Wade K. Copeland
18 April, 2020
What is the direction of most variability for x1 and x2?
What is the direction that explains the second most amount of variation?
This example is the same as the 2-Dimensional example, but we will add in a third data dimension. Call the new variable x3.
Control the 3D plot with your mouse. Scroll to zoom in and out.
The agricultural areas of eastern Washington State, known as the Valley, produce fruit and vegetable crops for national and international distribution.
It is a minority-majority area with most of the population identifying as Hispanic ethnicity, primarily from Mexico.
There are three agricultural periods.
The stress level of 100 farmworkers and non-farmworkers was measured using a validated 24 question survey.
We hypothesize that stress, as measured by the survey, will be different between farmworkers and non-farmworkers in the thinning season.
Name | Labels | Levels | Class | Storage | NAs |
---|---|---|---|---|---|
occupation | Occupation | 2 | integer | 1 | |
season | During the pre-thinning season (March-May), there are few jobs, and many farmworkers will not have worked since the harvest season (September-October). During the thinning season (June through August) and harvest season (June-October), jobs are plentiful, and farmworkers typically work long hours in the fields. During the non-spray season (November-February), crops are dormant, and employment diminishes. | 3 | integer | 0 | |
bills | In the past month have you felt stressed because you didn't have enough money to pay the bills? | numeric | double | 3 | |
lackwork | In the past month have you felt stressed because of lack of enough work? | numeric | double | 3 | |
injustice | In the past month have you felt stressed because of injustice at work? | numeric | double | 3 | |
injury | In the past month have you felt stressed because of painful injuries at work? | numeric | double | 3 | |
hardwork | In the past month have you felt stressed because you have to work too hard? | numeric | double | 3 | |
sickfam | In the past month have you had feelings of desperation because of sickness in your family? | numeric | double | 3 | |
medbills | In the past month have you had feelings of desperation due to lack of money to pay medical bills? | numeric | double | 3 | |
problems | In the past month have you had feelings of desperation because members of your family have problems that you cannot solve? | numeric | double | 3 | |
childcare | In the past month have you been stressed about where to leave your children while working? | numeric | double | 3 | |
distance | In the past month have you had feelings of desperation because members of your family are far away? | numeric | double | 3 | |
childprob | In the past month have you felt stress because of problems with your children? | numeric | double | 3 | |
communication | In the past month have you felt stress because there is a lack of communication in your home? | numeric | double | 3 | |
drinking | In the past month have you felt stress because of a drinking problem in your home? | numeric | double | 3 | |
druguse | In the past month have you felt stress because of drug use in your home? | numeric | double | 3 | |
violence | In the past month have you felt stress because of domestic violence in your home? | numeric | double | 3 | |
crime | In the past month have you felt stress because of crime in your community? | numeric | double | 3 | |
gang | In the past month have you felt stress because of gang-related violence in your community? | numeric | double | 3 | |
discrim | In the past month have you felt stress because of discrimination in your community? | numeric | double | 3 | |
english | In the past month have you felt stress because you do not speak English? | numeric | double | 3 | |
communyouth | In the past month have you felt stress because there is a lack of communication with the youth in your community? | numeric | double | 3 | |
discrimschool | In the past month have you felt stress because there is discrimination in schools? | numeric | double | 3 | |
energy | In the past month have you found it hard to work up the energy to do things? | numeric | double | 3 | |
sleep | In the past month have you lost sleep because of stress? | numeric | double | 3 | |
depressed | In the past month have you been depressed due to stress? | numeric | double | 3 |
Variable | Levels |
---|---|
occupation | Farmworker |
Non-Farmworker | |
season | Pre-thinning |
Thinning | |
No-spray |
## PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 PC9 PC10
## 101 -0.07 0.01 0.00 0.10 -0.16 -0.72 0.41 -0.09 0.12 -0.09
## 102 0.67 -0.14 -0.02 0.10 0.08 0.08 0.04 -0.01 -0.03 0.03
## 103 -1.18 -0.27 -0.36 -0.71 -0.08 0.37 0.49 -0.05 0.02 0.13
## 104 0.21 0.06 0.20 -0.27 0.17 0.05 0.14 0.10 0.17 0.04
## 105 -1.73 -0.42 0.29 -0.29 -0.46 0.08 0.18 -0.12 0.05 -0.31
## 106 0.25 -0.05 -0.01 -0.44 0.60 0.09 0.06 0.09 -0.01 0.24
## 107 0.47 0.12 -0.18 -0.19 0.19 -0.17 -0.27 0.18 -0.09 -0.06
## 108 0.68 0.00 0.04 0.15 0.00 0.20 -0.07 0.11 -0.04 0.04
## 109 -0.34 0.29 -1.19 0.03 -0.62 0.26 0.06 0.08 0.73 -0.02
## 110 0.17 0.47 -0.22 -0.10 0.28 -0.07 0.28 0.11 0.04 -0.26
## 111 -1.44 -0.44 -0.16 -0.06 -0.33 -0.62 -0.56 -0.19 -0.16 0.03
## 112 -0.16 -0.28 -0.57 0.61 0.03 -0.54 -0.24 0.19 0.05 0.36
## 113 0.74 -0.04 -0.04 0.06 0.01 0.12 -0.05 0.03 -0.05 0.05
## 114 0.26 -0.17 0.31 0.37 0.07 0.06 -0.11 -0.08 -0.10 0.16
## 115 0.29 -0.20 -0.05 -0.17 0.27 0.24 0.18 -0.03 0.28 -0.19
## 116 0.30 -0.06 0.00 -0.05 -0.14 -0.04 0.11 0.28 -0.23 0.37
## 117 0.21 0.03 0.29 -0.24 0.07 -0.04 0.00 0.06 0.15 -0.12
## 118 0.58 0.20 -0.06 -0.02 0.14 -0.08 -0.11 0.05 0.05 -0.21
## PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 PC9 PC10 PC11
## Standard deviation 0.70 0.35 0.33 0.31 0.27 0.25 0.23 0.22 0.20 0.19 0.18
## Proportion of Variance 0.37 0.09 0.08 0.07 0.05 0.05 0.04 0.03 0.03 0.03 0.03
## Cumulative Proportion 0.37 0.46 0.54 0.61 0.66 0.71 0.75 0.78 0.81 0.84 0.86
## PC12 PC13 PC14 PC15 PC16 PC17 PC18 PC19 PC20 PC21 PC22
## Standard deviation 0.17 0.16 0.16 0.15 0.13 0.13 0.11 0.11 0.10 0.09 0.07
## Proportion of Variance 0.02 0.02 0.02 0.02 0.01 0.01 0.01 0.01 0.01 0.01 0.00
## Cumulative Proportion 0.89 0.91 0.92 0.94 0.95 0.96 0.97 0.98 0.99 1.00 1.00
These are the extracted principal components and their relationship to the original variables (via correlation). The results below show the correlation of each stress variable with the first 10 PC axes.
Interpretation
## PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 PC9 PC10
## bills -0.27 0.48 0.02 -0.14 0.33 -0.18 0.11 -0.01 0.25 -0.42
## lackwork -0.24 -0.10 -0.01 -0.57 0.31 0.06 -0.05 0.16 0.07 0.48
## injustice -0.26 0.02 0.08 -0.03 -0.08 0.35 -0.03 -0.06 -0.41 0.01
## injury -0.06 0.05 -0.15 -0.11 -0.11 0.17 0.12 -0.14 0.29 -0.08
## hardwork -0.17 0.17 -0.04 -0.01 -0.01 0.15 -0.28 -0.67 -0.18 0.01
## sickfam -0.21 0.17 0.33 0.36 -0.03 0.32 -0.06 0.32 0.05 -0.04
## medbills -0.23 0.27 0.04 -0.20 0.32 0.12 0.00 0.07 -0.15 -0.16
## problems -0.30 0.05 0.28 0.31 0.07 -0.10 -0.18 0.29 -0.18 0.26
## childcare -0.12 -0.19 0.27 -0.25 -0.05 -0.05 -0.38 0.02 0.29 -0.02
## distance -0.23 0.13 0.45 0.05 -0.33 -0.31 0.09 -0.37 0.16 0.11
## childprob -0.10 0.01 -0.10 -0.03 -0.13 -0.42 -0.43 0.09 -0.09 -0.23
## communication -0.11 -0.02 -0.25 -0.03 -0.05 -0.36 -0.26 0.14 -0.12 -0.06
## drinking -0.03 0.00 0.02 0.10 -0.03 -0.25 0.05 0.14 0.13 0.08
## crime -0.24 -0.37 -0.03 0.13 0.20 -0.22 0.11 -0.18 -0.11 0.12
## gang -0.26 -0.39 0.10 0.14 0.29 -0.13 0.38 -0.18 0.09 -0.07
## discrim -0.20 -0.32 0.04 -0.03 0.01 0.16 -0.10 0.05 0.16 -0.21
## english -0.20 0.06 0.03 -0.41 -0.56 -0.08 0.35 0.15 -0.22 0.03
## communyouth -0.20 -0.18 -0.17 0.00 0.03 -0.03 0.06 0.01 -0.46 -0.31
## discrimschool -0.21 -0.30 -0.01 -0.05 -0.26 0.24 -0.02 0.12 0.22 -0.38
## energy -0.21 -0.06 -0.37 0.16 -0.08 0.17 -0.28 -0.08 0.22 0.11
## sleep -0.28 0.18 -0.42 0.23 -0.09 -0.08 0.26 0.13 0.13 0.09
## depressed -0.27 0.12 -0.28 0.09 -0.12 0.08 -0.02 -0.03 0.13 0.33
We can use multivariate analysis of variance to test the null hypothesis that stress does not differ by occupation in the thinning season.
## Df Pillai approx F num Df den Df Pr(>F)
## farmstressS1Occupation 1 0.32768 1.6837 22 76 0.05005 .
## Residuals 97
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Farmworker, Mean (SD) | Non-Farmworker, Mean (SD) | Difference [95% CI] | FDR Adjusted P-value | |
---|---|---|---|---|
In the past month have you felt stressed because you didn’t have enough money to pay the bills? (bills) | 0.3603 (0.32) | 0.2945 (0.31) | 0.0658 [-0.0073, 0.1389] | 0.2126 |
In the past month have you felt stressed because of lack of enough work? (lackwork) | 0.2137 (0.28) | 0.1737 (0.28) | 0.04 [-0.0263, 0.1062] | 0.3994 |
In the past month have you felt stressed because of injustice at work? (injustice) | 0.1466 (0.26) | 0.1038 (0.22) | 0.0428 [-0.0116, 0.0972] | 0.2825 |
In the past month have you felt stressed because of painful injuries at work? (injury) | 0.081 (0.2) | 0.0636 (0.17) | 0.0174 [-0.025, 0.0599] | 0.5758 |
In the past month have you felt stressed because you have to work too hard? (hardwork) | 0.1774 (0.27) | 0.1017 (0.21) | 0.0757 [0.0208, 0.1306] | 0.039 |
In the past month have you had feelings of desperation because of sickness in your family? (sickfam) | 0.1606 (0.26) | 0.1483 (0.26) | 0.0123 [-0.0491, 0.0738] | 0.7628 |
In the past month have you had feelings of desperation due to lack of money to pay medical bills? (medbills) | 0.2291 (0.29) | 0.178 (0.28) | 0.0511 [-0.015, 0.1172] | 0.2825 |
In the past month have you had feelings of desperation because members of your family have problems that you cannot solve? (problems) | 0.2165 (0.3) | 0.1695 (0.25) | 0.047 [-0.0158, 0.1098] | 0.2825 |
In the past month have you been stressed about where to leave your children while working? (childcare) | 0.1327 (0.25) | 0.0678 (0.19) | 0.0649 [0.0149, 0.1149] | 0.0493 |
In the past month have you had feelings of desperation because members of your family are far away? (distance) | 0.3268 (0.31) | 0.161 (0.26) | 0.1658 [0.101, 0.2306] | <0.0001 |
In the past month have you felt stress because of problems with your children? (childprob) | 0.1327 (0.23) | 0.0975 (0.19) | 0.0352 [-0.0133, 0.0837] | 0.2825 |
In the past month have you felt stress because there is a lack of communication in your home? (communication) | 0.1299 (0.21) | 0.0847 (0.19) | 0.0452 [-0.0012, 0.0915] | 0.1769 |
In the past month have you felt stress because of a drinking problem in your home? (drinking) | 0.0433 (0.16) | 0.036 (0.12) | 0.0073 [-0.0243, 0.0388] | 0.7526 |
In the past month have you felt stress because of crime in your community? (crime) | 0.1983 (0.26) | 0.1843 (0.25) | 0.014 [-0.0454, 0.0734] | 0.7526 |
In the past month have you felt stress because of gang-related violence in your community? (gang) | 0.2221 (0.28) | 0.2267 (0.28) | -0.0046 [-0.0693, 0.0601] | 0.8881 |
In the past month have you felt stress because of discrimination in your community? (discrim) | 0.1313 (0.23) | 0.1144 (0.23) | 0.0169 [-0.0368, 0.0706] | 0.6943 |
In the past month have you felt stress because you do not speak English? (english) | 0.3324 (0.31) | 0.1419 (0.22) | 0.1905 [0.1296, 0.2514] | <0.0001 |
In the past month have you felt stress because there is a lack of communication with the youth in your community? (communyouth) | 0.1676 (0.24) | 0.0911 (0.2) | 0.0765 [0.0259, 0.1271] | 0.0235 |
In the past month have you felt stress because there is discrimination in schools? (discrimschool) | 0.1341 (0.22) | 0.1059 (0.23) | 0.0282 [-0.0236, 0.0799] | 0.4474 |
In the past month have you found it hard to work up the energy to do things? (energy) | 0.1564 (0.24) | 0.0996 (0.21) | 0.0568 [0.0053, 0.1084] | 0.1133 |
In the past month have you lost sleep because of stress? (sleep) | 0.2095 (0.29) | 0.2013 (0.29) | 0.0082 [-0.0599, 0.0764] | 0.8509 |
In the past month have you been depressed due to stress? (depressed) | 0.1704 (0.26) | 0.1419 (0.25) | 0.0285 [-0.0314, 0.0883] | 0.5141 |