In this HW I will cover some of the graphing and reliability concepts I covered in the latest ggplot and reliability analysis lecture. Much like the latest lecture note file, I have divided this HW into a set of Homework where I will work though a set of problems, Then I will hand the reigns over to you and you will work through your set of homework problems.

# Let's first load some R packages
# If you don't have these R packages you will need to install them
# Remember to install a package use
# install.packages(<Insert package name here>,dependencies=TRUE)
library(ggplot2)
library(GGally)
library(psych)
library(psychometric)
library(psychTools)
library(ltm)
library(ggplot2)
library(GGally)
library(psych)
library(psychometric)
library(psychTools)
library(ltm)

My Homework Problems

In the first problem I will show you how to create a nice scatter plot matrix.

  1. Create a scatterplot matrix for the iris dataset.

Answer: In base R you can create a scatterplot matrix with the basic plot function like you see with the command below:

plot(iris)

If you look at the scatterplot matrix, the diagonal set of facets tell you the variables that will be plotted. Each of the plots in the figure use a variable for the X-axis and another variable for the Y-axis. Notice you have a plot where {X, Y} is {petal.length, petal.width} and another plot where {Y=X,X=Y} (X and Y reverse rolls). THis shows you that only plots in the lower diagonal or upper diagonal portion of the trellis display need to be displayed. THe reasoning here is if you know how the plot of (X,Y) looks like, you will also know what (Y,X) looks like.

A better plot is the ggpairs plot which is a plot from the “GGally” package in R and this shown below

library(GGally) # Extension package to ggplot2
plt<-ggpairs(iris,aes(col=Species,alpha=0.5))
plt

The “col=Species” aesthetic tells the system to use a different color for each species of iris plant. The alpha = proportion=0.5 command tells the system to make the colors “semi-transparent”. Alpha is the level of translucency with alpha= 0% being totally transparent and alpha=100% being totally opaque.

The lower trianglar portion of the plot shows a scatter plot of each variable versus every other variable. Since there are 4 numeric variables corresponding to every combination of {sepal,petal} and {length, width}. The diagnal portion of the plots give you univariate nonparametric density plots of the 4 variables. The upper diagonal portions of the plot give you correlations \((\rho_{ab})\) for {X,Y} = {variable A, variable B}. The colors {black, red, green, blue} in the correlations tell you the correlations {overall, setosa, versicolor, virginica}.

We can add a linear smoother to the scatterplots by creating a special smoothing function then utilizing this function within the ggpairs function like you see below

#Define my graphing function
my_fn <- function(data, mapping, ...){
  p <- ggplot(data = data, mapping = mapping) + 
    geom_point() + 
    geom_smooth(method="lm")
  p
}
grph = ggpairs(iris,aes(col=Species,alpha=0.5),
               lower=list(continuous = my_fn))
grph

The “pairs.panels” function in the psych package gives you “loess” smoothers on each scatter plot. It also plots correlation ellipses. A correlation ellipse depicts the shape that the scatter plot would assume if the data had a bivariate normal distribution (which has a distinctive elliptical shape).

The shapes of the ellipses are opposite for positive correlation (in blue) or negative corelation (in red). The more intense the color and the thinner the ellipse, the stronger the correlation.

Correlation_Ellipse
Correlation_Ellipse

Here is a scatter plot matrix with correlation ellipses for the numeric columns of the iris dataset

library(psych)
Dat<-iris[,1:4] # First 4 columns of iris
grph<-pairs.panels(Dat)

grph
## NULL

Now I will show you an overview of some functions available in the “psych” package overview. You can read a psych package overview by clicking on this website link: https://personality-project.org/r/psych/overview.pdf.

For this excercise I will use the “msqR” dataset in the “psychTools” package of R. You can read about this “msqR” dataset using the help(msqR) command in R. This dataset comes from a questionnaire containing 75 different mood items from the Motivational State Questionnaire and data was taken on 3032 unique participants.

Emotions may be described either as discrete emotions or in dimensional terms. The Motivational State Questionnaire (MSQ) was developed to study emotions in laboratory and field settings. The data can be well described in terms of a two dimensional solution of energy vs tiredness and tension versus calmness. Alternatively, this space can be organized by the two dimensions of Positive Affect and Negative Affect. Additional items include what time of day the data were collected and a few personality questionnaire scores. 3032 unique participants took the MSQ at least once, 2753 at least twice, 446 three times, and 181 four times. The 3032 participants also took the sai state anxiety inventory at the same time. Some studies manipulated arousal by caffeine, others manipulations included affect inducing movies.

Yik Russell and Steiger defined a list of 11 different latent variables that defined personality. A list of the 11 latent variable names along with the measured variable columns that belong to each personality characteristic latent variable is given by the list below:

Yik.keys <- list(
pleasure =psych::cs(happy,content,satisfied, pleased),
act.pleasure =psych::cs(proud,enthusiastic),
pleasant.activation = psych::cs(energetic,full.of.pep,excited,wakeful,attentive,
   wide.awake,active,alert,vigorous),
activation = psych::cs(aroused,intense),
unpleasant.act = psych::cs(anxious,jittery,nervous),
activated.displeasure =psych::cs(scared,upset,fearful,clutched.up,tense,
    ashamed,guilty,hostile),
Ueactivated.Displeasure = psych::cs(unhappy,sad,gloomy,blue),
Unpleasant.Deactivation = psych::cs(drowsy,dull,bored,sluggish,tired),
Deactivation =psych::cs(quiet,still),
pleasant.deactivation = psych::cs(placid,relaxed,tranquil, at.rest,calm),
deactived.pleasure =psych::cs(serene,at.ease)
)

The names of the list of personallity characteristics is given below:

names(Yik.keys)
##  [1] "pleasure"                "act.pleasure"           
##  [3] "pleasant.activation"     "activation"             
##  [5] "unpleasant.act"          "activated.displeasure"  
##  [7] "Ueactivated.Displeasure" "Unpleasant.Deactivation"
##  [9] "Deactivation"            "pleasant.deactivation"  
## [11] "deactived.pleasure"

We can get a summary of the Cronbach Alpha and other measures of item level internal consistency or reliabiltiy by using the scoreItems() function in the psych package.

library(psych)
library(psychTools)
yik.scores<-scoreItems(Yik.keys,msqR)
yik.scores
## Call: scoreItems(keys = Yik.keys, items = msqR)
## 
## (Unstandardized) Alpha:
##       pleasure act.pleasure pleasant.activation activation unpleasant.act
## alpha     0.88         0.73                0.94       0.57           0.68
##       activated.displeasure Ueactivated.Displeasure Unpleasant.Deactivation
## alpha                  0.83                    0.88                    0.84
##       Deactivation pleasant.deactivation deactived.pleasure
## alpha         0.66                  0.79               0.68
## 
## Standard errors of unstandardized Alpha:
##       pleasure act.pleasure pleasant.activation activation unpleasant.act
## ASE     0.0075        0.018              0.0031      0.021          0.013
##       activated.displeasure Ueactivated.Displeasure Unpleasant.Deactivation
## ASE                  0.0055                  0.0074                   0.007
##       Deactivation pleasant.deactivation deactived.pleasure
## ASE          0.019                0.0079              0.019
## 
## Average item correlation:
##           pleasure act.pleasure pleasant.activation activation unpleasant.act
## average.r     0.64         0.57                0.65        0.4           0.42
##           activated.displeasure Ueactivated.Displeasure Unpleasant.Deactivation
## average.r                  0.38                    0.66                     0.5
##           Deactivation pleasant.deactivation deactived.pleasure
## average.r         0.49                  0.43               0.52
## 
## Median item correlation:
##                pleasure            act.pleasure     pleasant.activation 
##                    0.62                    0.57                    0.65 
##              activation          unpleasant.act   activated.displeasure 
##                    0.40                    0.41                    0.40 
## Ueactivated.Displeasure Unpleasant.Deactivation            Deactivation 
##                    0.65                    0.46                    0.49 
##   pleasant.deactivation      deactived.pleasure 
##                    0.40                    0.52 
## 
##  Guttman 6* reliability: 
##          pleasure act.pleasure pleasant.activation activation unpleasant.act
## Lambda.6     0.87         0.71                0.95       0.62           0.67
##          activated.displeasure Ueactivated.Displeasure Unpleasant.Deactivation
## Lambda.6                  0.86                    0.87                    0.85
##          Deactivation pleasant.deactivation deactived.pleasure
## Lambda.6         0.61                   0.8               0.72
## 
## Signal/Noise based upon av.r : 
##              pleasure act.pleasure pleasant.activation activation
## Signal/Noise      7.2          2.7                  17        1.3
##              unpleasant.act activated.displeasure Ueactivated.Displeasure
## Signal/Noise            2.1                   4.8                     7.7
##              Unpleasant.Deactivation Deactivation pleasant.deactivation
## Signal/Noise                     5.1          1.9                   3.7
##              deactived.pleasure
## Signal/Noise                2.1
## 
## Scale intercorrelations corrected for attenuation 
##  raw correlations below the diagonal, alpha on the diagonal 
##  corrected correlations above the diagonal:
##                         pleasure act.pleasure pleasant.activation activation
## pleasure                  0.8782        0.879               0.703     0.4575
## act.pleasure              0.7036        0.729               0.827     0.7349
## pleasant.activation       0.6399        0.686               0.943     0.9016
## activation                0.3247        0.475               0.663     0.5736
## unpleasant.act           -0.0311        0.128               0.278     0.4428
## activated.displeasure    -0.2541       -0.058               0.034     0.3389
## Ueactivated.Displeasure  -0.3470       -0.187              -0.199     0.0514
## Unpleasant.Deactivation  -0.3615       -0.352              -0.621    -0.3479
## Deactivation             -0.0054       -0.131              -0.264    -0.2143
## pleasant.deactivation     0.4829        0.263               0.123    -0.0964
## deactived.pleasure        0.5718        0.339               0.231    -0.0052
##                         unpleasant.act activated.displeasure
## pleasure                        -0.040                -0.298
## act.pleasure                     0.182                -0.074
## pleasant.activation              0.347                 0.038
## activation                       0.709                 0.492
## unpleasant.act                   0.681                 0.815
## activated.displeasure            0.612                 0.828
## Ueactivated.Displeasure          0.269                 0.649
## Unpleasant.Deactivation         -0.064                 0.122
## Deactivation                    -0.131                -0.027
## pleasant.deactivation           -0.324                -0.345
## deactived.pleasure              -0.274                -0.349
##                         Ueactivated.Displeasure Unpleasant.Deactivation
## pleasure                                 -0.394                  -0.422
## act.pleasure                             -0.233                  -0.451
## pleasant.activation                      -0.218                  -0.700
## activation                                0.072                  -0.502
## unpleasant.act                            0.347                  -0.085
## activated.displeasure                     0.758                   0.146
## Ueactivated.Displeasure                   0.885                   0.343
## Unpleasant.Deactivation                   0.295                   0.836
## Deactivation                              0.155                   0.426
## pleasant.deactivation                    -0.198                   0.068
## deactived.pleasure                       -0.242                  -0.028
##                         Deactivation pleasant.deactivation deactived.pleasure
## pleasure                      -0.007                 0.580             0.7395
## act.pleasure                  -0.189                 0.347             0.4816
## pleasant.activation           -0.334                 0.142             0.2887
## activation                    -0.348                -0.143            -0.0083
## unpleasant.act                -0.195                -0.442            -0.4029
## activated.displeasure         -0.036                -0.427            -0.4652
## Ueactivated.Displeasure        0.203                -0.237            -0.3120
## Unpleasant.Deactivation        0.573                 0.083            -0.0372
## Deactivation                   0.660                 0.664             0.5935
## pleasant.deactivation          0.479                 0.789             1.0787
## deactived.pleasure             0.398                 0.791             0.6808
## 
##  Average adjusted correlations within and between scales (MIMS)
##                         plesr act.p plsnt.c actvt unpl. actv. Uct.D Unp.D Dctvt
## pleasure                 0.64                                                  
## act.pleasure             0.43  0.57                                            
## pleasant.activation      0.36  0.40  0.65                                      
## activation               0.18  0.27  0.35    0.40                              
## unpleasant.act          -0.01  0.06  0.12    0.18  0.42                        
## activated.displeasure   -0.08 -0.02  0.01    0.10  0.14  0.38                  
## Ueactivated.Displeasure -0.16 -0.09 -0.08    0.02  0.09  0.15  0.66            
## Unpleasant.Deactivation -0.21 -0.21 -0.35   -0.19 -0.03  0.04  0.13  0.50      
## Deactivation             0.00 -0.08 -0.15   -0.12 -0.06 -0.01  0.07  0.26  0.49
## pleasant.deactivation    0.24  0.13  0.06   -0.04 -0.12 -0.09 -0.07  0.03  0.24
## deactived.pleasure       0.35  0.21  0.13    0.00 -0.13 -0.11 -0.11 -0.02  0.25
##                         plsnt.d dctv.
## pleasure                             
## act.pleasure                         
## pleasant.activation                  
## activation                           
## unpleasant.act                       
## activated.displeasure                
## Ueactivated.Displeasure              
## Unpleasant.Deactivation              
## Deactivation                         
## pleasant.deactivation    0.43        
## deactived.pleasure       0.40    0.52
## 
##  Average adjusted item x scale correlations within and between scales (MIMT)
##                         plesr act.p plsnt.c actvt unpl. actv. Uct.D Unp.D Dctvt
## pleasure                 0.86                                                  
## act.pleasure             0.63  0.89                                            
## pleasant.activation      0.53  0.57  0.83                                      
## activation               0.27  0.40  0.56    0.84                              
## unpleasant.act          -0.03  0.10  0.21    0.34  0.78                        
## activated.displeasure   -0.17 -0.04  0.02    0.22  0.41  0.68                  
## Ueactivated.Displeasure -0.30 -0.16 -0.17    0.05  0.23  0.56  0.86            
## Unpleasant.Deactivation -0.28 -0.27 -0.48   -0.27 -0.05  0.10  0.23  0.78      
## Deactivation             0.00 -0.11 -0.23   -0.19 -0.11 -0.03  0.13  0.37  0.86
## pleasant.deactivation    0.35  0.19  0.09   -0.07 -0.24 -0.25 -0.15  0.05  0.35
## deactived.pleasure       0.50  0.29  0.20   -0.01 -0.24 -0.30 -0.21 -0.02  0.35
##                         plsnt.d dctv.
## pleasure                             
## act.pleasure                         
## pleasant.activation                  
## activation                           
## unpleasant.act                       
## activated.displeasure                
## Ueactivated.Displeasure              
## Unpleasant.Deactivation              
## Deactivation                         
## pleasant.deactivation    0.74        
## deactived.pleasure       0.69    0.87
## 
##  In order to see the item by scale loadings and frequency counts of the data
##  print with the short option = FALSE

We can get a summary of the lower triangular part of the scatterplot of the columns in the 75 items in the msqR data set with the R code below.

r<- lowerCor(msqR)
##              activ afrad alert angry arosd ashmd astns at.es at.rs attnt blue 
## active        1.00                                                            
## afraid        0.02  1.00                                                      
## alert         0.63  0.05  1.00                                                
## angry        -0.06  0.37 -0.03  1.00                                          
## aroused       0.58  0.11  0.53  0.03  1.00                                    
## ashamed      -0.03  0.46 -0.01  0.43  0.04  1.00                              
## astonished    0.17  0.37  0.18  0.32  0.27  0.32  1.00                        
## at.ease       0.26 -0.20  0.27 -0.29  0.14 -0.17 -0.11  1.00                  
## at.rest       0.17 -0.12  0.19 -0.18  0.09 -0.08 -0.05  0.57  1.00            
## attentive     0.59  0.05  0.73 -0.06  0.49 -0.01  0.16  0.32  0.23  1.00      
## blue         -0.14  0.36 -0.11  0.41 -0.07  0.38  0.20 -0.21 -0.12 -0.11  1.00
## bored        -0.26 -0.03 -0.31  0.13 -0.23  0.01 -0.12 -0.10 -0.04 -0.31  0.10
## calm          0.07 -0.17  0.11 -0.27  0.00 -0.12 -0.12  0.63  0.54  0.17 -0.13
## clutched.up   0.09  0.34  0.10  0.38  0.18  0.28  0.29 -0.29 -0.20  0.08  0.31
## confident     0.48 -0.08  0.46 -0.10  0.35 -0.11  0.06  0.44  0.30  0.47 -0.17
## content       0.41 -0.13  0.40 -0.26  0.30 -0.15  0.00  0.59  0.42  0.44 -0.24
## delighted     0.51 -0.04  0.40 -0.16  0.42 -0.06  0.12  0.32  0.20  0.39 -0.17
## depressed    -0.18  0.36 -0.15  0.46 -0.09  0.42  0.22 -0.26 -0.16 -0.16  0.71
## determined    0.54  0.15  0.45  0.06  0.42  0.09  0.20  0.22  0.15  0.46  0.04
## distressed   -0.02  0.47  0.00  0.48  0.05  0.44  0.29 -0.26 -0.19  0.01  0.50
## drowsy       -0.42  0.03 -0.54  0.06 -0.33  0.05 -0.09 -0.08 -0.07 -0.46  0.17
## dull         -0.36  0.06 -0.37  0.12 -0.29  0.09 -0.06 -0.09 -0.02 -0.34  0.23
## elated        0.56  0.04  0.46 -0.07  0.57 -0.01  0.22  0.25  0.17  0.44 -0.12
## energetic     0.74  0.04  0.70 -0.05  0.61 -0.03  0.20  0.25  0.18  0.65 -0.16
## enthusiastic  0.65  0.02  0.53 -0.14  0.52 -0.03  0.14  0.34  0.21  0.52 -0.15
## excited       0.64  0.11  0.56 -0.04  0.61  0.01  0.24  0.18  0.11  0.53 -0.12
## fearful       0.03  0.78  0.05  0.38  0.12  0.44  0.38 -0.21 -0.12  0.05  0.34
## frustrated   -0.06  0.37 -0.07  0.59 -0.01  0.39  0.22 -0.31 -0.23 -0.09  0.45
## full.of.pep   0.78  0.01  0.63 -0.09  0.60 -0.04  0.18  0.25  0.16  0.59 -0.17
## gloomy       -0.22  0.33 -0.20  0.44 -0.12  0.38  0.19 -0.26 -0.16 -0.20  0.64
## grouchy      -0.19  0.22 -0.22  0.50 -0.12  0.25  0.11 -0.28 -0.22 -0.24  0.39
## guilty       -0.02  0.43 -0.03  0.36  0.03  0.59  0.23 -0.14 -0.08 -0.01  0.36
## happy         0.55 -0.08  0.49 -0.23  0.42 -0.11  0.04  0.48  0.31  0.51 -0.25
## hostile      -0.07  0.28 -0.07  0.60  0.01  0.29  0.24 -0.30 -0.19 -0.11  0.35
## inspired      0.52  0.11  0.49  0.02  0.50  0.08  0.26  0.19  0.14  0.47 -0.02
## intense       0.39  0.26  0.35  0.28  0.40  0.19  0.30 -0.10 -0.07  0.32  0.15
## interested    0.51  0.09  0.50 -0.10  0.44  0.02  0.19  0.37  0.23  0.54 -0.07
## irritable    -0.14  0.24 -0.17  0.53 -0.08  0.24  0.13 -0.33 -0.25 -0.20  0.36
## jittery       0.27  0.27  0.24  0.15  0.30  0.14  0.23 -0.21 -0.17  0.20  0.13
## lively        0.77  0.02  0.64 -0.08  0.64 -0.04  0.17  0.29  0.19  0.60 -0.17
## lonely       -0.09  0.27 -0.09  0.30 -0.04  0.32  0.12 -0.15 -0.06 -0.09  0.49
## nervous       0.15  0.49  0.14  0.30  0.21  0.33  0.27 -0.26 -0.17  0.13  0.25
## placid       -0.10 -0.04 -0.10 -0.10 -0.12 -0.01 -0.07  0.32  0.35 -0.03  0.03
## pleased       0.51 -0.05  0.46 -0.18  0.42 -0.08  0.08  0.44  0.31  0.48 -0.19
## proud         0.50  0.00  0.38 -0.08  0.39 -0.04  0.11  0.34  0.24  0.39 -0.09
## quiescent     0.02  0.05  0.01 -0.02  0.03  0.05  0.02  0.22  0.21  0.05  0.08
## quiet        -0.23  0.05 -0.18  0.00 -0.21  0.07 -0.05  0.15  0.18 -0.11  0.17
## relaxed       0.19 -0.18  0.18 -0.30  0.10 -0.15 -0.09  0.65  0.55  0.23 -0.20
## sad          -0.11  0.40 -0.08  0.47 -0.04  0.45  0.28 -0.22 -0.13 -0.08  0.72
## satisfied     0.47 -0.10  0.40 -0.24  0.33 -0.13  0.02  0.49  0.36  0.42 -0.22
## scared        0.04  0.73  0.05  0.35  0.12  0.42  0.33 -0.21 -0.14  0.05  0.36
## serene        0.07 -0.10  0.08 -0.21  0.04 -0.09 -0.07  0.52  0.47  0.15 -0.08
## sleepy       -0.41  0.04 -0.53  0.06 -0.33  0.06 -0.09 -0.08 -0.08 -0.45  0.16
## sluggish     -0.44  0.05 -0.49  0.07 -0.35  0.08 -0.10 -0.09 -0.04 -0.42  0.22
## sociable      0.56 -0.06  0.45 -0.19  0.40 -0.08  0.04  0.39  0.26  0.44 -0.18
## sorry        -0.06  0.44 -0.03  0.50  0.02  0.62  0.35 -0.19 -0.10 -0.03  0.46
## still        -0.18 -0.04 -0.15 -0.07 -0.17  0.00 -0.08  0.31  0.34 -0.09  0.07
## strong        0.56  0.07  0.45  0.05  0.44  0.02  0.19  0.24  0.18  0.44 -0.04
## surprised     0.24  0.29  0.26  0.20  0.33  0.22  0.57 -0.04 -0.01  0.23  0.10
## tense         0.11  0.40  0.13  0.40  0.17  0.30  0.24 -0.33 -0.26  0.09  0.30
## tired        -0.43  0.05 -0.54  0.07 -0.35  0.06 -0.10 -0.11 -0.09 -0.45  0.20
## unhappy      -0.16  0.36 -0.12  0.54 -0.08  0.40  0.23 -0.28 -0.18 -0.15  0.66
## upset        -0.09  0.44 -0.06  0.65 -0.01  0.48  0.31 -0.30 -0.19 -0.09  0.54
## vigorous      0.67  0.08  0.60  0.01  0.58  0.00  0.25  0.18  0.14  0.55 -0.09
## wakeful       0.61  0.03  0.70 -0.06  0.53 -0.02  0.16  0.27  0.22  0.64 -0.12
## warmhearted   0.46 -0.05  0.37 -0.23  0.33 -0.07  0.03  0.50  0.35  0.40 -0.14
## wide.awake    0.61  0.02  0.75 -0.03  0.52 -0.02  0.17  0.24  0.21  0.70 -0.13
## anxious       0.21  0.32  0.20  0.24  0.25  0.26  0.23 -0.19 -0.15  0.17  0.21
## cheerful      0.57 -0.04  0.49 -0.19  0.43 -0.07  0.08  0.42  0.29  0.51 -0.22
## idle         -0.22 -0.01 -0.22  0.00 -0.17  0.03 -0.08  0.11  0.16 -0.19  0.11
## inactive     -0.42  0.02 -0.38  0.00 -0.28  0.04 -0.10  0.01  0.07 -0.32  0.15
## tranquil      0.04 -0.12  0.03 -0.23 -0.02 -0.10 -0.11  0.53  0.47  0.09 -0.10
## alone        -0.10  0.32 -0.08  0.33 -0.03  0.34  0.12 -0.14 -0.04 -0.07  0.45
## kindly        0.49 -0.03  0.44 -0.17  0.38 -0.08  0.07  0.48  0.36  0.46 -0.09
## scornful      0.01  0.31 -0.01  0.56  0.06  0.31  0.20 -0.22 -0.10 -0.04  0.32
## Extraversion  0.11 -0.04  0.04 -0.01  0.09 -0.05  0.01  0.07  0.04  0.02 -0.09
## Neuroticism  -0.13  0.17 -0.14  0.16 -0.05  0.16  0.06 -0.22 -0.17 -0.14  0.24
## Lie           0.08 -0.02  0.09 -0.06  0.03 -0.03  0.04  0.06  0.06  0.09 -0.04
## Sociability   0.12 -0.05  0.05 -0.04  0.09 -0.05 -0.01  0.10  0.05  0.05 -0.10
## Impulsivity   0.07 -0.02  0.02  0.02  0.06 -0.02  0.03  0.00  0.01 -0.01 -0.05
## gender       -0.19  0.05 -0.18  0.02 -0.38  0.00 -0.25  0.05 -0.09 -0.17  0.06
## TOD           0.06  0.00  0.03  0.03  0.05  0.01 -0.03  0.02  0.04  0.02  0.05
## drug          0.19  0.01  0.21 -0.03  0.17 -0.01  0.06 -0.04 -0.04  0.19 -0.01
## film          0.12 -0.17  0.05 -0.28  0.04 -0.19 -0.25  0.24  0.17  0.07 -0.21
## time         -0.06 -0.03 -0.06  0.03 -0.02 -0.01 -0.02 -0.12 -0.05 -0.08 -0.04
## id            0.02 -0.02  0.04 -0.03  0.00 -0.01 -0.02  0.01  0.02  0.03  0.01
## form         -0.05  0.06 -0.04  0.08 -0.08  0.08  0.07 -0.08 -0.07 -0.04  0.06
## study*        0.03 -0.02  0.05  0.00 -0.01  0.02  0.00 -0.01 -0.03  0.06  0.02
##              bored calm  cltc. cnfdn cntnt dlght dprss dtrmn dstrs drwsy dull 
## bored         1.00                                                            
## calm         -0.01  1.00                                                      
## clutched.up   0.03 -0.29  1.00                                                
## confident    -0.12  0.33 -0.04  1.00                                          
## content      -0.19  0.48 -0.18  0.61  1.00                                    
## delighted    -0.26  0.18 -0.05  0.41  0.45  1.00                              
## depressed     0.10 -0.17  0.32 -0.24 -0.31 -0.20  1.00                        
## determined   -0.21  0.11  0.13  0.46  0.35  0.40  0.00  1.00                  
## distressed    0.03 -0.23  0.45 -0.14 -0.24 -0.11  0.52  0.14  1.00            
## drowsy        0.37  0.07  0.01 -0.20 -0.18 -0.25  0.18 -0.21  0.08  1.00      
## dull          0.45  0.04  0.09 -0.22 -0.22 -0.30  0.24 -0.22  0.13  0.47  1.00
## elated       -0.19  0.10  0.06  0.40  0.40  0.61 -0.15  0.43 -0.05 -0.25 -0.25
## energetic    -0.29  0.07  0.09  0.47  0.42  0.52 -0.19  0.50 -0.03 -0.46 -0.37
## enthusiastic -0.29  0.17  0.01  0.49  0.49  0.63 -0.19  0.55 -0.08 -0.31 -0.33
## excited      -0.30  0.01  0.12  0.41  0.39  0.58 -0.15  0.55  0.02 -0.34 -0.35
## fearful      -0.03 -0.17  0.36 -0.08 -0.12 -0.04  0.35  0.15  0.47  0.02  0.06
## frustrated    0.20 -0.28  0.43 -0.15 -0.30 -0.16  0.49  0.09  0.58  0.13  0.20
## full.of.pep  -0.26  0.06  0.09  0.45  0.41  0.54 -0.21  0.48 -0.06 -0.43 -0.36
## gloomy        0.20 -0.15  0.32 -0.22 -0.31 -0.21  0.62 -0.05  0.48  0.27  0.37
## grouchy       0.32 -0.24  0.34 -0.18 -0.31 -0.24  0.40 -0.08  0.38  0.32  0.34
## guilty        0.05 -0.10  0.27 -0.08 -0.12 -0.04  0.37  0.11  0.41  0.07  0.12
## happy        -0.25  0.33 -0.10  0.58  0.67  0.59 -0.30  0.45 -0.18 -0.26 -0.32
## hostile       0.20 -0.27  0.37 -0.11 -0.28 -0.18  0.38  0.00  0.35  0.11  0.16
## inspired     -0.25  0.08  0.10  0.39  0.34  0.49 -0.05  0.56  0.07 -0.26 -0.25
## intense      -0.08 -0.19  0.39  0.20  0.04  0.16  0.14  0.41  0.29 -0.17 -0.12
## interested   -0.39  0.22  0.03  0.44  0.46  0.46 -0.11  0.50  0.00 -0.27 -0.29
## irritable     0.29 -0.29  0.39 -0.16 -0.33 -0.24  0.39 -0.04  0.40  0.23  0.28
## jittery      -0.04 -0.30  0.47  0.04 -0.05  0.09  0.11  0.19  0.25 -0.13 -0.07
## lively       -0.26  0.10  0.07  0.50  0.46  0.57 -0.21  0.52 -0.06 -0.42 -0.37
## lonely        0.15 -0.08  0.24 -0.13 -0.19 -0.12  0.50  0.06  0.37  0.15  0.23
## nervous      -0.03 -0.29  0.47 -0.04 -0.12  0.01  0.27  0.21  0.44 -0.03  0.03
## placid        0.13  0.41 -0.09  0.10  0.19 -0.02  0.00  0.00 -0.05  0.23  0.21
## pleased      -0.26  0.30 -0.08  0.53  0.61  0.60 -0.23  0.47 -0.14 -0.23 -0.29
## proud        -0.12  0.23 -0.01  0.55  0.46  0.49 -0.14  0.52 -0.05 -0.17 -0.20
## quiescent     0.07  0.26  0.03  0.12  0.18  0.05  0.06  0.10  0.04  0.16  0.16
## quiet         0.21  0.31  0.00 -0.04  0.02 -0.17  0.17 -0.08  0.08  0.32  0.36
## relaxed      -0.09  0.61 -0.32  0.38  0.51  0.31 -0.23  0.17 -0.26 -0.05 -0.07
## sad           0.06 -0.15  0.32 -0.16 -0.24 -0.15  0.72  0.05  0.53  0.12  0.17
## satisfied    -0.20  0.37 -0.13  0.52  0.63  0.56 -0.25  0.41 -0.20 -0.20 -0.25
## scared       -0.06 -0.19  0.37 -0.08 -0.13 -0.03  0.35  0.15  0.45  0.02  0.04
## serene        0.00  0.60 -0.19  0.30  0.46  0.16 -0.14  0.12 -0.18  0.10  0.08
## sleepy        0.36  0.06  0.01 -0.19 -0.19 -0.24  0.17 -0.20  0.08  0.84  0.46
## sluggish      0.33  0.05  0.03 -0.24 -0.22 -0.30  0.25 -0.22  0.11  0.68  0.49
## sociable     -0.21  0.23 -0.08  0.47  0.49  0.61 -0.23  0.42 -0.14 -0.27 -0.31
## sorry         0.04 -0.13  0.31 -0.12 -0.17 -0.09  0.48  0.08  0.50  0.08  0.14
## still         0.19  0.46 -0.13  0.04  0.16 -0.07  0.05 -0.08 -0.04  0.30  0.32
## strong       -0.12  0.13  0.10  0.51  0.35  0.37 -0.09  0.53  0.03 -0.23 -0.22
## surprised    -0.13 -0.08  0.24  0.13  0.08  0.24  0.09  0.25  0.20 -0.12 -0.10
## tense         0.04 -0.36  0.59 -0.05 -0.19 -0.07  0.32  0.18  0.52  0.00  0.05
## tired         0.34  0.04  0.03 -0.23 -0.21 -0.26  0.22 -0.21  0.11  0.78  0.46
## unhappy       0.14 -0.21  0.36 -0.21 -0.33 -0.22  0.68  0.00  0.53  0.15  0.26
## upset         0.09 -0.26  0.41 -0.16 -0.29 -0.17  0.57  0.06  0.61  0.10  0.15
## vigorous     -0.23  0.01  0.17  0.39  0.33  0.46 -0.13  0.48  0.03 -0.37 -0.29
## wakeful      -0.28  0.11  0.09  0.41  0.38  0.39 -0.17  0.41 -0.02 -0.53 -0.34
## warmhearted  -0.20  0.38 -0.13  0.48  0.56  0.55 -0.19  0.43 -0.12 -0.15 -0.23
## wide.awake   -0.26  0.08  0.09  0.43  0.38  0.37 -0.15  0.40 -0.01 -0.57 -0.35
## anxious       0.02 -0.24  0.44  0.05 -0.05  0.07  0.19  0.27  0.37 -0.06  0.01
## cheerful     -0.25  0.26 -0.09  0.50  0.58  0.61 -0.26  0.44 -0.16 -0.29 -0.32
## idle          0.38  0.22 -0.03 -0.05 -0.05 -0.13  0.11 -0.13  0.00  0.35  0.40
## inactive      0.37  0.19  0.00 -0.17 -0.16 -0.26  0.15 -0.25  0.04  0.53  0.47
## tranquil      0.04  0.61 -0.24  0.25  0.37  0.17 -0.13  0.08 -0.19  0.14  0.10
## alone         0.16 -0.07  0.23 -0.12 -0.16 -0.12  0.46  0.03  0.42  0.15  0.24
## kindly       -0.24  0.37 -0.06  0.50  0.57  0.48 -0.15  0.50 -0.06 -0.20 -0.23
## scornful      0.22 -0.19  0.35 -0.04 -0.16 -0.07  0.33  0.09  0.39  0.08  0.15
## Extraversion  0.05  0.01 -0.02  0.16  0.10  0.12 -0.11  0.06 -0.06 -0.02 -0.07
## Neuroticism   0.08 -0.20  0.17 -0.26 -0.25 -0.16  0.27 -0.04  0.23  0.13  0.16
## Lie          -0.13  0.06 -0.04  0.05  0.09  0.12 -0.04  0.07 -0.03 -0.09 -0.10
## Sociability   0.00  0.06 -0.04  0.18  0.15  0.13 -0.12  0.07 -0.06 -0.03 -0.09
## Impulsivity   0.07 -0.04  0.01  0.07  0.01  0.07 -0.05  0.02 -0.05 -0.02 -0.02
## gender       -0.15 -0.01  0.03 -0.28 -0.04 -0.20  0.07 -0.06  0.09  0.10  0.09
## TOD           0.05  0.02 -0.01  0.01  0.02  0.02  0.07  0.04  0.03 -0.07  0.00
## drug         -0.14 -0.09  0.08  0.09  0.06  0.10 -0.01  0.12  0.04 -0.22 -0.09
## film         -0.03  0.18 -0.19  0.13  0.21  0.32 -0.26  0.02 -0.24  0.00 -0.02
## time          0.06 -0.09 -0.03 -0.10 -0.09 -0.07 -0.04 -0.08 -0.02  0.00  0.00
## id            0.02 -0.01  0.00  0.00  0.00  0.01 -0.01  0.00 -0.01 -0.05  0.01
## form         -0.05 -0.07  0.04 -0.06 -0.08  0.00  0.07  0.00  0.08  0.05  0.00
## study*       -0.04 -0.04  0.01  0.00 -0.01  0.02 -0.01  0.01 -0.01 -0.07 -0.04
##              elatd enrgt enths exctd ferfl frstr fll.. glomy grchy gulty happy
## elated        1.00                                                            
## energetic     0.59  1.00                                                      
## enthusiastic  0.64  0.66  1.00                                                
## excited       0.65  0.70  0.67  1.00                                          
## fearful       0.03  0.05  0.02  0.11  1.00                                    
## frustrated   -0.09 -0.08 -0.14 -0.05  0.37  1.00                              
## full.of.pep   0.62  0.78  0.68  0.68  0.01 -0.10  1.00                        
## gloomy       -0.15 -0.22 -0.22 -0.18  0.33  0.48 -0.23  1.00                  
## grouchy      -0.16 -0.21 -0.24 -0.19  0.22  0.53 -0.22  0.51  1.00            
## guilty        0.00 -0.03 -0.01  0.02  0.41  0.37 -0.02  0.35  0.22  1.00      
## happy         0.55  0.58  0.62  0.56 -0.08 -0.24  0.57 -0.30 -0.32 -0.08  1.00
## hostile      -0.08 -0.07 -0.16 -0.07  0.28  0.49 -0.10  0.38  0.53  0.24 -0.26
## inspired      0.54  0.59  0.59  0.60  0.10  0.00  0.54 -0.09 -0.13  0.08  0.47
## intense       0.28  0.39  0.28  0.38  0.29  0.27  0.36  0.10  0.13  0.17  0.13
## interested    0.44  0.51  0.59  0.55  0.06 -0.12  0.49 -0.17 -0.23  0.02  0.51
## irritable    -0.14 -0.17 -0.22 -0.14  0.24  0.55 -0.17  0.43  0.66  0.22 -0.32
## jittery       0.17  0.27  0.18  0.29  0.28  0.21  0.28  0.09  0.11  0.15  0.05
## lively        0.63  0.77  0.70  0.69  0.02 -0.09  0.81 -0.23 -0.22 -0.02  0.61
## lonely       -0.07 -0.11 -0.09 -0.07  0.27  0.38 -0.12  0.45  0.30  0.33 -0.18
## nervous       0.08  0.15  0.10  0.22  0.50  0.36  0.13  0.24  0.21  0.34 -0.03
## placid       -0.01 -0.11 -0.03 -0.13 -0.04 -0.07 -0.12  0.04 -0.01  0.01  0.06
## pleased       0.57  0.55  0.61  0.57 -0.06 -0.21  0.52 -0.25 -0.28 -0.05  0.72
## proud         0.50  0.47  0.58  0.47 -0.01 -0.08  0.48 -0.15 -0.13 -0.01  0.53
## quiescent     0.08  0.01  0.06  0.01  0.05  0.02  0.00  0.08  0.04  0.08  0.11
## quiet        -0.19 -0.27 -0.20 -0.26  0.04  0.08 -0.26  0.22  0.14  0.09 -0.12
## relaxed       0.22  0.18  0.29  0.14 -0.18 -0.31  0.19 -0.24 -0.28 -0.13  0.42
## sad          -0.10 -0.12 -0.13 -0.09  0.39  0.48 -0.14  0.61  0.36  0.39 -0.24
## satisfied     0.47  0.45  0.56  0.43 -0.11 -0.26  0.47 -0.28 -0.29 -0.09  0.63
## scared        0.03  0.04  0.04  0.12  0.72  0.34  0.02  0.31  0.21  0.39 -0.08
## serene        0.13  0.08  0.16  0.05 -0.10 -0.24  0.07 -0.11 -0.19 -0.06  0.30
## sleepy       -0.25 -0.46 -0.30 -0.34  0.03  0.13 -0.42  0.27  0.31  0.08 -0.25
## sluggish     -0.28 -0.46 -0.35 -0.37  0.05  0.14 -0.45  0.31  0.32  0.09 -0.30
## sociable      0.50  0.53  0.61  0.51 -0.06 -0.17  0.56 -0.26 -0.29 -0.04  0.61
## sorry        -0.03 -0.05 -0.07 -0.03  0.43  0.46 -0.07  0.47  0.29  0.58 -0.16
## still        -0.13 -0.20 -0.13 -0.23 -0.05 -0.05 -0.20  0.10  0.01  0.00 -0.01
## strong        0.42  0.52  0.50  0.45  0.07  0.02  0.50 -0.09 -0.07  0.03  0.43
## surprised     0.31  0.32  0.27  0.37  0.30  0.14  0.27  0.08  0.05  0.16  0.17
## tense         0.03  0.11  0.01  0.14  0.40  0.51  0.08  0.32  0.36  0.28 -0.11
## tired        -0.28 -0.48 -0.32 -0.36  0.05  0.16 -0.45  0.30  0.33  0.09 -0.28
## unhappy      -0.15 -0.17 -0.20 -0.14  0.36  0.53 -0.19  0.64  0.48  0.36 -0.32
## upset        -0.09 -0.09 -0.15 -0.07  0.44  0.61 -0.12  0.55  0.52  0.42 -0.27
## vigorous      0.59  0.72  0.60  0.65  0.09 -0.01  0.70 -0.14 -0.13  0.02  0.47
## wakeful       0.45  0.65  0.51  0.53  0.04 -0.08  0.61 -0.20 -0.23 -0.03  0.48
## warmhearted   0.46  0.44  0.57  0.43 -0.05 -0.20  0.45 -0.22 -0.30 -0.02  0.65
## wide.awake    0.45  0.70  0.50  0.54  0.03 -0.07  0.65 -0.20 -0.22 -0.03  0.46
## anxious       0.14  0.23  0.16  0.29  0.33  0.35  0.20  0.19  0.19  0.28  0.03
## cheerful      0.59  0.63  0.66  0.59 -0.04 -0.22  0.62 -0.28 -0.30 -0.05  0.72
## idle         -0.14 -0.24 -0.18 -0.23 -0.01  0.04 -0.22  0.16  0.14  0.05 -0.11
## inactive     -0.25 -0.41 -0.32 -0.35  0.02  0.09 -0.39  0.24  0.21  0.08 -0.25
## tranquil      0.11  0.02  0.13  0.00 -0.14 -0.21  0.03 -0.11 -0.15 -0.07  0.27
## alone        -0.07 -0.13 -0.11 -0.08  0.30  0.34 -0.12  0.46  0.30  0.32 -0.20
## kindly        0.46  0.49  0.57  0.47 -0.03 -0.13  0.48 -0.18 -0.28 -0.01  0.64
## scornful      0.02  0.00 -0.05  0.01  0.32  0.47  0.00  0.35  0.48  0.30 -0.14
## Extraversion  0.12  0.11  0.12  0.11 -0.04 -0.03  0.13 -0.08 -0.03 -0.05  0.12
## Neuroticism  -0.11 -0.13 -0.12 -0.07  0.16  0.23 -0.13  0.24  0.22  0.19 -0.22
## Lie           0.07  0.09  0.10  0.06 -0.02 -0.07  0.07 -0.05 -0.12 -0.04  0.09
## Sociability   0.10  0.12  0.13  0.11 -0.05 -0.05  0.13 -0.09 -0.06 -0.05  0.16
## Impulsivity   0.10  0.07  0.07  0.08 -0.02 -0.01  0.09 -0.05  0.00 -0.03  0.03
## gender       -0.21 -0.20 -0.20 -0.26 -0.04  0.18 -0.23  0.01  0.09  0.11 -0.06
## TOD           0.05  0.06  0.04  0.03  0.00  0.05  0.05  0.03 -0.02  0.03  0.02
## drug          0.10  0.21  0.14  0.17  0.01  0.01  0.18 -0.06 -0.06 -0.01  0.12
## film          0.18  0.13  0.21  0.13 -0.19 -0.22  0.15 -0.24 -0.11 -0.11  0.26
## time         -0.04 -0.03 -0.09 -0.05 -0.02  0.04 -0.06  0.02  0.03 -0.02 -0.08
## id            0.02  0.01  0.03  0.00 -0.02 -0.01  0.03 -0.01 -0.02  0.00  0.01
## form         -0.04 -0.06 -0.03 -0.03  0.07  0.08 -0.06  0.06  0.03  0.06 -0.06
## study*        0.01  0.03  0.05  0.01 -0.01 -0.03  0.04 -0.02 -0.02  0.02  0.02
##              hostl inspr intns intrs irrtb jttry livly lonly nervs placd plesd
## hostile       1.00                                                            
## inspired     -0.04  1.00                                                      
## intense       0.28  0.33  1.00                                                
## interested   -0.15  0.49  0.25  1.00                                          
## irritable     0.60 -0.10  0.22 -0.22  1.00                                    
## jittery       0.24  0.18  0.42  0.14  0.19  1.00                              
## lively       -0.10  0.55  0.35  0.52 -0.18  0.26  1.00                        
## lonely        0.23  0.02  0.13 -0.05  0.29  0.11 -0.11  1.00                  
## nervous       0.25  0.16  0.39  0.11  0.26  0.50  0.13  0.25  1.00            
## placid       -0.07 -0.05 -0.10  0.03 -0.04 -0.14 -0.10  0.06 -0.09  1.00      
## pleased      -0.21  0.51  0.14  0.53 -0.27  0.04  0.56 -0.12 -0.02  0.07  1.00
## proud        -0.08  0.47  0.23  0.42 -0.12  0.07  0.52 -0.05  0.03  0.06  0.53
## quiescent    -0.02  0.05  0.04  0.09  0.00 -0.01  0.01  0.09  0.04  0.37  0.13
## quiet         0.01 -0.17 -0.10 -0.08  0.07 -0.10 -0.24  0.23 -0.01  0.35 -0.10
## relaxed      -0.31  0.16 -0.17  0.28 -0.33 -0.30  0.23 -0.13 -0.28  0.31  0.38
## sad           0.34 -0.01  0.18 -0.05  0.35  0.14 -0.14  0.48  0.29  0.01 -0.18
## satisfied    -0.25  0.39  0.09  0.47 -0.31  0.01  0.51 -0.14 -0.06  0.13  0.63
## scared        0.27  0.11  0.31  0.07  0.24  0.32  0.02  0.25  0.51 -0.06 -0.05
## serene       -0.21  0.10 -0.10  0.20 -0.23 -0.19  0.10 -0.04 -0.17  0.50  0.31
## sleepy        0.11 -0.25 -0.17 -0.27  0.23 -0.13 -0.42  0.14 -0.03  0.21 -0.23
## sluggish      0.13 -0.27 -0.18 -0.27  0.25 -0.10 -0.45  0.18 -0.01  0.23 -0.28
## sociable     -0.21  0.43  0.15  0.46 -0.26  0.09  0.60 -0.11 -0.01  0.03  0.55
## sorry         0.33  0.06  0.19 -0.02  0.28  0.12 -0.06  0.37  0.32 -0.01 -0.10
## still        -0.06 -0.12 -0.15 -0.05 -0.04 -0.20 -0.18  0.09 -0.13  0.44  0.00
## strong        0.04  0.44  0.47  0.39 -0.03  0.17  0.53 -0.03  0.11  0.01  0.40
## surprised     0.13  0.39  0.26  0.27  0.06  0.22  0.27  0.09  0.26 -0.07  0.21
## tense         0.37  0.10  0.45  0.03  0.42  0.50  0.08  0.27  0.57 -0.12 -0.09
## tired         0.13 -0.27 -0.17 -0.27  0.25 -0.12 -0.45  0.16 -0.01  0.21 -0.26
## unhappy       0.43 -0.06  0.18 -0.14  0.48  0.13 -0.19  0.45  0.27 -0.02 -0.25
## upset         0.47  0.00  0.24 -0.10  0.48  0.18 -0.12  0.40  0.35 -0.06 -0.21
## vigorous      0.00  0.55  0.43  0.45 -0.08  0.30  0.69 -0.07  0.19 -0.10  0.47
## wakeful      -0.08  0.43  0.32  0.48 -0.17  0.25  0.63 -0.08  0.12 -0.04  0.44
## warmhearted  -0.28  0.40  0.09  0.48 -0.31  0.01  0.50 -0.10 -0.04  0.15  0.58
## wide.awake   -0.07  0.46  0.33  0.45 -0.17  0.24  0.63 -0.09  0.12 -0.08  0.43
## anxious       0.24  0.20  0.40  0.13  0.27  0.48  0.19  0.20  0.52 -0.09  0.04
## cheerful     -0.22  0.49  0.14  0.50 -0.30  0.06  0.66 -0.14  0.01  0.03  0.67
## idle          0.05 -0.16 -0.11 -0.14  0.09 -0.10 -0.21  0.14 -0.07  0.27 -0.10
## inactive      0.06 -0.27 -0.21 -0.24  0.14 -0.15 -0.38  0.13 -0.08  0.28 -0.23
## tranquil     -0.20  0.06 -0.17  0.16 -0.21 -0.24  0.06 -0.04 -0.20  0.45  0.25
## alone         0.23  0.00  0.16 -0.03  0.28  0.11 -0.11  0.77  0.29  0.08 -0.12
## kindly       -0.23  0.44  0.17  0.52 -0.28  0.02  0.53 -0.09 -0.02  0.14  0.60
## scornful      0.51  0.04  0.22 -0.11  0.48  0.19  0.00  0.31  0.31 -0.01 -0.10
## Extraversion  0.01  0.06  0.02  0.04  0.00  0.01  0.15 -0.11 -0.05 -0.03  0.09
## Neuroticism   0.18 -0.05  0.09 -0.10  0.23  0.16 -0.14  0.25  0.23 -0.03 -0.16
## Lie          -0.11  0.09 -0.01  0.08 -0.11 -0.04  0.07 -0.03 -0.03 -0.02  0.09
## Sociability  -0.03  0.07  0.01  0.06 -0.04 -0.02  0.16 -0.14 -0.07 -0.03  0.11
## Impulsivity   0.04  0.04  0.04  0.01  0.04  0.03  0.10 -0.04 -0.01 -0.02  0.03
## gender       -0.06 -0.20 -0.09 -0.03  0.03  0.00 -0.20 -0.13  0.16  0.07 -0.11
## TOD           0.01  0.03  0.03 -0.01  0.01  0.01  0.06  0.08  0.00  0.02  0.04
## drug         -0.02  0.16  0.15  0.10  0.00  0.22  0.19 -0.03  0.12 -0.12  0.10
## film         -0.23  0.13 -0.21  0.12 -0.18 -0.13  0.17 -0.09 -0.13  0.03  0.28
## time          0.04 -0.05 -0.04 -0.17  0.04 -0.10 -0.06 -0.05 -0.03 -0.07 -0.04
## id           -0.01  0.01  0.02  0.01 -0.02  0.05  0.01  0.01  0.00  0.02  0.01
## form          0.06 -0.04  0.00 -0.05  0.07  0.02 -0.06  0.04  0.06 -0.06 -0.06
## study*       -0.01  0.02  0.02  0.02 -0.01  0.06  0.03  0.01  0.03 -0.02 -0.01
##              proud qscnt quiet relxd sad   stsfd scard seren slepy slggs socbl
## proud         1.00                                                            
## quiescent     0.10  1.00                                                      
## quiet        -0.06  0.25  1.00                                                
## relaxed       0.29  0.18  0.15  1.00                                          
## sad          -0.07  0.06  0.17 -0.21  1.00                                    
## satisfied     0.50  0.14 -0.04  0.49 -0.21  1.00                              
## scared        0.01  0.03  0.03 -0.20  0.40 -0.10  1.00                        
## serene        0.20  0.34  0.31  0.48 -0.12  0.35 -0.13  1.00                  
## sleepy       -0.15  0.16  0.31 -0.04  0.12 -0.20  0.03  0.08  1.00            
## sluggish     -0.19  0.16  0.31 -0.04  0.16 -0.23  0.04  0.07  0.66  1.00      
## sociable      0.48  0.05 -0.18  0.37 -0.17  0.56 -0.05  0.20 -0.27 -0.31  1.00
## sorry        -0.05  0.06  0.13 -0.17  0.54 -0.15  0.39 -0.09  0.09  0.09 -0.13
## still        -0.01  0.29  0.50  0.30  0.03  0.07 -0.06  0.45  0.29  0.28 -0.05
## strong        0.54  0.08 -0.08  0.19 -0.02  0.40  0.10  0.12 -0.22 -0.26  0.41
## surprised     0.20  0.04 -0.09 -0.04  0.14  0.12  0.26 -0.03 -0.12 -0.12  0.15
## tense         0.00  0.01  0.00 -0.38  0.33 -0.14  0.42 -0.24  0.00  0.01 -0.08
## tired        -0.19  0.14  0.31 -0.06  0.16 -0.22  0.04  0.05  0.81  0.68 -0.30
## unhappy      -0.14  0.04  0.14 -0.28  0.69 -0.30  0.36 -0.17  0.16  0.21 -0.25
## upset        -0.10  0.02  0.09 -0.30  0.61 -0.26  0.42 -0.19  0.10  0.14 -0.22
## vigorous      0.43  0.03 -0.25  0.11 -0.07  0.38  0.08  0.06 -0.37 -0.37  0.44
## wakeful       0.37  0.03 -0.16  0.19 -0.09  0.40  0.03  0.10 -0.54 -0.50  0.44
## warmhearted   0.50  0.15 -0.02  0.50 -0.14  0.61 -0.05  0.35 -0.14 -0.19  0.60
## wide.awake    0.35  0.01 -0.19  0.17 -0.09  0.36  0.03  0.08 -0.58 -0.50  0.42
## anxious       0.10  0.03  0.00 -0.23  0.21 -0.01  0.35 -0.15 -0.06 -0.04  0.06
## cheerful      0.49  0.08 -0.18  0.37 -0.20  0.58 -0.05  0.25 -0.28 -0.33  0.61
## idle         -0.05  0.20  0.38  0.12  0.07 -0.06 -0.04  0.26  0.33  0.33 -0.10
## inactive     -0.18  0.20  0.44  0.03  0.10 -0.17 -0.01  0.19  0.51  0.52 -0.26
## tranquil      0.19  0.36  0.28  0.50 -0.14  0.30 -0.16  0.62  0.14  0.11  0.20
## alone        -0.08  0.09  0.29 -0.12  0.47 -0.15  0.31  0.00  0.14  0.16 -0.15
## kindly        0.54  0.18  0.02  0.41 -0.08  0.56 -0.03  0.34 -0.19 -0.18  0.56
## scornful     -0.02  0.06  0.03 -0.21  0.32 -0.13  0.29 -0.11  0.07  0.07 -0.10
## Extraversion  0.14 -0.05 -0.14  0.07 -0.09  0.09 -0.05  0.00 -0.03 -0.03  0.19
## Neuroticism  -0.16 -0.01  0.07 -0.23  0.23 -0.20  0.17 -0.15  0.13  0.14 -0.15
## Lie           0.06 -0.02 -0.02  0.08 -0.01  0.09 -0.04  0.05 -0.08 -0.11  0.06
## Sociability   0.13 -0.06 -0.14  0.10 -0.10  0.12 -0.06  0.03 -0.03 -0.03  0.22
## Impulsivity   0.09 -0.03 -0.11  0.00 -0.04  0.02 -0.03 -0.05 -0.03 -0.03  0.09
## gender       -0.29  0.01  0.07 -0.03  0.10 -0.12  0.08  0.04  0.11  0.04 -0.12
## TOD           0.06 -0.02  0.00  0.02  0.07  0.05 -0.01  0.01 -0.09 -0.08  0.07
## drug          0.09 -0.03 -0.09 -0.08  0.01  0.07  0.03 -0.08 -0.22 -0.20  0.08
## film          0.13 -0.05 -0.06  0.25 -0.30  0.22 -0.17  0.13  0.01 -0.05  0.26
## time         -0.07 -0.04 -0.08 -0.11 -0.02 -0.13 -0.05 -0.06 -0.01 -0.06 -0.13
## id            0.01 -0.01  0.00  0.01  0.00  0.03 -0.02  0.01 -0.06 -0.01  0.03
## form         -0.05 -0.01  0.02 -0.06  0.09 -0.06  0.06 -0.10  0.07  0.05 -0.03
## study*        0.00 -0.03 -0.03 -0.02  0.01  0.03 -0.01 -0.02 -0.07 -0.05  0.05
##              sorry still strng srprs tense tired unhpp upset vigrs wakfl wrmhr
## sorry         1.00                                                            
## still         0.02  1.00                                                      
## strong        0.02 -0.04  1.00                                                
## surprised     0.21 -0.11  0.21  1.00                                          
## tense         0.30 -0.16  0.12  0.20  1.00                                    
## tired         0.09  0.27 -0.25 -0.13  0.02  1.00                              
## unhappy       0.47  0.01 -0.05  0.11  0.35  0.20  1.00                        
## upset         0.56 -0.05  0.00  0.19  0.45  0.14  0.63  1.00                  
## vigorous     -0.01 -0.18  0.51  0.31  0.17 -0.39 -0.10 -0.03  1.00            
## wakeful      -0.05 -0.12  0.42  0.22  0.09 -0.54 -0.14 -0.09  0.57  1.00      
## warmhearted  -0.09  0.08  0.41  0.12 -0.13 -0.17 -0.24 -0.21  0.36  0.37  1.00
## wide.awake   -0.05 -0.15  0.42  0.24  0.11 -0.57 -0.13 -0.07  0.60  0.71  0.35
## anxious       0.23 -0.12  0.18  0.25  0.57 -0.05  0.20  0.28  0.27  0.19  0.01
## cheerful     -0.11 -0.06  0.42  0.20 -0.09 -0.32 -0.26 -0.21  0.50  0.48  0.60
## idle          0.04  0.42 -0.08 -0.09 -0.08  0.31  0.08  0.00 -0.20 -0.19 -0.03
## inactive      0.09  0.44 -0.24 -0.12 -0.07  0.50  0.13  0.05 -0.34 -0.35 -0.15
## tranquil     -0.10  0.43  0.10 -0.05 -0.29  0.10 -0.18 -0.21  0.00  0.04  0.34
## alone         0.37  0.10 -0.01  0.09  0.29  0.16  0.44  0.43 -0.08 -0.06 -0.11
## kindly       -0.07  0.11  0.44  0.14 -0.08 -0.21 -0.18 -0.15  0.41  0.44  0.72
## scornful      0.36 -0.05  0.06  0.13  0.35  0.09  0.41  0.46  0.06 -0.02 -0.15
## Extraversion -0.06 -0.04  0.11  0.02 -0.06 -0.05 -0.10 -0.04  0.08  0.04  0.12
## Neuroticism   0.17 -0.02 -0.14  0.04  0.24  0.14  0.24  0.21 -0.09 -0.13 -0.15
## Lie          -0.03 -0.01  0.05  0.04 -0.05 -0.08 -0.06 -0.05  0.05  0.06  0.11
## Sociability  -0.07 -0.04  0.11  0.01 -0.07 -0.04 -0.11 -0.06  0.08  0.04  0.15
## Impulsivity  -0.03 -0.05  0.07  0.03 -0.02 -0.05 -0.04  0.00  0.06  0.03  0.04
## gender        0.08  0.04 -0.25 -0.23  0.09  0.18  0.01  0.15 -0.16 -0.09 -0.02
## TOD           0.03 -0.01  0.04 -0.01  0.02 -0.07  0.03  0.03  0.06  0.04  0.02
## drug         -0.03 -0.12  0.11  0.06  0.14 -0.20 -0.02  0.00  0.17  0.20  0.06
## film         -0.29 -0.01 -0.02 -0.08 -0.16 -0.01 -0.25 -0.28  0.07  0.06  0.26
## time         -0.01 -0.04 -0.09 -0.03 -0.01 -0.03  0.00  0.02 -0.03 -0.04 -0.14
## id           -0.01  0.01  0.01 -0.02  0.01 -0.05  0.00 -0.03  0.04  0.03  0.00
## form          0.08 -0.03  0.00  0.03  0.06  0.06  0.10  0.07 -0.05 -0.06 -0.05
## study*        0.00 -0.04  0.02 -0.01  0.02 -0.06  0.00 -0.01  0.03  0.06  0.02
##              wd.wk anxis chrfl idle  inctv trnql alone kndly scrnf Extrv Nrtcs
## wide.awake    1.00                                                            
## anxious       0.19  1.00                                                      
## cheerful      0.45  0.07  1.00                                                
## idle         -0.21 -0.05 -0.10  1.00                                          
## inactive     -0.37 -0.08 -0.28  0.53  1.00                                    
## tranquil      0.00 -0.19  0.26  0.29  0.25  1.00                              
## alone        -0.09  0.18  0.06  0.05  0.08  0.16  1.00                        
## kindly        0.43 -0.01 -0.13  0.18 -0.04  0.22 -0.08  1.00                  
## scornful      0.00  0.19  0.39  0.07  0.31  0.14  0.30 -0.12  1.00            
## Extraversion  0.04  0.00  0.15 -0.04 -0.07 -0.01 -0.09  0.06  0.01  1.00      
## Neuroticism  -0.14  0.20 -0.15  0.05  0.11 -0.11  0.22 -0.18  0.13 -0.14  1.00
## Lie           0.07 -0.02  0.07 -0.07 -0.11  0.05 -0.10  0.11 -0.08 -0.19 -0.19
## Sociability   0.04 -0.02  0.16 -0.06 -0.07  0.00 -0.13  0.14 -0.06  0.86 -0.23
## Impulsivity   0.03  0.02  0.09 -0.01 -0.06 -0.03 -0.02 -0.05  0.05  0.77  0.02
## gender       -0.19 -0.05 -0.14 -0.08  0.09 -0.02    NA    NA    NA  0.06  0.15
## TOD           0.07  0.00  0.01  0.00 -0.03 -0.02  0.02  0.05  0.05  0.01  0.04
## drug          0.20  0.16  0.08 -0.02 -0.14 -0.09 -0.04  0.11 -0.05  0.04  0.00
## film          0.05 -0.01  0.24  0.01 -0.02  0.15 -0.02  0.23 -0.14  0.08  0.01
## time         -0.04 -0.03 -0.08  0.00  0.00 -0.10 -0.08 -0.04  0.00  0.02  0.02
## id            0.04  0.02  0.03  0.05 -0.01  0.01 -0.02  0.00 -0.01  0.00  0.03
## form         -0.07  0.00  0.15  0.17  0.12  0.23    NA    NA    NA -0.06  0.04
## study*        0.04  0.07  0.12 -0.01 -0.07  0.00 -0.03 -0.06 -0.08  0.03  0.02
##             Lie   Scblt Impls gendr TOD   drug  film  time  id    form  stdy*
## Lie          1.00                                                            
## Sociability -0.08  1.00                                                      
## Impulsivity -0.21  0.40  1.00                                                
## gender      -0.06 -0.16  0.20  1.00                                          
## TOD          0.00 -0.01  0.02    NA  1.00                                    
## drug         0.02  0.04  0.01 -0.03 -0.02  1.00                              
## film        -0.02  0.07  0.08    NA  0.02  0.01  1.00                        
## time        -0.01  0.01  0.02  0.00  0.11  0.00  0.02  1.00                  
## id           0.00  0.00  0.00  0.04  0.03  0.01 -0.04  0.05  1.00            
## form         0.04 -0.05 -0.05    NA  0.04  0.01 -0.15 -0.06  0.03  1.00      
## study*       0.00  0.02  0.02    NA -0.03  0.00 -0.10  0.09  0.13  0.14  1.00

Yuo can plot the correlations of the items using the function below

corPlot(r)

Positive correlations are blue and negative ones are in red. You can see that there are so many items in this list that the graph is unreadable. We can ristrict our analysis to just a few columns and this gives a better summary.

Here is a list of measured variables for the first 1 of 11 different personality characteristics. This is the pleasure characteristic. The measured variables corresponding to the “pleasure” latent variable are

aa<-Yik.keys[[1]]
aa
## [1] "happy"     "content"   "satisfied" "pleased"

The 4 columns of data corresponding to pleasure are below

A<-msqR[,aa]
head(A)

Here is the lower digonal part of the correlation matrix (note that because the matrix is symmetric we don’t need to know the other parts)

rr<- lowerCor(A)
##           happy cntnt stsfd plesd
## happy     1.00                   
## content   0.67  1.00             
## satisfied 0.63  0.63  1.00       
## pleased   0.72  0.61  0.63  1.00

Here is the correlation plot

corPlot(rr)

Here is a correlation test for wherther the correlation values are equal to zero

E<-corTest(rr)
E
## Call:corTest(x = rr)
## Correlation matrix 
##           happy content satisfied pleased
## happy      1.00   -0.21     -0.51    0.12
## content   -0.21    1.00     -0.36   -0.54
## satisfied -0.51   -0.36      1.00   -0.41
## pleased    0.12   -0.54     -0.41    1.00
## Sample Size 
## [1] 4
## Probability values (Entries above the diagonal are adjusted for multiple tests.) 
##           happy content satisfied pleased
## happy      0.00    1.00      1.00       1
## content    0.79    0.00      1.00       1
## satisfied  0.49    0.64      0.00       1
## pleased    0.88    0.46      0.59       0
## 
##  To see confidence intervals of the correlations, print with the short=FALSE option

Your Problems

Your homework problem is based upon the “Garcia” dataset in the “psych” package. Here is a description of the dataset: Garcia, Schmitt, Branscombe, and Ellemers (2010) report data for 129 subjects on the effects of perceived sexism on anger and liking of women’s reactions to in-group members who protest discrimination. This data set is also used as the ‘protest’ data set by Hayes (2013 and 2018). It is a useful example of mediation and moderation in regression. It may also be used as an example of plotting interactions.

Here is a summary of the dataset: The reaction of women to women who protest discriminatory treatment was examined in an experiment reported by Garcia et al. (2010). 129 women were given a description of sex discrimination in the workplace. For example, “a male lawyer was promoted over a clearly more qualified female lawyer”. Subjects then read that the target lawyer felt that the decision was unfair. Subjects were then randomly assigned to three conditions: Control (no protest), Individual Protest (“They are treating me unfairly”) , or Collective Protest (“The firm is is treating women unfairly”).

Participants were then asked how much they liked the target (liking), how angry they were to the target (anger) and to evaluate the appropriateness of the target’s response (respappr).

Here is the first 6 rows of Garcia data, I made the binary variable “prot2” a categorical variable with levels (Yes,No) corresponding to (1,0).

library(psych)
Dat<-Garcia[,1:5]
Dat$protestcat<-factor(Garcia$prot2,labels=c("No","Yes"))
head(Dat)

Here are your problems from Dr King

  1. Produce a scatterplot matrix plots of the Garcia dataset using the ggpairs plot and the pairs.panels plot. What can you visually conclude by looking at the plots and forming your impressions of the raw data plots.
plot(Garcia)

library(psych) # Extension package to ggplot2
plt<-ggpairs(Garcia)
plt

#Define my graphing function
my_fn <- function(data, mapping, ...){
p <- ggplot(data = data, mapping = mapping) +
geom_point() +
geom_smooth(method="lm")
p
}
summary(Garcia$protest)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   0.000   0.000   1.000   1.031   2.000   2.000
Garcia$protest2 <- as.factor(Garcia$protest)
levels(Garcia$protest2)
## [1] "0" "1" "2"
Garcia <- Garcia %>% mutate( protest2 = factor(protest2, levels = c("0", "1", "2")))
grph = ggpairs(Garcia[c(2:5, 7)],aes(col=protest2,alpha=0.5),
lower=list(continuous = my_fn))
grph
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

# ggpairs plot
ggpairs(Garcia[,1:5])

# pairs.panels plot
pairs.panels(Garcia[,1:5])

ggpair plot: The protest ggpair plot has a sinusoidal wave with two cycles and similar medians. The protest amplitude ranges from 0.2 to 0.5. The sexism plot has a normal curve that is almost symmetrical with a median score that is almost centered, and a lot of variation (large spread). The anger plot has a lot of variation with a positive skew to the right and multiple small nodes below 3. The liking ggpair plot has a negative skew with a lot of variation. The respappr ggpair plot has a slight negative skew with a lot of variation.

In the ggpair plot, specifically the protest by sexism plot, there is more variation in sexism as you move from the control group (0) to the collective protest group (2). In contrast to this plot, the protest by liking and protest by raspappr plots show less variability in the collective protest group (3) relative to the control group (1). Irrespective of the score for sexism, the liking score is above four for the majority of the respondents. For the liking and respappr ggpair plot, most of the raw data plots are above a respappr score of four. The following ggpair plots are statistically significant: 1) anger by protest, 2) liking by anger, 3) respappr by protest, 4) respappor by anger and 5) respappr by liking.

pairs.panels plot: With the overlay on top of the histograms, we now see the distribution of the four noncategorical variables. Sexism has a normal curve that appears symmetrical with a median score that appears to be equivalent to the mean score, and a lot of variation. Anger is skewed to the right and liking and respappr are skewed to the left. The pairs.panels show correlation coefficients and density of the distribution by color.

QUESTION #2

  1. Evaluate the correlations between the 5 numeric variables of the Garcia dataset (first 5 columns of data). Use the lowerCor(), corPlot() and corTest() functions in the psych package of R. Which of the pairwise correlations are statistically significant?
# lowerCor
lower_cor <- lowerCor(Garcia[,1:5])
##          prtst sexsm anger likng rsppp
## protest   1.00                        
## sexism   -0.02  1.00                  
## anger    -0.31 -0.03  1.00            
## liking    0.17  0.09 -0.51  1.00      
## respappr  0.48  0.04 -0.53  0.49  1.00
print(lower_cor)
##              protest      sexism       anger      liking    respappr
## protest   1.00000000 -0.02090619 -0.30768448  0.16930838  0.48488889
## sexism   -0.02090619  1.00000000 -0.03180676  0.09139386  0.04218515
## anger    -0.30768448 -0.03180676  1.00000000 -0.50538104 -0.53329781
## liking    0.16930838  0.09139386 -0.50538104  1.00000000  0.49440350
## respappr  0.48488889  0.04218515 -0.53329781  0.49440350  1.00000000
knitr::opts_chunk$set(echo = TRUE, fig.width = 10, fig.height = 7)
# corPlot
# Adjusting margins
par(mar = c(5, 4, 4, 2) + 0.1) 

# Ensure plot area is clear
dev.off() # Clear any previous plots
## null device 
##           1
# corPlot
corPlot(lower_cor, numbers = TRUE)
# corTest
cor_test <- cor.ci(Garcia[,1:5])

print(cor_test)
## Call:corCi(x = x, keys = keys, n.iter = n.iter, p = p, overlap = overlap, 
##     poly = poly, method = method, plot = plot, minlength = minlength, 
##     n = n)
## 
##  Coefficients and bootstrapped confidence intervals 
##          prtst sexsm anger likng rsppp
## protest   1.00                        
## sexism   -0.02  1.00                  
## anger    -0.31 -0.03  1.00            
## liking    0.17  0.09 -0.51  1.00      
## respappr  0.48  0.04 -0.53  0.49  1.00
## 
##  scale correlations and bootstrapped confidence intervals 
##             lower.emp lower.norm estimate upper.norm upper.emp    p
## prtst-sexsm     -0.19      -0.20    -0.02       0.17      0.13 0.89
## prtst-anger     -0.47      -0.47    -0.31      -0.11     -0.12 0.00
## prtst-likng     -0.06      -0.04     0.17       0.33      0.31 0.13
## prtst-rsppp      0.33       0.32     0.48       0.60      0.61 0.00
## sexsm-anger     -0.19      -0.20    -0.03       0.13      0.16 0.64
## sexsm-likng     -0.08      -0.08     0.09       0.27      0.28 0.28
## sexsm-rsppp     -0.08      -0.10     0.04       0.21      0.20 0.51
## anger-likng     -0.63      -0.63    -0.51      -0.33     -0.31 0.00
## anger-rsppp     -0.69      -0.67    -0.53      -0.36     -0.37 0.00
## likng-rsppp      0.34       0.33     0.49       0.62      0.62 0.00
# Extract p-values and determine statistically significant correlations
p_values <- cor_test$p
significant_correlations <- which(p_values < 0.05, arr.ind=TRUE)
print("Statistically significant correlations (p < 0.05):")
## [1] "Statistically significant correlations (p < 0.05):"
print(significant_correlations)
## [1]  2  4  8  9 10
p_values 
##  [1] 4.464978e-01 1.613550e-03 6.508367e-02 3.319381e-07 3.175054e-01
##  [6] 1.409286e-01 2.525793e-01 7.416171e-07 8.575003e-07 2.766657e-07

The lowerCor() There is no relationship between sexism and protest (-0.02).

For protest and sexism, there is a negative moderate relationship (-0.31). As we go from control to collective protest, the anger score decreases. Thus, the anger score in the control group would be higher compared to the collective protest group.

For protest and liking, there is a positive small relationship (0.17). As we go from control to collective protest, the liking score slightly increases.

There is a moderate positive relation between protest and respappr (0.48). As you go from the control to the collective protest, the respappr score increases moderately.

There is no relationship between sexism and anger (-0.03), sexism and liking (0.09), and sexism and respappr (0.04).

Anger has a negative large relationship with liking (-0.51) and respappr (-0.53). As anger increases, then the liking and respappr score decreases moderately.

Liking and respappr have a positive moderate relationship (0.49). As liking increases, the respappr score increases moderately.

corPlot() The correlation plot shows the correlation by color. Protest by anger has a negative medium correlation (-0.31) Protest by liking has a positive small correlation (0.17) Protest by respappr has a positive large correlation (0.48) Sexism does not have a relation with protest, anger, liking or respappr. Anger has a positive negative relationship with liking (-0.51) and respappr (-0.53). Liking has a positive medium relationship with respappr (0.49)

corTest() The corTest shows the statistically significant correlations (p < 0.05). Below are the statistically significant correlations. Protest by anger [2] 9.987358e-04 Protest by liking [3] 3.553016e-02 Protest by respappr [4] 2.653728e-09 Anger by liking [8] 3.951392e-05 Anger by respappr [9] 1.680695e-05 Liking by respappr [10] 1.637657e-07

  1. Evaluate the item level consistency or reliability and using the scoreItems() function in the “psych” package and the “cronbach.alpha(data,CI=TRUE)” function in the “ltm” package of R. Is there evidence that the items of the survey aren’t internally consistent?
# Create a keys list for scoreItems
keys <- make.keys(Garcia[,1:4], list(scale = 1:4))
# scoreItems
score_items <- scoreItems(keys, Garcia[,1:4])
## Number of categories should be increased  in order to count frequencies.
## Warning in sqrt(corrected.var * item.var): NaNs produced
## Warning in sqrt(Q/n.subjects): NaNs produced
print(score_items)
## Call: scoreItems(keys = keys, items = Garcia[, 1:4])
## 
## (Unstandardized) Alpha:
##       scale
## alpha  -1.1
## 
## Standard errors of unstandardized Alpha:
##       scale
## ASE     NaN
## 
## Average item correlation:
##           scale
## average.r -0.15
## 
## Median item correlation:
##  scale 
## -0.026 
## 
##  Guttman 6* reliability: 
##          scale
## Lambda.6 -0.37
## 
## Signal/Noise based upon av.r : 
##              scale
## Signal/Noise -0.51
## 
## Scale intercorrelations corrected for attenuation 
##  raw correlations below the diagonal, alpha on the diagonal 
##  corrected correlations above the diagonal:
##       scale
## scale  -1.1
## 
##  Average adjusted correlations within and between scales (MIMS)
## [1] -0.15
## 
##  Average adjusted item x scale correlations within and between scales (MIMT)
## [1] 0.38
## 
##  In order to see the item by scale loadings and frequency counts of the data
##  print with the short option = FALSE
# Cronbach's alpha
cronbach_alpha <- cronbach.alpha(Garcia[,1:5], CI=TRUE)
print(cronbach_alpha)
## 
## Cronbach's alpha for the 'Garcia[, 1:5]' data-set
## 
## Items: 5
## Sample units: 129
## alpha: -0.537
## 
## Bootstrap 95% CI based on 1000 samples
##   2.5%  97.5% 
## -1.172 -0.084
# Checking internal consistency
if (cronbach_alpha$alpha >= 0.7) {
print("The items of the survey are internally consistent.")
} else {
print("The items of the survey are not internally consistent.")
}
## [1] "The items of the survey are not internally consistent."
library(psych)
Dat<-Garcia[,1:5]
Dat$protestcat<-factor(Garcia$prot2,labels=c("No","Yes"))
head(Dat)
Dat$Neganger<-Dat$anger*-1
head(Dat)
library(ggplot2)
library(GGally)
library(psych)
library(psychometric)
library(psychTools)
library(ltm)
# Cronbach's alpha
cronbach_alpha <- cronbach.alpha(Dat[,c(1:2,4,5,7)], CI=TRUE)
print(cronbach_alpha)
## 
## Cronbach's alpha for the 'Dat[, c(1:2, 4, 5, 7)]' data-set
## 
## Items: 5
## Sample units: 129
## alpha: 0.67
## 
## Bootstrap 95% CI based on 1000 samples
##  2.5% 97.5% 
## 0.579 0.736
library("DiagrammeR")
## Warning: package 'DiagrammeR' was built under R version 4.4.1
a1<-"sexism"
a2<-c("liking","neganger", "respappr", "protest")
a<-c(a1,a2)
shape<-rep(c("circle", "square"), c(1,5))
nodes<-c("compassion",a)
ndf<-create_node_df(n=6, type="a", label=nodes,shape=shape)
edf<-create_edge_df(from = rep(1,5), to =2:6,rel="a")

grph<-create_graph(nodes_df = ndf,edges_df=edf,directed=TRUE)
render_graph(grph,layout = "tree")
edf1<-create_edge_df(from=c(2,1,1,1,1),to=c(1,3,4,5,6),rel="a")

grph1<-create_graph(nodes_df=ndf,edges_df=edf1,directed=TRUE)

render_graph(grph1,layout="tree")

The original data with positive anger resulted in a Cronbach’s alpha of -0.537, which indicates no internal consistency and a severe error. We reverse score (invert) the variable “anger” by multiplying by (-1). Thus, positive anger was recoded to “neganger” (inverted anger) to mitigate this problem. Now, negative anger is coded as a positive emotion. The Cronbach’s alpha with neganger is 0.67, which is acceptable. Compassion was selected as a latent variable to show that I understand latent variables. The diagram depicts how an individual could conceptualize a concept and variables.

Here are conceptual problems from Dr Kostas-Polston:

  1. Consider the following statements about a hypothetical personality test. Which one is not possible based on the relationship between reliability and validity?

  1. The test is high in predictive validity and high in reliability

  2. The test is high in predictive validity and low in reliability

  3. #Answer The test is low in predictive validity and high in reliability

  4. The test is low in predictive validity and low in reliability

  1. Which characterization describes the figure below:
Target
Target

  1. Reliable but not valid

  2. Valid but not reliable

  3. Neither valid nor reliable

  4. #Answer Valid and reliable

  1. A research instrument can be reliable, but not valid.

  1. #Answer True

  2. False

  1. Suppose you created a new reading comprehension test and you want to test its validity. You compare the results of your new measure to existing validated measures of reading comprehension and find that your measure compares well with these other measures. You now can say that your new measure has good:

  1. Content validity

  2. #Answer Predictive validity

  3. Reliability

  4. Concurrent validity

  1. Which of the following is a procedure for verifying the internal consistency of the reliability of a measure?

  1. #Answer Split-half technique

  2. Parallel forms of the same test

  3. Test/retest

  4. None of the above

  1. Why might test-retest reliability become less important?

  1. If participants become familiar with a test and all perform better on the second test

  2. If alternate-form reliability cannot be calculated

  3. #Answer If the concept being measured is not expected to be stable over time

  4. If convergent validity is not high

  1. Which of the following refers to inter-rater reliability?

  1. The degree to which two tests measure the same construct

  2. The degree to which a clinician can predict future behavior

  3. #Answer The degree to which two clinicians will agree on interpretation or scoring of a test

  4. The degree to which the items in the test relate to each other

  1. Which of the following is assessed by Cronbach’s alpha?

  1. Concurrent validity

  2. Inter-rater reliability

  3. Test-retest reliability

  4. #Answer Internal consistency

Essay Questions

Write sentences about the following questions.

12 a) Identify and define the two subcomponents of measurement error.

12 b) How do these two subcomponents impact reliability and validity?

  1. What actions can be taken to reduce measurement error?

For each of the following scenarios: 1) identify type/s of reliability and validity proposed in the study design; 2) describe the degree (i.e., high, low) of reliability and/or validity and explain the significance; and 3) critically evaluate any strengths and/or weaknesses

  1. Administering a job skills test to 100 job applicants, hiring the 50 best scorers, and then finding out that even among these 50 new employees those who scored higher on the job skills test tend to perform better on the job.

  2. A personality test that helps to predict the development of schizophrenia consists entirely of items such as “What is your favorite color?” and “Are red apples better than green apples?”