Assignment 2: Working Space
PSYC40005: Advanced Design and Data Analysis
Melbourne School of Psychological Sciences
03/04/2025
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# You can start writing code here and use separate R Chunks as needed
# You may wish to start by clearing out your Environment, and loading your data by adapting the following code:
load("ADDA_Assignment_2_1307187.RData")load packages
library(tidyverse) # Data wrangling## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr 1.1.4 ✔ readr 2.1.5
## ✔ forcats 1.0.0 ✔ stringr 1.5.1
## ✔ ggplot2 3.5.1 ✔ tibble 3.2.1
## ✔ lubridate 1.9.4 ✔ tidyr 1.3.1
## ✔ purrr 1.0.4
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorslibrary(psych) # Used to undertake the EFA and related analyses ##
## Attaching package: 'psych'
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## The following objects are masked from 'package:ggplot2':
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## %+%, alphalibrary(GPArotation) # Called by psych to run certain parts of the EFA ##
## Attaching package: 'GPArotation'
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## The following objects are masked from 'package:psych':
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## equamax, variminlibrary(EFA.dimensions) # Used for the RAWPAR function## **************************************************************************************************
## EFA.dimensions 0.1.8.4
##
## Please contact Brian O'Connor at brian.oconnor@ubc.ca if you have questions or suggestions.
## **************************************************************************************************library(knitr) # Used knitting the R Markdown document
library(dplyr)
library(ggplot2)
library(MVN)
library(lavaan) # CFA/SEM## This is lavaan 0.6-19
## lavaan is FREE software! Please report any bugs.
##
## Attaching package: 'lavaan'
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## The following object is masked from 'package:psych':
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## cor2covlibrary(semPlot) # For use of the `semPaths()` function to create the figure
library(kableExtra)##
## Attaching package: 'kableExtra'
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## The following object is masked from 'package:dplyr':
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## group_rowssummary data/descriptive statistics
summary(data)## q1 q2 q3 q4
## Min. :2.000 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:4.000 1st Qu.:3.000 1st Qu.:2.000 1st Qu.:3.000
## Median :5.000 Median :3.000 Median :3.000 Median :4.000
## Mean :5.049 Mean :3.273 Mean :3.021 Mean :3.569
## 3rd Qu.:6.000 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:4.000
## Max. :8.000 Max. :6.000 Max. :6.000 Max. :8.000
## q5 q6 q7 q8
## Min. :1.000 Min. :1.000 Min. :2.000 Min. :2.000
## 1st Qu.:3.000 1st Qu.:4.000 1st Qu.:4.000 1st Qu.:4.000
## Median :4.000 Median :4.000 Median :5.000 Median :4.000
## Mean :3.935 Mean :4.416 Mean :4.551 Mean :4.501
## 3rd Qu.:5.000 3rd Qu.:5.000 3rd Qu.:5.000 3rd Qu.:5.000
## Max. :7.000 Max. :7.000 Max. :7.000 Max. :8.000
## q9 q10 q11 q12
## Min. :2.000 Min. :1.000 Min. :1.000 Min. :2.000
## 1st Qu.:4.000 1st Qu.:2.000 1st Qu.:3.000 1st Qu.:4.000
## Median :5.000 Median :3.000 Median :4.000 Median :5.000
## Mean :4.779 Mean :3.309 Mean :4.239 Mean :4.527
## 3rd Qu.:5.000 3rd Qu.:4.000 3rd Qu.:5.000 3rd Qu.:5.000
## Max. :8.000 Max. :8.000 Max. :8.000 Max. :7.000
## q13 q14 q15 q16
## Min. :2.000 Min. :2.000 Min. :1.000 Min. :1.000
## 1st Qu.:4.000 1st Qu.:4.000 1st Qu.:3.000 1st Qu.:4.000
## Median :5.000 Median :5.000 Median :3.000 Median :4.000
## Mean :4.852 Mean :4.595 Mean :3.081 Mean :4.242
## 3rd Qu.:6.000 3rd Qu.:5.000 3rd Qu.:4.000 3rd Qu.:5.000
## Max. :8.000 Max. :7.000 Max. :5.000 Max. :7.000
## q17 q18 q19 q20
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:4.000 1st Qu.:3.000 1st Qu.:3.000 1st Qu.:3.000
## Median :5.000 Median :3.000 Median :3.000 Median :3.000
## Mean :4.571 Mean :3.187 Mean :3.436 Mean :3.403
## 3rd Qu.:6.000 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:4.000
## Max. :8.000 Max. :6.000 Max. :6.000 Max. :6.000
## q21 q22 q23 q24 q25
## Min. :2.000 Min. :1.000 Min. :1.000 Min. :1.00 Min. :1.000
## 1st Qu.:4.000 1st Qu.:3.000 1st Qu.:4.000 1st Qu.:3.00 1st Qu.:4.000
## Median :5.000 Median :4.000 Median :4.000 Median :4.00 Median :4.000
## Mean :4.522 Mean :3.984 Mean :4.475 Mean :3.94 Mean :4.361
## 3rd Qu.:5.000 3rd Qu.:5.000 3rd Qu.:5.000 3rd Qu.:5.00 3rd Qu.:5.000
## Max. :8.000 Max. :8.000 Max. :8.000 Max. :7.00 Max. :7.000
## q26 q27 q28 q29 q30
## Min. :1.000 Min. :1.000 Min. :1.00 Min. :1.000 Min. :1.000
## 1st Qu.:3.000 1st Qu.:2.000 1st Qu.:4.00 1st Qu.:4.000 1st Qu.:4.000
## Median :4.000 Median :3.000 Median :4.00 Median :4.000 Median :5.000
## Mean :3.862 Mean :3.086 Mean :4.47 Mean :4.335 Mean :4.694
## 3rd Qu.:5.000 3rd Qu.:4.000 3rd Qu.:5.00 3rd Qu.:5.000 3rd Qu.:6.000
## Max. :7.000 Max. :5.000 Max. :7.00 Max. :7.000 Max. :8.000describe(data)assumption tests
multivariant normality
data_no <- data %>%
select(-q10, -q4, -q17, -q23, -q11, -q29, -q7, -q5, -q9, -q25, -q8, -q16, -q21, -q14)
mvn(data = data, mvnTest = "mardia")$multivariateNormalitymvn(data = data_no, mvnTest = "mardia")$multivariateNormalityunivariant normaility
SkewKurtosis=function(x) {
# Arguments
N=length(!is.na(x))
m1=mean(x, na.rm = TRUE)
dev=(x-m1)
s1=sd(x)
# Skew calculation
skew=sum(dev^3)/(N*s1^3)
seskew=sqrt(6/N)
crskew = skew/seskew
# Kurtosis calculation
top_half = 1/N * sum((x - m1)^4)
bottom_half = (1/N * sum((x - m1)^2))^2
kurtosis = top_half / bottom_half - 3
sekurtosis=sqrt(24/N)
crkurtosis = kurtosis/sekurtosis
# Print
result <- c(skew = skew, seskew = seskew, crskew = crskew, kurtosis= kurtosis, sekurtosis = sekurtosis, crkurtosis = crkurtosis)
return(result)
}
spss_normality <-
mapply(SkewKurtosis, data[, names(data)]) %>%
t() %>%
as.data.frame() %>%
rownames_to_column(var = "variable") %>%
mutate(across(where(is.numeric), \(x) round(x, digits = 3)))
# Univariate kurtosis and skew - similar to Amos 'Assessment of Normality' table.
data %>%
describe(skew = FALSE) %>%
as_tibble() %>%
mutate(variable = rownames(describe(data))) %>%
mutate_if(is.numeric, round, digits=3) %>%
left_join(spss_normality, by = "variable") %>%
select(variable, min, max, skew, crskew, kurtosis, crkurtosis) %>%
print(n = Inf)## # A tibble: 30 × 7
## variable min max skew crskew kurtosis crkurtosis
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 q1 2 8 -0.098 -0.785 -0.177 -0.71
## 2 q2 1 6 -0.013 -0.102 -0.022 -0.087
## 3 q3 1 6 0.162 1.30 0.06 0.24
## 4 q4 1 8 0.313 2.50 0.497 1.99
## 5 q5 1 7 0.021 0.168 0.08 0.32
## 6 q6 1 7 -0.078 -0.627 -0.004 -0.014
## 7 q7 2 7 0.01 0.082 -0.159 -0.636
## 8 q8 2 8 0.152 1.22 -0.203 -0.812
## 9 q9 2 8 -0.08 -0.644 0.445 1.78
## 10 q10 1 8 0.275 2.20 0.084 0.335
## 11 q11 1 8 -0.092 -0.735 -0.372 -1.49
## 12 q12 2 7 -0.197 -1.58 -0.144 -0.578
## 13 q13 2 8 0.131 1.05 0.121 0.485
## 14 q14 2 7 0.017 0.134 0.099 0.395
## 15 q15 1 5 0.08 0.644 -0.121 -0.483
## 16 q16 1 7 -0.022 -0.173 -0.107 -0.427
## 17 q17 1 8 -0.055 -0.439 -0.253 -1.01
## 18 q18 1 6 0.117 0.935 -0.105 -0.42
## 19 q19 1 6 0.011 0.086 -0.309 -1.24
## 20 q20 1 6 -0.063 -0.502 -0.467 -1.87
## 21 q21 2 8 0.124 0.992 0.018 0.074
## 22 q22 1 8 0.164 1.32 0.256 1.02
## 23 q23 1 8 0.154 1.24 -0.034 -0.136
## 24 q24 1 7 0.159 1.28 0.02 0.082
## 25 q25 1 7 0.035 0.281 -0.001 -0.002
## 26 q26 1 7 -0.066 -0.527 -0.229 -0.917
## 27 q27 1 5 0.051 0.41 -0.328 -1.31
## 28 q28 1 7 -0.106 -0.852 -0.178 -0.713
## 29 q29 1 7 -0.185 -1.48 -0.011 -0.043
## 30 q30 1 8 0.127 1.01 -0.241 -0.965univariant outliers
long_data <- data %>%
pivot_longer(cols = q1:q30, names_to = "Item", values_to = "Score")
ggplot(long_data, aes(x = Item, y = Score)) +
geom_boxplot() +
theme_minimal() +
theme() +
labs(title = "Boxplots of All 30 Items",
x = "Item",
y = "Score")
outlier_value <- boxplot.stats(data$q2)$out
outlier_rownumber <- which(data$q2 %in% c(outlier_value))
q2out <- tibble(outlier_rownumber, outlier_value)multivarient outliers
#mahlanobis distance - mulitvariant outliers
nvar <- 30 # Number of variables in the dataset determines the degrees of freedom for the Chi Square test to see whether the Mahalanobis d-squared values are significant
get_mahal_p2 = function(p1){
amos_p2 <- numeric(length(p1))
N <- length(p1)
amos_p1 <- sort(p1)
p1_index <- sort(p1, index.return=TRUE)$ix
for (i in 1:length(amos_p1))
{
k <- i;
p1_value <- amos_p1[i];
start_value <- 1;
while (k >= 1)
{
start_value = start_value - choose(N,N-k+1) * (1-p1_value)^(N-k+1) * (p1_value)^(k-1)
k <- k-1;
}
amos_p2[i] <- start_value;
}
return(amos_p2[order(p1_index)])
}
data %>%
mutate(`Observation number` = seq.int(from = 1, to = nrow(data)),
`Mahalanobis d-squared` = mahalanobis(x = data, center = colMeans(data), cov = cov(data)),
p1 = pchisq(`Mahalanobis d-squared`, df = nvar, lower.tail = FALSE),
p2 = get_mahal_p2(as.numeric(unlist(p1)))) %>%
mutate_if(is.numeric, round, digits=3) %>%
arrange(desc(`Mahalanobis d-squared`)) %>%
select(`Observation number`, `Mahalanobis d-squared`, p1, p2) %>%
slice(1:50) # This outputs rows 1 through to 50, though more can be retained if desiredfactorability
#Factorability, multicolliniarity and singularity
cortest.bartlett(data, n = 385) ## R was not square, finding R from data## $chisq
## [1] 3887.582
##
## $p.value
## [1] 0
##
## $df
## [1] 435#acceptable, p<0.01
#sampling - common variance
KMO_results <- KMO(data)
KMO_results$MSA %>%
round(3)## [1] 0.888#overall 0.88 meritorious Kaiser & rice (1974)
KMO_results$Image %>%
round(3) %>%
kable() %>%
kable_styling("striped", position = "left", full_width = FALSE) %>%
column_spec(1, bold = TRUE, color = "black")| q1 | q2 | q3 | q4 | q5 | q6 | q7 | q8 | q9 | q10 | q11 | q12 | q13 | q14 | q15 | q16 | q17 | q18 | q19 | q20 | q21 | q22 | q23 | q24 | q25 | q26 | q27 | q28 | q29 | q30 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| q1 | 1.000 | -0.027 | -0.070 | -0.029 | -0.061 | 0.010 | 0.046 | -0.009 | 0.049 | 0.044 | -0.149 | -0.040 | -0.172 | -0.076 | -0.032 | 0.031 | -0.234 | -0.034 | 0.054 | 0.164 | -0.094 | 0.069 | -0.139 | -0.106 | 0.002 | 0.009 | -0.066 | 0.026 | 0.045 | -0.189 |
| q2 | -0.027 | 1.000 | -0.095 | -0.026 | 0.003 | -0.041 | 0.042 | 0.083 | -0.041 | -0.013 | -0.013 | 0.078 | -0.022 | 0.052 | -0.113 | 0.061 | 0.036 | -0.151 | -0.011 | -0.163 | 0.105 | -0.025 | 0.006 | -0.032 | -0.010 | -0.077 | -0.185 | -0.048 | -0.108 | -0.005 |
| q3 | -0.070 | -0.095 | 1.000 | -0.046 | -0.005 | -0.004 | -0.048 | 0.041 | -0.014 | -0.064 | -0.093 | 0.044 | 0.008 | 0.004 | -0.199 | -0.045 | 0.011 | -0.209 | -0.058 | -0.188 | 0.055 | 0.010 | -0.046 | 0.009 | 0.070 | -0.049 | 0.001 | 0.029 | 0.072 | 0.041 |
| q4 | -0.029 | -0.026 | -0.046 | 1.000 | -0.014 | 0.136 | 0.087 | 0.086 | -0.064 | -0.079 | -0.030 | 0.022 | 0.072 | 0.014 | -0.061 | -0.019 | -0.035 | -0.118 | -0.069 | -0.033 | 0.027 | -0.007 | 0.036 | -0.092 | 0.014 | -0.018 | 0.026 | 0.077 | -0.137 | -0.085 |
| q5 | -0.061 | 0.003 | -0.005 | -0.014 | 1.000 | -0.067 | 0.017 | 0.045 | -0.009 | -0.063 | 0.022 | -0.027 | -0.008 | 0.066 | -0.077 | -0.070 | 0.055 | -0.035 | -0.092 | -0.043 | -0.005 | 0.045 | 0.005 | -0.154 | -0.092 | -0.060 | -0.061 | 0.006 | -0.004 | 0.012 |
| q6 | 0.010 | -0.041 | -0.004 | 0.136 | -0.067 | 1.000 | -0.122 | -0.093 | 0.038 | 0.003 | 0.023 | -0.262 | 0.093 | -0.034 | -0.017 | -0.085 | 0.057 | -0.071 | -0.070 | 0.123 | -0.132 | -0.080 | 0.061 | -0.027 | 0.063 | 0.055 | 0.162 | -0.061 | -0.126 | 0.036 |
| q7 | 0.046 | 0.042 | -0.048 | 0.087 | 0.017 | -0.122 | 1.000 | 0.014 | -0.094 | -0.061 | -0.026 | -0.095 | 0.078 | -0.112 | -0.020 | 0.006 | -0.040 | 0.037 | 0.059 | -0.051 | 0.005 | -0.157 | -0.104 | 0.009 | -0.066 | 0.083 | -0.043 | -0.138 | -0.105 | 0.010 |
| q8 | -0.009 | 0.083 | 0.041 | 0.086 | 0.045 | -0.093 | 0.014 | 1.000 | 0.018 | -0.006 | -0.011 | -0.001 | 0.037 | 0.198 | -0.041 | -0.012 | 0.069 | -0.080 | 0.025 | -0.105 | 0.172 | -0.069 | 0.028 | -0.073 | 0.043 | -0.012 | -0.061 | 0.048 | -0.038 | -0.090 |
| q9 | 0.049 | -0.041 | -0.014 | -0.064 | -0.009 | 0.038 | -0.094 | 0.018 | 1.000 | 0.033 | 0.003 | -0.028 | -0.100 | -0.156 | 0.013 | 0.103 | 0.025 | 0.007 | 0.037 | 0.057 | -0.240 | 0.087 | -0.035 | 0.075 | -0.103 | -0.062 | -0.036 | 0.047 | -0.006 | 0.008 |
| q10 | 0.044 | -0.013 | -0.064 | -0.079 | -0.063 | 0.003 | -0.061 | -0.006 | 0.033 | 1.000 | -0.015 | 0.092 | 0.054 | -0.023 | -0.118 | -0.008 | 0.068 | -0.074 | -0.057 | -0.061 | 0.022 | 0.056 | 0.009 | -0.239 | 0.043 | -0.051 | -0.115 | 0.050 | 0.029 | 0.000 |
| q11 | -0.149 | -0.013 | -0.093 | -0.030 | 0.022 | 0.023 | -0.026 | -0.011 | 0.003 | -0.015 | 1.000 | -0.031 | -0.060 | 0.015 | -0.111 | 0.051 | -0.065 | 0.026 | 0.078 | -0.034 | -0.061 | -0.008 | -0.073 | 0.030 | 0.083 | -0.071 | 0.076 | 0.006 | -0.043 | -0.163 |
| q12 | -0.040 | 0.078 | 0.044 | 0.022 | -0.027 | -0.262 | -0.095 | -0.001 | -0.028 | 0.092 | -0.031 | 1.000 | -0.021 | -0.028 | -0.038 | 0.003 | 0.029 | 0.007 | 0.096 | -0.037 | -0.094 | -0.194 | 0.042 | -0.068 | -0.033 | 0.034 | -0.026 | -0.272 | -0.073 | -0.019 |
| q13 | -0.172 | -0.022 | 0.008 | 0.072 | -0.008 | 0.093 | 0.078 | 0.037 | -0.100 | 0.054 | -0.060 | -0.021 | 1.000 | 0.025 | 0.005 | -0.029 | -0.083 | -0.019 | -0.001 | 0.030 | 0.002 | 0.020 | -0.075 | -0.051 | 0.013 | -0.023 | 0.031 | -0.045 | -0.117 | -0.292 |
| q14 | -0.076 | 0.052 | 0.004 | 0.014 | 0.066 | -0.034 | -0.112 | 0.198 | -0.156 | -0.023 | 0.015 | -0.028 | 0.025 | 1.000 | 0.015 | 0.141 | 0.087 | -0.045 | -0.018 | 0.020 | -0.212 | 0.033 | -0.072 | -0.006 | -0.242 | 0.015 | -0.035 | -0.004 | -0.011 | -0.073 |
| q15 | -0.032 | -0.113 | -0.199 | -0.061 | -0.077 | -0.017 | -0.020 | -0.041 | 0.013 | -0.118 | -0.111 | -0.038 | 0.005 | 0.015 | 1.000 | -0.049 | 0.019 | -0.143 | -0.087 | -0.138 | 0.028 | -0.088 | -0.035 | 0.079 | -0.085 | 0.071 | -0.188 | 0.035 | -0.045 | 0.074 |
| q16 | 0.031 | 0.061 | -0.045 | -0.019 | -0.070 | -0.085 | 0.006 | -0.012 | 0.103 | -0.008 | 0.051 | 0.003 | -0.029 | 0.141 | -0.049 | 1.000 | 0.060 | -0.029 | 0.045 | 0.034 | 0.054 | -0.118 | 0.022 | -0.055 | 0.124 | -0.116 | -0.017 | -0.082 | 0.072 | -0.008 |
| q17 | -0.234 | 0.036 | 0.011 | -0.035 | 0.055 | 0.057 | -0.040 | 0.069 | 0.025 | 0.068 | -0.065 | 0.029 | -0.083 | 0.087 | 0.019 | 0.060 | 1.000 | -0.074 | -0.075 | 0.033 | 0.036 | 0.018 | -0.071 | -0.033 | -0.065 | 0.009 | -0.050 | 0.004 | 0.014 | -0.162 |
| q18 | -0.034 | -0.151 | -0.209 | -0.118 | -0.035 | -0.071 | 0.037 | -0.080 | 0.007 | -0.074 | 0.026 | 0.007 | -0.019 | -0.045 | -0.143 | -0.029 | -0.074 | 1.000 | -0.030 | -0.095 | 0.020 | 0.065 | 0.022 | 0.014 | 0.075 | -0.027 | -0.147 | -0.064 | 0.036 | 0.082 |
| q19 | 0.054 | -0.011 | -0.058 | -0.069 | -0.092 | -0.070 | 0.059 | 0.025 | 0.037 | -0.057 | 0.078 | 0.096 | -0.001 | -0.018 | -0.087 | 0.045 | -0.075 | -0.030 | 1.000 | -0.023 | -0.033 | -0.079 | -0.089 | -0.246 | -0.055 | -0.079 | -0.101 | 0.115 | -0.006 | -0.077 |
| q20 | 0.164 | -0.163 | -0.188 | -0.033 | -0.043 | 0.123 | -0.051 | -0.105 | 0.057 | -0.061 | -0.034 | -0.037 | 0.030 | 0.020 | -0.138 | 0.034 | 0.033 | -0.095 | -0.023 | 1.000 | -0.106 | 0.099 | -0.004 | 0.015 | 0.005 | -0.028 | -0.084 | 0.025 | -0.062 | -0.054 |
| q21 | -0.094 | 0.105 | 0.055 | 0.027 | -0.005 | -0.132 | 0.005 | 0.172 | -0.240 | 0.022 | -0.061 | -0.094 | 0.002 | -0.212 | 0.028 | 0.054 | 0.036 | 0.020 | -0.033 | -0.106 | 1.000 | -0.030 | 0.098 | 0.027 | -0.058 | 0.015 | -0.143 | -0.044 | -0.079 | 0.024 |
| q22 | 0.069 | -0.025 | 0.010 | -0.007 | 0.045 | -0.080 | -0.157 | -0.069 | 0.087 | 0.056 | -0.008 | -0.194 | 0.020 | 0.033 | -0.088 | -0.118 | 0.018 | 0.065 | -0.079 | 0.099 | -0.030 | 1.000 | -0.033 | -0.021 | 0.047 | -0.009 | 0.016 | -0.096 | -0.123 | 0.042 |
| q23 | -0.139 | 0.006 | -0.046 | 0.036 | 0.005 | 0.061 | -0.104 | 0.028 | -0.035 | 0.009 | -0.073 | 0.042 | -0.075 | -0.072 | -0.035 | 0.022 | -0.071 | 0.022 | -0.089 | -0.004 | 0.098 | -0.033 | 1.000 | -0.012 | 0.077 | 0.029 | -0.006 | -0.054 | -0.057 | -0.194 |
| q24 | -0.106 | -0.032 | 0.009 | -0.092 | -0.154 | -0.027 | 0.009 | -0.073 | 0.075 | -0.239 | 0.030 | -0.068 | -0.051 | -0.006 | 0.079 | -0.055 | -0.033 | 0.014 | -0.246 | 0.015 | 0.027 | -0.021 | -0.012 | 1.000 | -0.020 | -0.361 | 0.007 | -0.086 | -0.050 | 0.083 |
| q25 | 0.002 | -0.010 | 0.070 | 0.014 | -0.092 | 0.063 | -0.066 | 0.043 | -0.103 | 0.043 | 0.083 | -0.033 | 0.013 | -0.242 | -0.085 | 0.124 | -0.065 | 0.075 | -0.055 | 0.005 | -0.058 | 0.047 | 0.077 | -0.020 | 1.000 | -0.032 | 0.205 | -0.077 | -0.010 | 0.042 |
| q26 | 0.009 | -0.077 | -0.049 | -0.018 | -0.060 | 0.055 | 0.083 | -0.012 | -0.062 | -0.051 | -0.071 | 0.034 | -0.023 | 0.015 | 0.071 | -0.116 | 0.009 | -0.027 | -0.079 | -0.028 | 0.015 | -0.009 | 0.029 | -0.361 | -0.032 | 1.000 | -0.013 | -0.069 | 0.057 | 0.103 |
| q27 | -0.066 | -0.185 | 0.001 | 0.026 | -0.061 | 0.162 | -0.043 | -0.061 | -0.036 | -0.115 | 0.076 | -0.026 | 0.031 | -0.035 | -0.188 | -0.017 | -0.050 | -0.147 | -0.101 | -0.084 | -0.143 | 0.016 | -0.006 | 0.007 | 0.205 | -0.013 | 1.000 | -0.013 | -0.023 | -0.034 |
| q28 | 0.026 | -0.048 | 0.029 | 0.077 | 0.006 | -0.061 | -0.138 | 0.048 | 0.047 | 0.050 | 0.006 | -0.272 | -0.045 | -0.004 | 0.035 | -0.082 | 0.004 | -0.064 | 0.115 | 0.025 | -0.044 | -0.096 | -0.054 | -0.086 | -0.077 | -0.069 | -0.013 | 1.000 | -0.186 | -0.006 |
| q29 | 0.045 | -0.108 | 0.072 | -0.137 | -0.004 | -0.126 | -0.105 | -0.038 | -0.006 | 0.029 | -0.043 | -0.073 | -0.117 | -0.011 | -0.045 | 0.072 | 0.014 | 0.036 | -0.006 | -0.062 | -0.079 | -0.123 | -0.057 | -0.050 | -0.010 | 0.057 | -0.023 | -0.186 | 1.000 | 0.069 |
| q30 | -0.189 | -0.005 | 0.041 | -0.085 | 0.012 | 0.036 | 0.010 | -0.090 | 0.008 | 0.000 | -0.163 | -0.019 | -0.292 | -0.073 | 0.074 | -0.008 | -0.162 | 0.082 | -0.077 | -0.054 | 0.024 | 0.042 | -0.194 | 0.083 | 0.042 | 0.103 | -0.034 | -0.006 | 0.069 | 1.000 |
#Low anti-image correlations less than absolute size of 0.3
#high MSAi
KMO_results$MSAi %>%
round(3) %>%
kable(col.names = "MSAi") %>%
kable_styling("striped", position = "left", full_width = FALSE) %>%
column_spec(1, bold = TRUE, color = "black")| MSAi | |
|---|---|
| q1 | 0.825 |
| q2 | 0.932 |
| q3 | 0.939 |
| q4 | 0.932 |
| q5 | 0.928 |
| q6 | 0.865 |
| q7 | 0.891 |
| q8 | 0.823 |
| q9 | 0.844 |
| q10 | 0.945 |
| q11 | 0.851 |
| q12 | 0.887 |
| q13 | 0.820 |
| q14 | 0.857 |
| q15 | 0.918 |
| q16 | 0.862 |
| q17 | 0.860 |
| q18 | 0.936 |
| q19 | 0.916 |
| q20 | 0.916 |
| q21 | 0.849 |
| q22 | 0.859 |
| q23 | 0.853 |
| q24 | 0.838 |
| q25 | 0.864 |
| q26 | 0.883 |
| q27 | 0.908 |
| q28 | 0.869 |
| q29 | 0.820 |
| q30 | 0.805 |
preferred solutions
parallel test
RAWPAR_output <-
RAWPAR(data = data_no, # Specify the name of your raw data
factormodel = 'PCA', # Leave the option as 'PCA' here
Ndatasets = 100, # Number of sets of random data
percentile = 95, # Percentile of the random data
Ncases = 1247, # Specify the sample size
verbose = TRUE) # Required to display the output##
##
## PARALLEL ANALYSIS##
## Randomization method: generated data##
## Type of correlations specified for the real data eigenvalues: Pearson##
## Type of correlations specified for the random data eigenvalues: pearson##
## Extraction Method: Principal Components##
## Variables = 16##
## Cases = 385##
## Ndatasets = 100##
## Percentile = 95##
## Compare the Real Data eigenvalues below to the corresponding## random data Mean and Percentile eigenvalues## Root Real Data Mean Percentile
## 1 4.737 1.362 1.435
## 2 2.361 1.288 1.338
## 3 1.740 1.230 1.278
## 4 1.211 1.179 1.213
## 5 0.727 1.129 1.167
## 6 0.648 1.086 1.115
## 7 0.586 1.048 1.077
## 8 0.568 1.011 1.043
## 9 0.524 0.970 1.004
## 10 0.490 0.933 0.973
## 11 0.463 0.895 0.924
## 12 0.435 0.856 0.885
## 13 0.406 0.819 0.850
## 14 0.377 0.777 0.813
## 15 0.368 0.734 0.766
## 16 0.358 0.682 0.725##
## The number of factors according to the parallel analysis = 3## RAWPAR_output## $eigenvalues
## Root Real Data Mean Percentile
## 1 4.7374371 1.3618805 1.4350858
## 2 2.3605052 1.2878706 1.3375657
## 3 1.7402950 1.2298930 1.2777305
## 4 1.2113429 1.1786306 1.2133784
## 5 0.7271847 1.1289619 1.1670642
## 6 0.6479845 1.0861187 1.1154472
## 7 0.5861679 1.0483630 1.0772129
## 8 0.5681592 1.0108843 1.0429748
## 9 0.5241456 0.9701263 1.0041104
## 10 0.4901179 0.9326786 0.9725842
## 11 0.4625913 0.8954996 0.9236346
## 12 0.4350556 0.8560368 0.8854171
## 13 0.4060664 0.8194630 0.8501011
## 14 0.3771119 0.7771653 0.8133320
## 15 0.3681223 0.7342353 0.7660262
## 16 0.3577127 0.6821924 0.7252751
##
## $NfactorsPA
## [1] 3#
#plotting the parallel test
plot <- RAWPAR_output$eigenvalues %>%
data.frame() %>%
rename("Component.Number" = "Root",
"Eigenvalue.Data" = "Real.Data",
"Random.Mean" = "Mean",
"Random.95" = "Percentile")
# Pivot longer the data so that it can be plotted in ggplot:
plot_long <- plot %>%
pivot_longer(cols = c(Eigenvalue.Data, Random.Mean, Random.95),
names_to = "Group",
values_to = "Value")
# Plot the data:
plot_long %>%
ggplot(mapping = aes(x = Component.Number, y = Value, group = Group, colour = Group) ) +
geom_line() +
geom_point() +
theme_bw() +
scale_x_continuous(breaks = seq(1, 24, 1)) +
scale_y_continuous(breaks = seq(1, 7, 1)) +
labs(
x = "Component Number",
y = "Eigenvalue Size"
)
MAP(data_no)##
##
## MINIMUM AVERAGE PARTIAL (MAP) TEST##
## Number of cases = 385##
## Number of variables = 16##
## Specified kind of correlations for this analysis: Pearson##
##
## Total Variance Explained (Initial Eigenvalues):## Eigenvalues Proportion of Variance Cumulative Prop. Variance
## Factor 1 4.74 0.30 0.30
## Factor 2 2.36 0.15 0.44
## Factor 3 1.74 0.11 0.55
## Factor 4 1.21 0.08 0.63
## Factor 5 0.73 0.05 0.67
## Factor 6 0.65 0.04 0.71
## Factor 7 0.59 0.04 0.75
## Factor 8 0.57 0.04 0.79
## Factor 9 0.52 0.03 0.82
## Factor 10 0.49 0.03 0.85
## Factor 11 0.46 0.03 0.88
## Factor 12 0.44 0.03 0.91
## Factor 13 0.41 0.03 0.93
## Factor 14 0.38 0.02 0.95
## Factor 15 0.37 0.02 0.98
## Factor 16 0.36 0.02 1.00##
## Velicer's Average Squared Correlations## root Avg.Corr.Sq. Avg.Corr.power4
## 0 0.08173 0.01656
## 1 0.03179 0.00323
## 2 0.02943 0.00291
## 3 0.02448 0.00254
## 4 0.02578 0.00392
## 5 0.03517 0.00690
## 6 0.04745 0.00962
## 7 0.06193 0.01596
## 8 0.07542 0.02147
## 9 0.09527 0.02966
## 10 0.12703 0.04615
## 11 0.15885 0.06604
## 12 0.21269 0.10616
## 13 0.30422 0.18733
## 14 0.46749 0.34400
## 15 1.00000 1.00000##
## The smallest average squared correlation is 0.02448##
## The smallest average 4rth power correlation is 0.00254##
## The number of components according to the original (1976) MAP Test is = 3##
## The number of components according to the revised (2000) MAP Test is = 3factorability after removal
#Factorability, multicolliniarity and singularity
cortest.bartlett(data_no, n = 385) ## R was not square, finding R from data## $chisq
## [1] 2099.966
##
## $p.value
## [1] 0
##
## $df
## [1] 120#acceptable, p<0.01
#sampling - common variance
KMO_results <- KMO(data_no)
KMO_results$MSA %>%
round(3)## [1] 0.854#overall 0.88 meritorious Kaiser & rice (1974)EFA no rotation for variance
ml <-
fa(r = data,
nfactors = 5,
rotate = "none",
fm = "ml")
ml_communalities <-
data.frame(ml$communality)
# Reformat for ease of interpretation:
ml_communalities <-
rename(ml_communalities,'Extraction Communality' = 'ml.communality')
# Put output in a table for visual inspection:
ml_communalities %>%
round(3)ml_loadings <- ml$loadings %>%
fa.sort() %>%
print(cut = 0.3)##
## Loadings:
## ML1 ML2 ML3 ML5 ML4
## q3 0.698
## q18 0.694
## q10 0.682
## q15 0.639 0.354
## q27 0.637
## q2 0.633
## q20 0.606 0.326
## q19 0.598
## q24 0.592 0.346 -0.482
## q26 0.540
## q4 0.536
## q12 -0.463 0.452 0.393
## q5 0.435
## q25 -0.415 -0.375
## q7 -0.352 0.325 0.333
## q30 -0.592 0.390
## q6 -0.373 0.532
## q22 0.482
## q17 -0.459 0.308
## q28 -0.330 0.436 0.379
## q13 -0.424 0.417
## q16
## q1 -0.460 0.474
## q14 -0.390 0.443 -0.413
## q21 -0.390 0.425
## q29 0.351 0.387
## q23 -0.335 0.385
## q11 0.341
## q9 0.314 -0.344
## q8 0.324
##
## ML1 ML2 ML3 ML5 ML4
## SS loadings 5.972 2.714 2.283 1.187 1.066
## Proportion Var 0.199 0.090 0.076 0.040 0.036
## Cumulative Var 0.199 0.290 0.366 0.405 0.441EFA ML oblique rotation no q10
data_no_q10 <- data %>%
select(-q10)
mlr <-
fa(r = data_no_q10,
nfactors = 5,
rotate = "oblimin",
fm = "ml")
# Extract communalities:
mlr_communalities <-
data.frame(mlr$communality)
# Reformat for ease of interpretation:
mlr_communalities <-
rename(mlr_communalities, 'Extraction Communality' = 'mlr.communality')
# Put output in a table for visual inspection:
mlr_communalities %>%
round(3)mlr_pattern <- mlr$loadings %>%
fa.sort() %>%
print(cut = 0.3)##
## Loadings:
## ML1 ML3 ML2 ML5 ML4
## q15 0.791
## q20 0.704
## q18 0.697
## q3 0.685
## q27 0.666
## q2 0.644
## q4 0.339
## q12 0.737
## q28 0.680
## q22 0.637
## q6 0.621
## q29 0.550
## q7 0.537
## q30 0.755
## q1 0.685
## q13 0.649
## q17 0.578
## q23 0.554
## q11 0.486
## q14 0.713
## q9 0.586
## q21 0.586
## q25 0.529
## q8 -0.471
## q16 -0.449
## q24 0.853
## q26 0.619
## q19 0.427
## q5 0.382
##
## ML1 ML3 ML2 ML5 ML4
## SS loadings 3.362 2.624 2.428 2.005 1.596
## Proportion Var 0.116 0.090 0.084 0.069 0.055
## Cumulative Var 0.116 0.206 0.290 0.359 0.414mlr_factcorr <- mlr$Phi %>% # Factor correlations are stored in Phi
as.matrix() %>%
print(digits = 3)## ML1 ML3 ML2 ML5 ML4
## ML1 1.000 -0.231 0.1237 -0.271 0.4646
## ML3 -0.231 1.000 -0.1947 0.258 -0.0780
## ML2 0.124 -0.195 1.0000 0.115 0.0324
## ML5 -0.271 0.258 0.1149 1.000 -0.2483
## ML4 0.465 -0.078 0.0324 -0.248 1.0000EFA removal of items no rotation
ml <-
fa(r = data_no,
nfactors = 4,
rotate = "none",
fm = "ml")
ml_communalities <-
data.frame(ml$communality)
# Reformat for ease of interpretation:
ml_communalities <-
rename(ml_communalities,'Extraction Communality' = 'ml.communality')
# Put output in a table for visual inspection:
ml_communalities %>%
round(3)ml_loadings <- ml$loadings %>%
fa.sort() %>%
print(cut = 0.3)##
## Loadings:
## ML1 ML2 ML3 ML4
## q3 0.705
## q18 0.704
## q2 0.658
## q27 0.657
## q15 0.656 0.337
## q20 0.623
## q24 0.616 0.442 0.323 -0.337
## q19 0.614
## q26 0.548
## q12 -0.425 0.583 0.368
## q6 -0.346 0.553
## q28 0.521
## q22 0.505
## q13 0.573
## q30 -0.440 0.557
## q1 0.548
##
## ML1 ML2 ML3 ML4
## SS loadings 4.207 1.789 1.253 0.951
## Proportion Var 0.263 0.112 0.078 0.059
## Cumulative Var 0.263 0.375 0.453 0.513EFA removal of itmes rotation
mlr <-
fa(r = data_no,
nfactors = 4,
rotate = "oblimin",
fm = "ml")
# Extract communalities:
mlr_communalities <-
data.frame(mlr$communality)
# Reformat for ease of interpretation:
mlr_communalities <-
rename(mlr_communalities, 'Extraction Communality' = 'mlr.communality')
# Put output in a table for visual inspection:
mlr_communalities %>%
round(2)mlr_pattern <- mlr$loadings %>%
fa.sort() %>%
print(cut = .3)##
## Loadings:
## ML1 ML2 ML3 ML4
## q15 0.817
## q18 0.729
## q3 0.703
## q20 0.689
## q27 0.671
## q2 0.661
## q12 0.830
## q28 0.679
## q6 0.610
## q22 0.561
## q30 0.742
## q13 0.678
## q1 0.664
## q24 0.905
## q26 0.592
## q19 0.394
##
## ML1 ML2 ML3 ML4
## SS loadings 3.151 1.891 1.524 1.361
## Proportion Var 0.197 0.118 0.095 0.085
## Cumulative Var 0.197 0.315 0.410 0.495mlr_factcorr <- mlr$Phi %>% # Factor correlations are stored in Phi
as.matrix() %>%
print(digits = 3)## ML1 ML2 ML3 ML4
## ML1 1.0000 -0.3173 0.0599 0.4808
## ML2 -0.3173 1.0000 -0.1787 -0.0967
## ML3 0.0599 -0.1787 1.0000 0.0152
## ML4 0.4808 -0.0967 0.0152 1.0000CFA first round no .4s ML unstandardised
cfa_model <- "
PositiveImpulsivity =~ q15 + q20 + q18 + q3 + q27 + q2
SensationSeeking =~ q30 + q1 + q13
Forethought =~ q12 + q28 + q22 + q6
NegativeImpulsivity =~ q24 + q26 + q19"
fit_cor <- cfa(model = cfa_model,
data = data,
estimator = "ML",
likelihood = "wishart",
orthogonal = FALSE)
semPaths(object = fit_cor,
whatLabels = "par",
nCharNodes = 0,
exoVar = TRUE,
optimizeLatRes = TRUE,
layout = "circle",
rotation = 1,
edge.color = "black",
color = "pink",
sizeLat = 7,
sizeLat2 = 4,
sizeMan = 4,
sizeMan2 = 2.5,
edge.label.cex = 0.5,
edge.label.position = 0.4
)
CFA first round no .4s ML standardised
semPaths(object = fit_cor,
whatLabels = "std",
nCharNodes = 0,
exoVar = FALSE,
optimizeLatRes = TRUE,
layout = "circle",
rotation = 1,
edge.color = "black",
color = "pink",
sizeLat = 7,
sizeLat2 = 4,
sizeMan = 4,
sizeMan2 = 2.5,
edge.label.cex = 0.5,
edge.label.position = 0.4
)
summary(fit_cor, standardized = TRUE, ci= TRUE, header= FALSE)##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## PositiveImpulsivity =~
## q15 1.000 1.000 1.000
## q20 1.037 0.082 12.663 0.000 0.877 1.198
## q18 1.096 0.078 14.054 0.000 0.943 1.249
## q3 1.164 0.084 13.818 0.000 0.998 1.329
## q27 0.945 0.073 12.858 0.000 0.801 1.089
## q2 1.045 0.080 12.999 0.000 0.887 1.202
## SensationSeeking =~
## q30 1.000 1.000 1.000
## q1 0.674 0.074 9.135 0.000 0.529 0.818
## q13 0.753 0.082 9.154 0.000 0.592 0.914
## Forethought =~
## q12 1.000 1.000 1.000
## q28 0.969 0.087 11.187 0.000 0.799 1.139
## q22 0.751 0.076 9.851 0.000 0.601 0.900
## q6 0.874 0.077 11.320 0.000 0.722 1.025
## NegativeImpulsivity =~
## q24 1.000 1.000 1.000
## q26 0.867 0.082 10.544 0.000 0.706 1.028
## q19 0.762 0.075 10.183 0.000 0.615 0.909
## Std.lv Std.all
##
## 0.657 0.733
## 0.681 0.684
## 0.720 0.760
## 0.764 0.747
## 0.620 0.695
## 0.686 0.702
##
## 1.028 0.754
## 0.692 0.656
## 0.774 0.663
##
## 0.797 0.807
## 0.772 0.657
## 0.598 0.568
## 0.696 0.668
##
## 0.900 0.750
## 0.780 0.684
## 0.686 0.645
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## PositiveImpulsivity ~~
## SensationSekng 0.047 0.043 1.079 0.280 -0.038 0.131
## Forethought -0.176 0.035 -5.021 0.000 -0.244 -0.107
## NegatvImplsvty 0.371 0.049 7.626 0.000 0.275 0.466
## SensationSeeking ~~
## Forethought -0.177 0.056 -3.152 0.002 -0.288 -0.067
## NegatvImplsvty 0.027 0.064 0.420 0.675 -0.098 0.152
## Forethought ~~
## NegatvImplsvty -0.147 0.049 -3.006 0.003 -0.243 -0.051
## Std.lv Std.all
##
## 0.069 0.069
## -0.335 -0.335
## 0.627 0.627
##
## -0.217 -0.217
## 0.029 0.029
##
## -0.205 -0.205
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .q15 0.372 0.032 11.556 0.000 0.309 0.435
## .q20 0.527 0.044 12.115 0.000 0.442 0.613
## .q18 0.379 0.034 11.137 0.000 0.312 0.446
## .q3 0.463 0.041 11.349 0.000 0.383 0.543
## .q27 0.413 0.034 12.010 0.000 0.345 0.480
## .q2 0.484 0.041 11.928 0.000 0.404 0.563
## .q30 0.803 0.116 6.924 0.000 0.576 1.030
## .q1 0.635 0.065 9.785 0.000 0.508 0.763
## .q13 0.762 0.079 9.586 0.000 0.606 0.918
## .q12 0.339 0.048 7.117 0.000 0.246 0.432
## .q28 0.784 0.071 11.038 0.000 0.645 0.923
## .q22 0.751 0.062 12.149 0.000 0.630 0.872
## .q6 0.603 0.056 10.859 0.000 0.494 0.712
## .q24 0.631 0.076 8.292 0.000 0.482 0.780
## .q26 0.692 0.069 10.004 0.000 0.557 0.828
## .q19 0.661 0.061 10.784 0.000 0.541 0.781
## PositvImplsvty 0.431 0.054 7.930 0.000 0.325 0.538
## SensationSekng 1.056 0.157 6.716 0.000 0.748 1.364
## Forethought 0.635 0.078 8.189 0.000 0.483 0.787
## NegatvImplsvty 0.811 0.112 7.259 0.000 0.592 1.029
## Std.lv Std.all
## 0.372 0.463
## 0.527 0.532
## 0.379 0.422
## 0.463 0.442
## 0.413 0.518
## 0.484 0.507
## 0.803 0.432
## 0.635 0.570
## 0.762 0.560
## 0.339 0.348
## 0.784 0.568
## 0.751 0.677
## 0.603 0.554
## 0.631 0.438
## 0.692 0.532
## 0.661 0.584
## 1.000 1.000
## 1.000 1.000
## 1.000 1.000
## 1.000 1.000lavInspect(fit_cor, "rsquare") %>%
round(3)## q15 q20 q18 q3 q27 q2 q30 q1 q13 q12 q28 q22 q6
## 0.537 0.468 0.578 0.558 0.482 0.493 0.568 0.430 0.440 0.652 0.432 0.323 0.446
## q24 q26 q19
## 0.562 0.468 0.416CFA first roun no .4s model identification
show(fit_cor)## lavaan 0.6-19 ended normally after 33 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 38
##
## Number of observations 385
##
## Model Test User Model:
##
## Test statistic 185.830
## Degrees of freedom 98
## P-value (Chi-square) 0.000fitmeasures(fit_cor, c("chisq", "df", "pvalue", "cfi", "srmr", "rmsea"))## chisq df pvalue cfi srmr rmsea
## 185.830 98.000 0.000 0.956 0.055 0.048CFA second round no .4s
cfa_model_respe <- "
PositiveImpulsivity =~ q15 + q20 + q18 + q3 + q27 + q2 + q19
SensationSeeking =~ q30 + q1 + q13
Forethought =~ q12 + q28 + q22 + q6 + q19 + q24
NegativeImpulsivity =~ q24 + q26 + q19"
fit_cor_respe <- cfa(model = cfa_model_respe,
data = data,
estimator = "ML",
likelihood = "wishart",
orthogonal = FALSE)
semPaths(object = fit_cor_respe,
whatLabels = "std",
nCharNodes = 0,
exoVar = FALSE,
optimizeLatRes = TRUE,
layout = "circle",
rotation = 1,
edge.color = "black",
color = "pink",
sizeLat = 7,
sizeLat2 = 4,
sizeMan = 4,
sizeMan2 = 2.5,
edge.label.cex = 0.5,
edge.label.position = 0.4
)
summary(fit_cor_respe, standardized = TRUE, ci= TRUE, header= FALSE)##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## PositiveImpulsivity =~
## q15 1.000 1.000 1.000
## q20 1.032 0.081 12.705 0.000 0.873 1.191
## q18 1.090 0.077 14.103 0.000 0.938 1.241
## q3 1.158 0.083 13.875 0.000 0.994 1.321
## q27 0.943 0.073 12.952 0.000 0.801 1.086
## q2 1.037 0.080 13.022 0.000 0.881 1.193
## q19 0.418 0.102 4.091 0.000 0.218 0.619
## SensationSeeking =~
## q30 1.000 1.000 1.000
## q1 0.673 0.074 9.129 0.000 0.528 0.817
## q13 0.752 0.082 9.148 0.000 0.591 0.913
## Forethought =~
## q12 1.000 1.000 1.000
## q28 0.973 0.086 11.362 0.000 0.805 1.140
## q22 0.744 0.075 9.860 0.000 0.596 0.891
## q6 0.866 0.076 11.395 0.000 0.717 1.016
## q19 -0.108 0.074 -1.456 0.145 -0.254 0.037
## q24 0.259 0.103 2.520 0.012 0.058 0.461
## NegativeImpulsivity =~
## q24 1.000 1.000 1.000
## q26 0.740 0.080 9.213 0.000 0.583 0.898
## q19 0.432 0.074 5.874 0.000 0.288 0.576
## Std.lv Std.all
##
## 0.659 0.736
## 0.680 0.683
## 0.718 0.759
## 0.763 0.746
## 0.622 0.697
## 0.684 0.700
## 0.276 0.259
##
## 1.028 0.754
## 0.692 0.655
## 0.774 0.663
##
## 0.799 0.810
## 0.777 0.661
## 0.594 0.564
## 0.692 0.664
## -0.086 -0.081
## 0.207 0.173
##
## 1.046 0.871
## 0.774 0.679
## 0.452 0.425
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## PositiveImpulsivity ~~
## SensationSekng 0.049 0.043 1.137 0.255 -0.036 0.134
## Forethought -0.178 0.035 -5.053 0.000 -0.247 -0.109
## NegatvImplsvty 0.381 0.054 7.019 0.000 0.275 0.487
## SensationSeeking ~~
## Forethought -0.176 0.056 -3.119 0.002 -0.286 -0.065
## NegatvImplsvty 0.043 0.073 0.584 0.559 -0.101 0.186
## Forethought ~~
## NegatvImplsvty -0.206 0.076 -2.705 0.007 -0.356 -0.057
## Std.lv Std.all
##
## 0.073 0.073
## -0.337 -0.337
## 0.552 0.552
##
## -0.214 -0.214
## 0.040 0.040
##
## -0.247 -0.247
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .q15 0.369 0.032 11.529 0.000 0.306 0.431
## .q20 0.528 0.044 12.133 0.000 0.443 0.614
## .q18 0.381 0.034 11.180 0.000 0.314 0.448
## .q3 0.464 0.041 11.377 0.000 0.384 0.544
## .q27 0.410 0.034 12.002 0.000 0.343 0.478
## .q2 0.486 0.041 11.962 0.000 0.407 0.566
## .q19 0.671 0.055 12.251 0.000 0.564 0.779
## .q30 0.801 0.116 6.902 0.000 0.574 1.029
## .q1 0.636 0.065 9.792 0.000 0.509 0.763
## .q13 0.762 0.079 9.589 0.000 0.606 0.918
## .q12 0.336 0.047 7.171 0.000 0.244 0.427
## .q28 0.776 0.070 11.035 0.000 0.638 0.914
## .q22 0.756 0.062 12.223 0.000 0.635 0.878
## .q6 0.608 0.055 10.993 0.000 0.500 0.717
## .q24 0.411 0.101 4.081 0.000 0.214 0.609
## .q26 0.702 0.072 9.691 0.000 0.560 0.844
## PositvImplsvty 0.435 0.054 7.980 0.000 0.328 0.542
## SensationSekng 1.058 0.157 6.719 0.000 0.749 1.366
## Forethought 0.638 0.077 8.269 0.000 0.487 0.789
## NegatvImplsvty 1.095 0.157 6.985 0.000 0.787 1.402
## Std.lv Std.all
## 0.369 0.459
## 0.528 0.533
## 0.381 0.425
## 0.464 0.443
## 0.410 0.515
## 0.486 0.510
## 0.671 0.593
## 0.801 0.431
## 0.636 0.570
## 0.762 0.560
## 0.336 0.345
## 0.776 0.563
## 0.756 0.682
## 0.608 0.559
## 0.411 0.285
## 0.702 0.539
## 1.000 1.000
## 1.000 1.000
## 1.000 1.000
## 1.000 1.000lavInspect(fit_cor, "rsquare") %>%
round(3)## q15 q20 q18 q3 q27 q2 q30 q1 q13 q12 q28 q22 q6
## 0.537 0.468 0.578 0.558 0.482 0.493 0.568 0.430 0.440 0.652 0.432 0.323 0.446
## q24 q26 q19
## 0.562 0.468 0.416show(fit_cor_respe)## lavaan 0.6-19 ended normally after 36 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 41
##
## Number of observations 385
##
## Model Test User Model:
##
## Test statistic 146.963
## Degrees of freedom 95
## P-value (Chi-square) 0.001fitmeasures(fit_cor_respe, c("chisq", "df", "pvalue", "cfi", "srmr", "rmsea"))## chisq df pvalue cfi srmr rmsea
## 146.963 95.000 0.001 0.974 0.046 0.038CFA local test stats
resid(fit_cor, type = "normalized")## $type
## [1] "normalized"
##
## $cov
## q15 q20 q18 q3 q27 q2 q30 q1 q13 q12
## q15 0.000
## q20 0.194 0.000
## q18 -0.068 -0.400 0.000
## q3 0.326 0.265 0.288 0.000
## q27 0.392 -0.077 0.074 -0.945 0.000
## q2 -0.177 0.205 -0.060 -0.430 0.399 0.000
## q30 -1.186 -0.754 -1.247 -0.233 0.805 -0.479 0.000
## q1 1.152 -1.125 1.485 2.089 2.619 1.294 -0.109 0.000
## q13 -0.873 -1.408 -0.606 -0.277 0.302 0.111 0.031 0.115 0.000
## q12 1.090 -0.297 -0.324 -1.405 -0.212 -0.567 0.731 0.825 1.791 0.000
## q28 1.000 -0.006 0.762 -0.700 0.394 1.146 0.333 0.433 2.106 0.362
## q22 2.657 -0.101 0.386 0.141 0.503 1.065 -1.498 -1.733 -0.512 -0.265
## q6 0.923 -1.172 0.390 -0.928 -1.606 -0.106 -2.293 -1.815 -1.592 -0.102
## q24 -1.445 -1.343 -0.545 -0.922 -0.571 -0.267 -1.629 1.891 0.359 1.017
## q26 -1.367 -0.420 0.073 0.063 -0.339 0.503 -2.389 0.450 -0.290 -1.165
## q19 1.649 1.046 1.450 1.630 2.154 1.337 1.113 1.963 0.698 -2.807
## q28 q22 q6 q24 q26 q19
## q15
## q20
## q18
## q3
## q27
## q2
## q30
## q1
## q13
## q12
## q28 0.000
## q22 0.211 0.000
## q6 -0.562 0.371 0.000
## q24 2.375 2.225 1.343 0.000
## q26 0.814 0.593 -0.774 0.846 0.000
## q19 -2.214 0.135 -1.238 -0.150 -1.202 0.000resid(fit_cor_respe, type = "normalized")## $type
## [1] "normalized"
##
## $cov
## q15 q20 q18 q3 q27 q2 q19 q30 q1 q13
## q15 0.000
## q20 0.166 0.000
## q18 -0.090 -0.373 0.000
## q3 0.296 0.283 0.316 0.000
## q27 0.331 -0.093 0.066 -0.962 0.000
## q2 -0.189 0.237 -0.017 -0.395 0.399 0.000
## q19 0.053 -0.436 -0.162 0.043 0.657 -0.161 0.000
## q30 -1.230 -0.791 -1.287 -0.273 0.765 -0.516 0.604 0.000
## q1 1.115 -1.156 1.451 2.055 2.586 1.263 1.524 -0.110 0.000
## q13 -0.911 -1.439 -0.640 -0.312 0.268 0.080 0.251 0.028 0.122 0.000
## q12 1.136 -0.273 -0.301 -1.379 -0.174 -0.550 -0.630 0.704 0.799 1.765
## q28 1.049 0.025 0.794 -0.666 0.437 1.172 -0.409 0.319 0.418 2.092
## q22 2.663 -0.109 0.375 0.133 0.505 1.052 1.682 -1.533 -1.766 -0.545
## q6 0.935 -1.176 0.382 -0.933 -1.599 -0.116 0.569 -2.332 -1.851 -1.628
## q24 -0.814 -0.723 0.135 -0.254 0.030 0.369 0.175 -1.276 2.197 0.671
## q26 -0.632 0.287 0.850 0.824 0.358 1.226 -0.429 -2.496 0.358 -0.384
## q12 q28 q22 q6 q24 q26
## q15
## q20
## q18
## q3
## q27
## q2
## q19
## q30
## q1
## q13
## q12 0.000
## q28 0.279 0.000
## q22 -0.228 0.216 0.000
## q6 -0.075 -0.569 0.458 0.000
## q24 -0.743 0.941 0.979 -0.119 0.000
## q26 -0.736 1.177 0.881 -0.434 -0.003 0.000CFA MI
modindices(fit_cor,
sort = TRUE, # Sorts modification indices in descending order of MI
minimum.value = 5) # Requests modification indices above a certain number (e.g., 10) though the choice of cutoff is fairly arbitraryCFA correlation matrix
lower <- cor(data) %>%
as.matrix() %>%
round(2)
lower[upper.tri(lower)] <- ""
lower <- as.data.frame(lower)
lowerCFA multiple r squared
lavInspect(fit_cor, "rsquare") %>%
round(3)## q15 q20 q18 q3 q27 q2 q30 q1 q13 q12 q28 q22 q6
## 0.537 0.468 0.578 0.558 0.482 0.493 0.568 0.430 0.440 0.652 0.432 0.323 0.446
## q24 q26 q19
## 0.562 0.468 0.416