = c("center", "scale"))
cl <- trainControl(method="repeatedcv", repeats = 5)
knn_model <- train(Suicide ~ ., data = train_knn,
method = "knn",
trControl = cl,
preProcess = c("center","scale"),
tuneLength = 20)
knn_model
# Evaluate Model
plot(knn_model)
knn_predict <- predict(knn_model, newdata = test_knn)
mean(knn_predict == test_knn$Suicide) # accuracy
conf.mat.knn <- confusionMatrix(knn_predict, test_knn$Suicide)
accuracy <- round(conf.mat.knn$overall[[1]], 3)*100
conf.mat.knn
# partitioning for train and test
partition <- createDataPartition(adhd_transformed$Suicide, p=0.75, list = FALSE)
training <- adhd_transformed[partition,]
testing <- adhd_transformed[-partition,]
set.seed(622)
# fit with svmLinear
svm_lin_fit <- train(Suicide ~ .,
data = training,
method = "svmLinear",
preProcess = c("center","scale"),
tuneLength = 5,
trControl = trainControl(method = "cv"))
pred_lin_suicide <- predict(svm_lin_fit, testing)
cm_lin <- confusionMatrix(testing$Suicide, pred_lin_suicide)
# fit with svmRadial
svm_rad_fit <- train(Suicide ~ .,
data = training,
method = "svmRadial",
preProcess = c("center","scale"),
tuneLength = 5,
trControl = trainControl(method = "cv"))
pred_rad_suicide <- predict(svm_rad_fit, testing)
cm_rad <- confusionMatrix(testing$Suicide, pred_rad_suicide)
# fit with svmPoly
svm_poly_fit <- train(Suicide ~ .,
data = training,
method = "svmPoly",
preProcess = c("center","scale"),
tuneLength = 5,
trControl = trainControl(method = "cv"))
pred_poly_suicide <- predict(svm_poly_fit, testing)
cm_poly <- confusionMatrix(testing$Suicide, pred_poly_suicide)
#Compare 3 models:
svm_resamps <- resamples(list(Linear = svm_lin_fit, Radial = svm_rad_fit, Poly = svm_poly_fit))
summary(svm_resamps)
dtrain <- xgb.DMatrix(gb__train, label=y_label_tr)
dtest <- xgb.DMatrix(gb_test, label=y_label_test)
xgb <- xgb.train(
params = list(
booster = "gbtree"
, eta = 0.01
, max_depth = 10
, min_child_weight = 1
, subsample = .5
, objective = "binary:logistic"
, eval_metric = "auc"
)
, data = dtrain
, nround = 100
, maximize = TRUE
, verbose = 0)
xgbpred <- predict(xgb,dtest)
xgbpred <- ifelse (xgbpred > 0.5,1,0)
y_label_test <- as.numeric(y_label_test)
confusionMatrix(table(xgbpred, y_label_test))