Using Principal Components Analysis (PCA) to Analyze Latino Stress by Agricultural Season and Occupation

Wade K. Copeland

18 April, 2020

Introduction

Outline

  1. What is PCA?
    • General Description
    • Geometric Interpretation
  2. Application
    • Description
    • Output
    • Graphical Interpretation
    • Inference

What is PCA?

General Description Part 1

General Description Part 2

2-Dimensional PCA Example

Simulated Data

What is the direction of most variability for x1 and x2?

PC1

What is the direction that explains the second most amount of variation?

PC2

Projection of Data onto PC1

Projection of Data onto PC2

3-Dimensional PCA Example

Simulated Data

Projection of Data onto PC1

Projection of Data onto PC2

Projection of Data onto PC3

Application

Publication

Situation

Task

Latino Stress Analytic Data


Data frame:farmstress

300 observations and 26 variables, maximum # NAs:3  
NameLabelsLevelsClassStorageNAs
occupationOccupation2integer1
seasonDuring 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.3integer0
billsIn the past month have you felt stressed because you didn't have enough money to pay the bills?numericdouble3
lackworkIn the past month have you felt stressed because of lack of enough work?numericdouble3
injusticeIn the past month have you felt stressed because of injustice at work?numericdouble3
injuryIn the past month have you felt stressed because of painful injuries at work?numericdouble3
hardworkIn the past month have you felt stressed because you have to work too hard?numericdouble3
sickfamIn the past month have you had feelings of desperation because of sickness in your family?numericdouble3
medbillsIn the past month have you had feelings of desperation due to lack of money to pay medical bills?numericdouble3
problemsIn the past month have you had feelings of desperation because members of your family have problems that you cannot solve?numericdouble3
childcareIn the past month have you been stressed about where to leave your children while working?numericdouble3
distanceIn the past month have you had feelings of desperation because members of your family are far away?numericdouble3
childprobIn the past month have you felt stress because of problems with your children?numericdouble3
communicationIn the past month have you felt stress because there is a lack of communication in your home?numericdouble3
drinkingIn the past month have you felt stress because of a drinking problem in your home?numericdouble3
druguseIn the past month have you felt stress because of drug use in your home?numericdouble3
violenceIn the past month have you felt stress because of domestic violence in your home?numericdouble3
crimeIn the past month have you felt stress because of crime in your community?numericdouble3
gangIn the past month have you felt stress because of gang-related violence in your community?numericdouble3
discrimIn the past month have you felt stress because of discrimination in your community?numericdouble3
englishIn the past month have you felt stress because you do not speak English?numericdouble3
communyouthIn the past month have you felt stress because there is a lack of communication with the youth in your community?numericdouble3
discrimschoolIn the past month have you felt stress because there is discrimination in schools?numericdouble3
energyIn the past month have you found it hard to work up the energy to do things?numericdouble3
sleepIn the past month have you lost sleep because of stress?numericdouble3
depressedIn the past month have you been depressed due to stress?numericdouble3

VariableLevels
occupationFarmworker
Non-Farmworker
seasonPre-thinning
Thinning
No-spray

Scores Matrix

##       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

PC Axis Importance

##                         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

Loading Matrix

##                 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

PC Biplot

Principal Component Regression

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

Post-Hoc Analyses

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

Questions?