## global variables
runMplusLCA <- FALSE
## set to lower values to reduce compilation time:
nRep_def = 100 # 100
n.lambda_def = 40 # 40
LCArunsDef = 6 # 10First analyses of weight bias scales
Background Information
This is an R Markdown document, whereby I am using the Quarto framework. Instructions for writing these documents and background information can be found in the book written by Xie, Allaire, and Grolemund (2018). When you execute code within the document, the results appear beneath the code.
This file contains the pre-processing step (clean, transform data), and the analysis step (test hypotheses and exploratory analyses). In larger projects you would split this file into multiple subfiles like data processing and data analyses steps, which follows the classical data-analysis pipeline (see Peng and Matsui 2016; Wickham and Grolemund 2017).
Notes
Global variables to control output:
get packages
### install and load packages
# if packages are not already installed, the function will install and activate them
usePackage <- function(p) {
if (!is.element(p, installed.packages()[,1]))
install.packages(p, dep = TRUE, repos = "http://cran.us.r-project.org")
require(p, character.only = TRUE)
}
usePackage("readxl") # read .xlsx files
usePackage("writexl") # write .xlsx files
usePackage("tidyverse") # data cleaning and summarizing
## psychometric analysis
usePackage("moments") # skewness, kurtosis
usePackage("psych") # psychometric analysis (EFA), reliability measures
usePackage("lavaan") # for CFA, SEM
usePackage("regsem") # for regularizations -> local item dependencies
usePackage("mirt") # for IRT
usePackage("MplusAutomation") # to apply statistical software Mplus (LCA)
## outputs
usePackage("stargazer") # create tables
usePackage("report") # get reports of statistical tests in APA7
rm(usePackage)raw data, functions
### load functions
# print(getwd())
setwd("functions")
for(i in 1:length(dir())){
# print(dir()[i])
source(dir()[i], encoding = "utf-8")
}
### load data files
## change working directory
setwd("../../dataPreperation/outputs/questionnaire")
## load data
dat <- readRDS(file = "ques_combined.rds")
rm(i)compute mean variables
However, multiple scales are not undimensional!
dat$mean_pair <- rowMeans(x = dat[,str_subset(string = colnames(dat), pattern = "^pair")])
dat$mean_PathogenDisgus <- rowMeans(x = dat[,str_subset(string = colnames(dat), pattern = "^PathogenDisgus")])
dat$mean_GermAversion <- rowMeans(x = dat[,str_subset(string = colnames(dat), pattern = "^GermAversion")])
dat$mean_BeliefsAboutObesePersons <- rowMeans(x = dat[,str_subset(string = colnames(dat), pattern = "^BeliefsAboutObesePersons")])
dat$mean_AttitudeTowardsObesePeople <- rowMeans(x = dat[,str_subset(string = colnames(dat), pattern = "^AttitudeTowardsObesePeople")])
dat$mean_PerceivedCausesofObesity <- rowMeans(x = dat[,str_subset(string = colnames(dat), pattern = "^PerceivedCausesofObesity")])Descriptive Statistics
sample
table(dat$sociodemo_gender)
female intersex male
178 3 182 psych::describe(dat[, c("sociodemo_age", "sociodemo_BMI", "weight_avatar_choice2")]) vars n mean sd median trimmed mad min max
sociodemo_age 1 363 35.87 12.95 32.00 34.25 10.38 18.00 77.0
sociodemo_BMI 2 268 27.10 7.09 25.06 26.23 5.07 14.04 61.5
weight_avatar_choice2 3 123 10.33 3.79 9.00 10.03 2.97 2.00 20.0
range skew kurtosis se
sociodemo_age 59.00 1.05 0.31 0.68
sociodemo_BMI 47.45 1.40 2.56 0.43
weight_avatar_choice2 18.00 0.57 -0.25 0.34mean variables
Using the stargazer package you can create nice tables:
# Descriptive stats for all mean_* variables
mean_vars <- str_subset(names(dat), "^mean_")
tmp_desc <- dat %>%
summarise(
N = n(),
across(all_of(mean_vars), list(mean = ~mean(.x, na.rm = TRUE),
sd = ~sd(.x, na.rm = TRUE)),
.names = "{.col}_{.fn}")
) %>%
pivot_longer(
cols = -N,
names_to = c("variable", ".value"),
names_pattern = "(.*)_(mean|sd)"
)
tmp_desc# A tibble: 6 × 4
N variable mean sd
<int> <chr> <dbl> <dbl>
1 363 mean_pair 3.95 0.711
2 363 mean_PathogenDisgus 4.67 1.16
3 363 mean_GermAversion 4.36 1.12
4 363 mean_BeliefsAboutObesePersons 2.52 0.722
5 363 mean_AttitudeTowardsObesePeople 3.38 0.666
6 363 mean_PerceivedCausesofObesity 3.58 0.587# Save descriptive table as HTML
setwd("outputs")
tmp_desc$mean <- round(x = tmp_desc$mean, digits = 2)
tmp_desc$sd <- round(x = tmp_desc$sd, digits = 2)
stargazer(tmp_desc, type = "html", summary = FALSE, out = "summaryTable_meansSDs.html")
<table style="text-align:center"><tr><td colspan="5" style="border-bottom: 1px solid black"></td></tr><tr><td style="text-align:left"></td><td>N</td><td>variable</td><td>mean</td><td>sd</td></tr>
<tr><td colspan="5" style="border-bottom: 1px solid black"></td></tr><tr><td style="text-align:left">1</td><td>363</td><td>mean_pair</td><td>3.95</td><td>0.71</td></tr>
<tr><td style="text-align:left">2</td><td>363</td><td>mean_PathogenDisgus</td><td>4.67</td><td>1.16</td></tr>
<tr><td style="text-align:left">3</td><td>363</td><td>mean_GermAversion</td><td>4.36</td><td>1.12</td></tr>
<tr><td style="text-align:left">4</td><td>363</td><td>mean_BeliefsAboutObesePersons</td><td>2.52</td><td>0.72</td></tr>
<tr><td style="text-align:left">5</td><td>363</td><td>mean_AttitudeTowardsObesePeople</td><td>3.38</td><td>0.67</td></tr>
<tr><td style="text-align:left">6</td><td>363</td><td>mean_PerceivedCausesofObesity</td><td>3.58</td><td>0.59</td></tr>
<tr><td colspan="5" style="border-bottom: 1px solid black"></td></tr></table># Correlation plot of mean variables
psych::cor.plot(
r = cor(dat[, c(mean_vars, "sociodemo_BMI")], use = "pairwise.complete.obs"),
main = "Correlation Plot of Mean Scales"
)
mean_PathogenDisgus between sources
tmp_desc <- dat %>%
group_by(source) %>%
summarise(N = n(),
mean = mean(mean_PathogenDisgus, na.rm = TRUE),
sd = sd(mean_PathogenDisgus, na.rm = TRUE))
tmp_desc# A tibble: 3 × 4
source N mean sd
<chr> <int> <dbl> <dbl>
1 study1 240 4.54 1.15
2 study2_BMI_high 23 4.77 1.40
3 study2_BMI_mixed 100 4.97 1.06# ! Individualism-Communitarianism is not unidimensional, as such not show here
ggstatsplot::ggbetweenstats(data = dat, x = source, y = mean_PathogenDisgus, type = "parametric")
#> output to html
setwd("outputs")
tmp_desc$mean <- round(x = tmp_desc$mean, digits = 2)
tmp_desc$sd <- round(x = tmp_desc$sd, digits = 2)
stargazer(tmp_desc, type = "html", summary = FALSE, out = "summaryTable_between.html")
<table style="text-align:center"><tr><td colspan="5" style="border-bottom: 1px solid black"></td></tr><tr><td style="text-align:left"></td><td>source</td><td>N</td><td>mean</td><td>sd</td></tr>
<tr><td colspan="5" style="border-bottom: 1px solid black"></td></tr><tr><td style="text-align:left">1</td><td>study1</td><td>240</td><td>4.54</td><td>1.15</td></tr>
<tr><td style="text-align:left">2</td><td>study2_BMI_high</td><td>23</td><td>4.77</td><td>1.4</td></tr>
<tr><td style="text-align:left">3</td><td>study2_BMI_mixed</td><td>100</td><td>4.97</td><td>1.06</td></tr>
<tr><td colspan="5" style="border-bottom: 1px solid black"></td></tr></table>Inferential Statistics
Overall EFA
#### Overall EFA
regExOverall <- "^pair|^PathogenDisgus|^GermAversion|^BeliefsAboutObesePersons|^AttitudeTowardsObesePeople|^PerceivedCausesofObesity"
psych::cor.plot(r = cor(dat[, str_detect(string = colnames(dat),
pattern = regExOverall)]
, use = "pairwise.complete.obs"),
upper = FALSE, xlas = 2, main = "Overall")
#> parallel analysis
tmp_parallelAnalysis <- dimensionalityTest(label = "Overall",
regEx = regExOverall, dataset = dat)
Parallel analysis suggests that the number of factors = 9 and the number of components = 7
Overall
Number of components: 7 Remark: factors scores were computed using “tenBerge”, which preserves correlation structure, but not as widely used in applied psych research (often “regression” used).
#> EFA (# of factors=5)
tmp_EFA_overall <- explorativeFactorAnalysis(label = "Overall",
regEx = regExOverall,
dataset = dat, nfac = 8)Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
The estimated weights for the factor scores are probably incorrect. Try a
different factor score estimation method.tmp_EFA_overall[[1]]Factor Analysis using method = minres
Call: fa(r = tmp_dat, nfactors = nfac, rotate = "promax", cor = "cor")
Standardized loadings (pattern matrix) based upon correlation matrix
MR1 MR3 MR8 MR2 MR6 MR5 MR7 MR4
pair01 0.69 -0.12 -0.07 0.02 -0.10 0.01 0.06 -0.05
pair02 0.51 -0.01 -0.09 0.04 -0.02 -0.15 -0.23 -0.03
pair03 0.63 -0.27 -0.01 -0.03 0.08 0.01 -0.05 -0.05
pair04 0.78 -0.10 0.07 -0.11 0.09 0.11 0.01 0.08
pair05 0.85 -0.04 0.04 -0.03 0.02 0.16 0.10 0.03
pair06 0.61 -0.09 0.02 0.00 -0.03 0.05 -0.08 0.05
pair07 0.82 -0.02 0.05 -0.07 -0.06 0.13 0.05 0.07
pair08 0.68 0.00 0.03 0.09 0.03 0.17 -0.13 -0.04
pair09 0.52 0.11 0.01 0.00 0.04 -0.06 -0.08 0.00
pair10 0.40 0.02 -0.02 0.12 -0.29 0.06 -0.03 -0.15
pair11 0.53 -0.04 -0.12 0.06 0.03 0.03 0.10 0.05
pair12 0.54 0.12 0.08 -0.03 -0.11 -0.06 -0.03 0.02
pair13 0.64 0.04 0.03 -0.07 0.01 -0.30 0.19 0.10
pair14 0.69 0.09 0.05 -0.06 0.02 -0.27 0.19 0.06
PathogenDisgust-1 -0.08 0.06 0.04 0.64 -0.13 -0.05 0.00 -0.02
PathogenDisgust-2 0.06 -0.06 0.03 0.66 -0.05 -0.01 0.04 -0.07
PathogenDisgust-3 -0.04 -0.13 -0.01 0.66 0.00 -0.03 0.03 0.03
PathogenDisgust-4 0.04 0.11 0.11 0.40 -0.10 -0.12 0.00 0.08
PathogenDisgust-5 -0.03 0.08 -0.01 0.59 -0.03 0.12 -0.06 0.13
PathogenDisgust-6 0.04 0.00 0.04 0.49 0.12 -0.04 -0.08 0.05
PathogenDisgust-7 -0.03 -0.09 -0.11 0.75 -0.04 0.10 -0.04 -0.07
GermAversion-1 0.03 -0.11 -0.09 0.14 0.01 0.12 0.16 0.59
GermAversion-2 0.00 -0.21 0.02 0.11 0.13 0.11 0.06 0.64
GermAversion-3 0.06 0.02 0.11 0.16 -0.10 0.04 -0.10 0.37
GermAversion-4 -0.09 -0.22 -0.03 0.26 -0.22 0.17 0.00 0.20
GermAversion-5r 0.04 0.04 -0.04 0.02 -0.06 -0.18 0.12 0.48
GermAversion-6 0.05 0.07 0.07 0.22 -0.04 -0.03 -0.15 0.33
GermAversion-7r -0.03 0.03 -0.13 0.31 0.14 -0.23 -0.16 0.33
GermAversion-8r 0.02 0.12 -0.01 -0.10 0.11 -0.06 -0.02 0.63
BeliefsAboutObesePersons-1r -0.07 0.12 -0.15 0.07 0.39 0.16 -0.15 -0.03
BeliefsAboutObesePersons-2 0.01 0.00 0.04 -0.02 -0.06 0.10 0.55 0.01
BeliefsAboutObesePersons-3r -0.09 0.07 0.00 -0.02 0.65 0.10 0.01 0.06
BeliefsAboutObesePersons-4r 0.10 0.22 0.13 0.00 0.66 -0.07 -0.08 -0.04
BeliefsAboutObesePersons-5r -0.13 0.06 0.08 -0.06 0.63 0.15 -0.07 0.18
BeliefsAboutObesePersons-6r 0.00 -0.06 0.11 -0.10 0.76 0.06 0.04 0.07
BeliefsAboutObesePersons-7 0.04 -0.09 -0.01 -0.07 0.00 0.13 0.53 0.06
BeliefsAboutObesePersons-8r 0.01 -0.17 -0.19 0.02 0.44 0.12 0.04 -0.11
AttitudeTowardsObesePeople-1 0.00 0.20 0.07 -0.07 0.03 0.51 0.13 0.06
AttitudeTowardsObesePeople-10r -0.07 0.68 -0.16 0.04 -0.15 0.08 -0.11 -0.04
AttitudeTowardsObesePeople-11r 0.08 0.31 0.00 0.11 0.14 -0.07 -0.26 -0.09
AttitudeTowardsObesePeople-12r -0.06 0.53 0.07 -0.03 0.15 -0.13 -0.19 -0.01
AttitudeTowardsObesePeople-13 0.09 -0.23 -0.01 0.08 0.11 0.52 0.07 0.00
AttitudeTowardsObesePeople-14r -0.08 0.54 0.03 -0.01 -0.14 -0.03 0.07 -0.10
AttitudeTowardsObesePeople-15r 0.02 0.44 0.00 -0.06 0.13 -0.02 -0.22 -0.02
AttitudeTowardsObesePeople-16r 0.10 0.47 -0.02 0.03 -0.05 0.11 0.30 0.03
AttitudeTowardsObesePeople-17 -0.12 -0.13 -0.04 0.04 0.25 0.39 0.24 0.04
AttitudeTowardsObesePeople-18 -0.09 0.08 0.13 -0.09 0.18 0.30 0.32 0.15
AttitudeTowardsObesePeople-19r -0.03 0.58 -0.04 -0.03 -0.08 0.14 -0.06 0.01
AttitudeTowardsObesePeople-20r -0.06 0.47 0.04 -0.15 0.11 0.04 0.02 0.19
AttitudeTowardsObesePeople-2r -0.03 0.47 -0.13 0.13 0.06 0.45 -0.19 -0.09
AttitudeTowardsObesePeople-3r 0.08 0.12 0.01 -0.06 0.01 0.29 -0.03 -0.10
AttitudeTowardsObesePeople-4r -0.06 0.63 0.04 0.05 -0.07 -0.15 0.26 0.06
AttitudeTowardsObesePeople-5r -0.01 0.54 0.05 0.03 0.05 0.09 0.24 0.03
AttitudeTowardsObesePeople-6r 0.03 0.49 0.08 -0.04 0.30 0.08 0.00 0.05
AttitudeTowardsObesePeople-7 -0.07 0.25 -0.04 0.02 -0.22 0.38 0.21 0.08
AttitudeTowardsObesePeople-8 0.03 -0.11 0.03 -0.01 0.12 0.61 0.05 -0.07
AttitudeTowardsObesePeople-9 -0.04 0.19 0.01 0.01 0.05 0.50 0.17 -0.03
PerceivedCausesofObesity-1 -0.03 -0.01 0.53 -0.05 -0.16 0.18 -0.36 0.05
PerceivedCausesofObesity-10 0.08 0.13 0.54 0.16 0.08 0.06 0.15 -0.10
PerceivedCausesofObesity-11 0.16 0.06 0.66 0.04 0.11 0.10 0.22 0.04
PerceivedCausesofObesity-12 -0.09 0.02 0.35 0.11 0.17 -0.12 0.02 -0.04
PerceivedCausesofObesity-13 -0.02 -0.02 0.52 -0.08 0.03 -0.11 0.11 -0.07
PerceivedCausesofObesity-14 0.03 0.03 0.56 -0.08 -0.17 -0.02 -0.09 0.05
PerceivedCausesofObesity-2 0.02 -0.02 0.53 -0.01 -0.20 0.03 -0.29 -0.07
PerceivedCausesofObesity-3 -0.08 -0.11 0.45 -0.06 -0.07 0.05 -0.19 0.01
PerceivedCausesofObesity-4 0.00 0.01 0.46 0.25 0.06 0.10 0.35 -0.21
PerceivedCausesofObesity-5 -0.02 0.01 0.63 -0.08 -0.06 0.06 0.01 0.11
PerceivedCausesofObesity-6 0.07 0.01 0.69 -0.04 0.14 -0.09 -0.07 0.07
PerceivedCausesofObesity-7 -0.02 0.00 0.43 0.13 0.07 0.06 0.03 -0.08
PerceivedCausesofObesity-8 -0.07 -0.20 0.26 0.06 -0.02 0.00 0.10 -0.06
PerceivedCausesofObesity-9 0.04 -0.10 0.43 -0.09 -0.09 0.05 -0.31 0.12
h2 u2 com
pair01 0.54 0.46 1.1
pair02 0.52 0.48 1.7
pair03 0.49 0.51 1.4
pair04 0.55 0.45 1.2
pair05 0.60 0.40 1.1
pair06 0.44 0.56 1.1
pair07 0.65 0.35 1.1
pair08 0.46 0.54 1.3
pair09 0.33 0.67 1.2
pair10 0.33 0.67 2.5
pair11 0.25 0.75 1.3
pair12 0.40 0.60 1.3
pair13 0.57 0.43 1.7
pair14 0.60 0.40 1.6
PathogenDisgust-1 0.44 0.56 1.2
PathogenDisgust-2 0.46 0.54 1.1
PathogenDisgust-3 0.50 0.50 1.1
PathogenDisgust-4 0.27 0.73 1.8
PathogenDisgust-5 0.43 0.57 1.3
PathogenDisgust-6 0.27 0.73 1.2
PathogenDisgust-7 0.54 0.46 1.1
GermAversion-1 0.49 0.51 1.5
GermAversion-2 0.52 0.48 1.5
GermAversion-3 0.30 0.70 2.1
GermAversion-4 0.34 0.66 5.0
GermAversion-5r 0.28 0.72 1.5
GermAversion-6 0.28 0.72 2.6
GermAversion-7r 0.34 0.66 4.2
GermAversion-8r 0.37 0.63 1.2
BeliefsAboutObesePersons-1r 0.30 0.70 2.4
BeliefsAboutObesePersons-2 0.32 0.68 1.1
BeliefsAboutObesePersons-3r 0.56 0.44 1.1
BeliefsAboutObesePersons-4r 0.50 0.50 1.4
BeliefsAboutObesePersons-5r 0.52 0.48 1.5
BeliefsAboutObesePersons-6r 0.56 0.44 1.1
BeliefsAboutObesePersons-7 0.32 0.68 1.3
BeliefsAboutObesePersons-8r 0.31 0.69 2.1
AttitudeTowardsObesePeople-1 0.40 0.60 1.6
AttitudeTowardsObesePeople-10r 0.44 0.56 1.3
AttitudeTowardsObesePeople-11r 0.19 0.81 3.2
AttitudeTowardsObesePeople-12r 0.40 0.60 1.7
AttitudeTowardsObesePeople-13 0.32 0.68 1.6
AttitudeTowardsObesePeople-14r 0.28 0.72 1.3
AttitudeTowardsObesePeople-15r 0.29 0.71 1.8
AttitudeTowardsObesePeople-16r 0.31 0.69 2.0
AttitudeTowardsObesePeople-17 0.48 0.52 3.1
AttitudeTowardsObesePeople-18 0.44 0.56 4.0
AttitudeTowardsObesePeople-19r 0.35 0.65 1.2
AttitudeTowardsObesePeople-20r 0.36 0.64 1.8
AttitudeTowardsObesePeople-2r 0.49 0.51 2.8
AttitudeTowardsObesePeople-3r 0.11 0.89 1.9
AttitudeTowardsObesePeople-4r 0.44 0.56 1.6
AttitudeTowardsObesePeople-5r 0.43 0.57 1.5
AttitudeTowardsObesePeople-6r 0.46 0.54 1.8
AttitudeTowardsObesePeople-7 0.31 0.69 3.4
AttitudeTowardsObesePeople-8 0.41 0.59 1.2
AttitudeTowardsObesePeople-9 0.44 0.56 1.6
PerceivedCausesofObesity-1 0.49 0.51 2.3
PerceivedCausesofObesity-10 0.39 0.61 1.7
PerceivedCausesofObesity-11 0.51 0.49 1.5
PerceivedCausesofObesity-12 0.16 0.84 2.1
PerceivedCausesofObesity-13 0.27 0.73 1.3
PerceivedCausesofObesity-14 0.41 0.59 1.3
PerceivedCausesofObesity-2 0.51 0.49 2.0
PerceivedCausesofObesity-3 0.25 0.75 1.7
PerceivedCausesofObesity-4 0.50 0.50 3.1
PerceivedCausesofObesity-5 0.41 0.59 1.1
PerceivedCausesofObesity-6 0.47 0.53 1.2
PerceivedCausesofObesity-7 0.22 0.78 1.4
PerceivedCausesofObesity-8 0.14 0.86 2.8
PerceivedCausesofObesity-9 0.36 0.64 2.4
MR1 MR3 MR8 MR2 MR6 MR5 MR7 MR4
SS loadings 6.22 4.19 4.00 3.32 3.27 2.87 2.29 2.21
Proportion Var 0.09 0.06 0.06 0.05 0.05 0.04 0.03 0.03
Cumulative Var 0.09 0.15 0.20 0.25 0.30 0.34 0.37 0.40
Proportion Explained 0.22 0.15 0.14 0.12 0.12 0.10 0.08 0.08
Cumulative Proportion 0.22 0.37 0.51 0.62 0.74 0.84 0.92 1.00
With factor correlations of
MR1 MR3 MR8 MR2 MR6 MR5 MR7 MR4
MR1 1.00 -0.16 0.11 0.00 -0.40 -0.41 -0.38 0.05
MR3 -0.16 1.00 0.01 -0.22 0.38 0.11 0.04 -0.01
MR8 0.11 0.01 1.00 0.28 -0.27 -0.05 -0.01 0.09
MR2 0.00 -0.22 0.28 1.00 -0.17 -0.01 0.11 0.43
MR6 -0.40 0.38 -0.27 -0.17 1.00 0.18 0.35 -0.16
MR5 -0.41 0.11 -0.05 -0.01 0.18 1.00 0.30 -0.03
MR7 -0.38 0.04 -0.01 0.11 0.35 0.30 1.00 -0.05
MR4 0.05 -0.01 0.09 0.43 -0.16 -0.03 -0.05 1.00
Mean item complexity = 1.8
Test of the hypothesis that 8 factors are sufficient.
df null model = 2485 with the objective function = 31.9 with Chi Square = 10765.74
df of the model are 1945 and the objective function was 8.72
The root mean square of the residuals (RMSR) is 0.04
The df corrected root mean square of the residuals is 0.04
The harmonic n.obs is 363 with the empirical chi square 2269.73 with prob < 3.7e-07
The total n.obs was 363 with Likelihood Chi Square = 2895.16 with prob < 1.2e-40
Tucker Lewis Index of factoring reliability = 0.85
RMSEA index = 0.037 and the 90 % confidence intervals are 0.034 0.039
BIC = -8569.46
Fit based upon off diagonal values = 0.96
Measures of factor score adequacy
MR1 MR3 MR8 MR2 MR6 MR5
Correlation of (regression) scores with factors 0.96 0.93 0.94 0.93 0.93 0.91
Multiple R square of scores with factors 0.93 0.87 0.88 0.86 0.86 0.82
Minimum correlation of possible factor scores 0.86 0.75 0.75 0.72 0.72 0.64
MR7 MR4
Correlation of (regression) scores with factors 0.89 0.89
Multiple R square of scores with factors 0.80 0.80
Minimum correlation of possible factor scores 0.59 0.59tmp_EFA_overall[[1]]$loadings
Loadings:
MR1 MR3 MR8 MR2 MR6 MR5 MR7
pair01 0.689 -0.116
pair02 0.511 -0.147 -0.232
pair03 0.631 -0.268
pair04 0.783 -0.104 -0.107 0.112
pair05 0.848 0.157
pair06 0.605
pair07 0.824 0.133
pair08 0.684 0.175 -0.130
pair09 0.524 0.115
pair10 0.399 0.120 -0.286
pair11 0.527 -0.123
pair12 0.538 0.118 -0.107
pair13 0.645 -0.296 0.190
pair14 0.690 -0.275 0.188
PathogenDisgust-1 0.637 -0.135
PathogenDisgust-2 0.659
PathogenDisgust-3 -0.126 0.656
PathogenDisgust-4 0.110 0.109 0.397 -0.119
PathogenDisgust-5 0.592 0.123
PathogenDisgust-6 0.493 0.120
PathogenDisgust-7 -0.105 0.746
GermAversion-1 -0.110 0.139 0.119 0.161
GermAversion-2 -0.207 0.111 0.130 0.113
GermAversion-3 0.107 0.161 -0.102
GermAversion-4 -0.222 0.258 -0.218 0.173
GermAversion-5r -0.178 0.121
GermAversion-6 0.219 -0.152
GermAversion-7r -0.132 0.309 0.144 -0.234 -0.159
GermAversion-8r 0.122 -0.105 0.110
BeliefsAboutObesePersons-1r 0.120 -0.153 0.394 0.156 -0.150
BeliefsAboutObesePersons-2 0.555
BeliefsAboutObesePersons-3r 0.647 0.102
BeliefsAboutObesePersons-4r 0.105 0.218 0.128 0.663
BeliefsAboutObesePersons-5r -0.129 0.629 0.147
BeliefsAboutObesePersons-6r 0.112 -0.102 0.759
BeliefsAboutObesePersons-7 0.132 0.534
BeliefsAboutObesePersons-8r -0.174 -0.188 0.438 0.121
AttitudeTowardsObesePeople-1 0.198 0.511 0.129
AttitudeTowardsObesePeople-10r 0.679 -0.162 -0.148 -0.105
AttitudeTowardsObesePeople-11r 0.308 0.110 0.141 -0.258
AttitudeTowardsObesePeople-12r 0.529 0.154 -0.133 -0.191
AttitudeTowardsObesePeople-13 -0.226 0.110 0.524
AttitudeTowardsObesePeople-14r 0.539 -0.140
AttitudeTowardsObesePeople-15r 0.436 0.128 -0.224
AttitudeTowardsObesePeople-16r 0.474 0.107 0.298
AttitudeTowardsObesePeople-17 -0.121 -0.127 0.249 0.389 0.240
AttitudeTowardsObesePeople-18 0.130 0.180 0.304 0.319
AttitudeTowardsObesePeople-19r 0.579 0.140
AttitudeTowardsObesePeople-20r 0.466 -0.151 0.115
AttitudeTowardsObesePeople-2r 0.465 -0.128 0.132 0.451 -0.188
AttitudeTowardsObesePeople-3r 0.119 0.290
AttitudeTowardsObesePeople-4r 0.628 -0.148 0.261
AttitudeTowardsObesePeople-5r 0.538 0.239
AttitudeTowardsObesePeople-6r 0.491 0.299
AttitudeTowardsObesePeople-7 0.254 -0.216 0.378 0.212
AttitudeTowardsObesePeople-8 -0.111 0.115 0.613
AttitudeTowardsObesePeople-9 0.190 0.496 0.166
PerceivedCausesofObesity-1 0.526 -0.163 0.177 -0.359
PerceivedCausesofObesity-10 0.130 0.539 0.156 0.151
PerceivedCausesofObesity-11 0.161 0.657 0.113 0.102 0.216
PerceivedCausesofObesity-12 0.349 0.112 0.166 -0.115
PerceivedCausesofObesity-13 0.522 -0.114 0.114
PerceivedCausesofObesity-14 0.559 -0.167
PerceivedCausesofObesity-2 0.531 -0.205 -0.294
PerceivedCausesofObesity-3 -0.108 0.449 -0.188
PerceivedCausesofObesity-4 0.464 0.249 0.100 0.346
PerceivedCausesofObesity-5 0.626
PerceivedCausesofObesity-6 0.689 0.141
PerceivedCausesofObesity-7 0.426 0.131
PerceivedCausesofObesity-8 -0.202 0.257 0.102
PerceivedCausesofObesity-9 0.430 -0.311
MR4
pair01
pair02
pair03
pair04
pair05
pair06
pair07
pair08
pair09
pair10 -0.150
pair11
pair12
pair13
pair14
PathogenDisgust-1
PathogenDisgust-2
PathogenDisgust-3
PathogenDisgust-4
PathogenDisgust-5 0.132
PathogenDisgust-6
PathogenDisgust-7
GermAversion-1 0.593
GermAversion-2 0.641
GermAversion-3 0.366
GermAversion-4 0.202
GermAversion-5r 0.477
GermAversion-6 0.329
GermAversion-7r 0.329
GermAversion-8r 0.625
BeliefsAboutObesePersons-1r
BeliefsAboutObesePersons-2
BeliefsAboutObesePersons-3r
BeliefsAboutObesePersons-4r
BeliefsAboutObesePersons-5r 0.181
BeliefsAboutObesePersons-6r
BeliefsAboutObesePersons-7
BeliefsAboutObesePersons-8r -0.107
AttitudeTowardsObesePeople-1
AttitudeTowardsObesePeople-10r
AttitudeTowardsObesePeople-11r
AttitudeTowardsObesePeople-12r
AttitudeTowardsObesePeople-13
AttitudeTowardsObesePeople-14r -0.103
AttitudeTowardsObesePeople-15r
AttitudeTowardsObesePeople-16r
AttitudeTowardsObesePeople-17
AttitudeTowardsObesePeople-18 0.153
AttitudeTowardsObesePeople-19r
AttitudeTowardsObesePeople-20r 0.190
AttitudeTowardsObesePeople-2r
AttitudeTowardsObesePeople-3r
AttitudeTowardsObesePeople-4r
AttitudeTowardsObesePeople-5r
AttitudeTowardsObesePeople-6r
AttitudeTowardsObesePeople-7
AttitudeTowardsObesePeople-8
AttitudeTowardsObesePeople-9
PerceivedCausesofObesity-1
PerceivedCausesofObesity-10
PerceivedCausesofObesity-11
PerceivedCausesofObesity-12
PerceivedCausesofObesity-13
PerceivedCausesofObesity-14
PerceivedCausesofObesity-2
PerceivedCausesofObesity-3
PerceivedCausesofObesity-4 -0.212
PerceivedCausesofObesity-5 0.109
PerceivedCausesofObesity-6
PerceivedCausesofObesity-7
PerceivedCausesofObesity-8
PerceivedCausesofObesity-9 0.115
MR1 MR3 MR8 MR2 MR6 MR5 MR7 MR4
SS loadings 6.100 3.998 4.009 3.192 3.047 2.616 2.185 2.163
Proportion Var 0.086 0.056 0.056 0.045 0.043 0.037 0.031 0.030
Cumulative Var 0.086 0.142 0.199 0.244 0.287 0.323 0.354 0.385## correlation factor scores
psych::cor.plot(tmp_EFA_overall[[1]]$scores)
Descriptives, correlation plot, EFA, CFA
Here we could apply a self-written function for example to check the reliability and amount of explained variance for the first factor:
Fat Phobia Scale
regEx <- "^pair"
nameVariable <- "FatPhobia"
sum(str_detect(string = colnames(dat), pattern = regEx))[1] 14tmp_dat <- na.omit(dat[,str_detect(string = colnames(dat), pattern = regEx)])
tmp <- CFAstats(dataset = tmp_dat, regularExp = regEx, labelLatent = str_remove(string = nameVariable, pattern = "mean_"),
showPlots = TRUE,
computeEFA = TRUE,
computeCFA = TRUE,
computeCFAMplus = FALSE)
descriptive statistics:
Mean SD Median CoeffofVariation Minimum Maximun Lower Quantile
pair01 3.83 1.05 4 0.27 1 5 1
pair02 3.75 1.11 4 0.30 1 5 1
pair03 3.68 1.12 4 0.31 1 5 1
pair04 4.08 1.09 4 0.27 1 5 1
pair05 4.23 1.00 5 0.24 1 5 1
pair06 3.93 1.05 4 0.27 1 5 1
pair07 4.16 1.04 4 0.25 1 5 1
pair08 3.52 1.08 4 0.31 1 5 1
pair09 3.85 1.17 4 0.30 1 5 1
pair10 4.51 0.67 5 0.15 2 5 2
pair11 3.52 1.35 4 0.38 1 5 1
pair12 4.41 0.91 5 0.21 1 5 1
pair13 3.92 1.00 4 0.26 1 5 1
pair14 3.98 1.00 4 0.25 1 5 1
Upper Quantile Skewness Kurtosis(-3) KS-Test
pair01 5 -0.71 0.02 0
pair02 5 -0.78 -0.06 0
pair03 5 -0.62 -0.20 0
pair04 5 -1.28 0.96 0
pair05 5 -1.52 2.07 0
pair06 5 -0.81 0.01 0
pair07 5 -1.36 1.29 0
pair08 5 -0.35 -0.43 0
pair09 5 -0.99 0.22 0
pair10 5 -1.15 0.50 0
pair11 5 -0.51 -0.95 0
pair12 5 -1.83 3.41 0
pair13 5 -0.93 0.55 0
pair14 5 -1.07 0.85 0
variables under investigation: pair01 pair02 pair03 pair04 pair05 pair06 pair07 pair08 pair09 pair10 pair11 pair12 pair13 pair14
Cronbachs Alpha: 0.91 
Parallel analysis suggests that the number of factors = 3 and the number of components = 1
FatPhobia
Number of components: 1
EFA factor loadings (1 factor solution):
Loadings:
MR1
pair01 0.766
pair02 0.715
pair03 0.692
pair04 0.808
pair05 0.820
pair06 0.726
pair07 0.850
pair08 0.691
pair09 0.633
pair10 0.625
pair11 0.530
pair12 0.744
pair13 0.719
pair14 0.731
MR1
SS loadings 7.304
Proportion Var 0.522
CFA summary and fit statistics:
lavaan 0.6-19 ended normally after 25 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 28
Number of observations 363
Model Test User Model:
Standard Scaled
Test Statistic 248.324 191.672
Degrees of freedom 77 77
P-value (Chi-square) 0.000 0.000
Scaling correction factor 1.296
Yuan-Bentler correction (Mplus variant)
Model Test Baseline Model:
Test statistic 2279.126 1552.255
Degrees of freedom 91 91
P-value 0.000 0.000
Scaling correction factor 1.468
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.922 0.922
Tucker-Lewis Index (TLI) 0.907 0.907
Robust Comparative Fit Index (CFI) 0.931
Robust Tucker-Lewis Index (TLI) 0.918
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -6372.609 -6372.609
Scaling correction factor 1.857
for the MLR correction
Loglikelihood unrestricted model (H1) -6248.447 -6248.447
Scaling correction factor 1.445
for the MLR correction
Akaike (AIC) 12801.219 12801.219
Bayesian (BIC) 12910.262 12910.262
Sample-size adjusted Bayesian (SABIC) 12821.431 12821.431
Root Mean Square Error of Approximation:
RMSEA 0.078 0.064
90 Percent confidence interval - lower 0.068 0.054
90 Percent confidence interval - upper 0.089 0.074
P-value H_0: RMSEA <= 0.050 0.000 0.011
P-value H_0: RMSEA >= 0.080 0.410 0.004
Robust RMSEA 0.073
90 Percent confidence interval - lower 0.060
90 Percent confidence interval - upper 0.086
P-value H_0: Robust RMSEA <= 0.050 0.002
P-value H_0: Robust RMSEA >= 0.080 0.191
Standardized Root Mean Square Residual:
SRMR 0.043 0.043
Parameter Estimates:
Standard errors Sandwich
Information bread Observed
Observed information based on Hessian
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
FatPhobia =~
pair01 1.000 0.751 0.715
pair02 0.952 0.093 10.269 0.000 0.715 0.644
pair03 0.969 0.084 11.606 0.000 0.728 0.649
pair04 1.061 0.091 11.698 0.000 0.797 0.732
pair05 1.003 0.081 12.397 0.000 0.753 0.757
pair06 0.929 0.093 10.022 0.000 0.697 0.664
pair07 1.097 0.102 10.781 0.000 0.824 0.790
pair08 0.928 0.084 11.060 0.000 0.697 0.644
pair09 0.840 0.089 9.399 0.000 0.631 0.540
pair10 0.443 0.068 6.547 0.000 0.333 0.494
pair11 0.806 0.101 8.009 0.000 0.605 0.449
pair12 0.734 0.074 9.925 0.000 0.551 0.607
pair13 0.912 0.076 11.950 0.000 0.685 0.683
pair14 0.933 0.086 10.813 0.000 0.701 0.700
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.pair01 0.538 0.063 8.537 0.000 0.538 0.488
.pair02 0.723 0.094 7.731 0.000 0.723 0.586
.pair03 0.729 0.075 9.689 0.000 0.729 0.579
.pair04 0.551 0.085 6.460 0.000 0.551 0.464
.pair05 0.422 0.076 5.569 0.000 0.422 0.427
.pair06 0.618 0.073 8.466 0.000 0.618 0.560
.pair07 0.409 0.073 5.575 0.000 0.409 0.376
.pair08 0.684 0.068 10.115 0.000 0.684 0.585
.pair09 0.968 0.123 7.883 0.000 0.968 0.708
.pair10 0.343 0.033 10.514 0.000 0.343 0.756
.pair11 1.448 0.116 12.515 0.000 1.448 0.798
.pair12 0.522 0.085 6.114 0.000 0.522 0.632
.pair13 0.538 0.057 9.476 0.000 0.538 0.534
.pair14 0.511 0.055 9.215 0.000 0.511 0.510
FatPhobia 0.564 0.084 6.705 0.000 1.000 1.000
CFA first 6 Modification Indices:
lhs op rhs mi epc sepc.lv sepc.all sepc.nox
120 pair13 ~~ pair14 105.216 0.310 0.310 0.592 0.592
77 pair05 ~~ pair07 20.694 0.118 0.118 0.284 0.284
67 pair04 ~~ pair06 16.106 0.136 0.136 0.233 0.233
35 pair01 ~~ pair07 7.875 -0.080 -0.080 -0.172 -0.172
83 pair05 ~~ pair13 7.636 -0.078 -0.078 -0.163 -0.163
49 pair02 ~~ pair09 7.210 0.124 0.124 0.149 0.149check modification indices - one strong local item dependency
Subscale Pathogen Disgust
regEx <- "^PathogenDisgus"
nameVariable <- "PatDis"
sum(str_detect(string = colnames(dat), pattern = regEx))[1] 7tmp_dat <- na.omit(dat[,str_detect(string = colnames(dat), pattern = regEx)])
tmp <- CFAstats(dataset = tmp_dat, regularExp = regEx, labelLatent = str_remove(string = nameVariable, pattern = "mean_"),
showPlots = TRUE,
computeEFA = TRUE,
computeCFA = TRUE,
computeCFAMplus = FALSE)
descriptive statistics:
Mean SD Median CoeffofVariation Minimum Maximun
PathogenDisgust-1 4.60 1.75 5 0.38 1 7
PathogenDisgust-2 4.99 1.54 5 0.31 1 7
PathogenDisgust-3 4.10 1.61 4 0.39 1 7
PathogenDisgust-4 5.75 1.31 6 0.23 1 7
PathogenDisgust-5 4.97 1.78 5 0.36 1 7
PathogenDisgust-6 4.40 1.88 5 0.43 1 7
PathogenDisgust-7 3.91 1.88 4 0.48 1 7
Lower Quantile Upper Quantile Skewness Kurtosis(-3) KS-Test
PathogenDisgust-1 1 7 -0.32 -0.93 0
PathogenDisgust-2 1 7 -0.40 -0.73 0
PathogenDisgust-3 1 7 0.14 -0.95 0
PathogenDisgust-4 1 7 -0.89 0.07 0
PathogenDisgust-5 1 7 -0.56 -0.70 0
PathogenDisgust-6 1 7 -0.17 -1.10 0
PathogenDisgust-7 1 7 0.11 -1.07 0
variables under investigation: PathogenDisgust1 PathogenDisgust2 PathogenDisgust3 PathogenDisgust4 PathogenDisgust5 PathogenDisgust6 PathogenDisgust7
Cronbachs Alpha: 0.81 
Parallel analysis suggests that the number of factors = 3 and the number of components = 1
PatDis
Number of components: 1
EFA factor loadings (1 factor solution):
Loadings:
MR1
PathogenDisgust1 0.668
PathogenDisgust2 0.706
PathogenDisgust3 0.728
PathogenDisgust4 0.541
PathogenDisgust5 0.677
PathogenDisgust6 0.523
PathogenDisgust7 0.697
MR1
SS loadings 2.985
Proportion Var 0.426
CFA summary and fit statistics:
lavaan 0.6-19 ended normally after 27 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 14
Number of observations 363
Model Test User Model:
Standard Scaled
Test Statistic 68.287 56.975
Degrees of freedom 14 14
P-value (Chi-square) 0.000 0.000
Scaling correction factor 1.199
Yuan-Bentler correction (Mplus variant)
Model Test Baseline Model:
Test statistic 734.814 599.414
Degrees of freedom 21 21
P-value 0.000 0.000
Scaling correction factor 1.226
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.924 0.926
Tucker-Lewis Index (TLI) 0.886 0.889
Robust Comparative Fit Index (CFI) 0.927
Robust Tucker-Lewis Index (TLI) 0.891
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -4566.704 -4566.704
Scaling correction factor 0.947
for the MLR correction
Loglikelihood unrestricted model (H1) -4532.561 -4532.561
Scaling correction factor 1.073
for the MLR correction
Akaike (AIC) 9161.409 9161.409
Bayesian (BIC) 9215.930 9215.930
Sample-size adjusted Bayesian (SABIC) 9171.515 9171.515
Root Mean Square Error of Approximation:
RMSEA 0.103 0.092
90 Percent confidence interval - lower 0.080 0.070
90 Percent confidence interval - upper 0.128 0.115
P-value H_0: RMSEA <= 0.050 0.000 0.001
P-value H_0: RMSEA >= 0.080 0.947 0.822
Robust RMSEA 0.101
90 Percent confidence interval - lower 0.074
90 Percent confidence interval - upper 0.129
P-value H_0: Robust RMSEA <= 0.050 0.001
P-value H_0: Robust RMSEA >= 0.080 0.905
Standardized Root Mean Square Residual:
SRMR 0.052 0.052
Parameter Estimates:
Standard errors Sandwich
Information bread Observed
Observed information based on Hessian
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
PatDis =~
PathogenDsgst1 1.000 1.092 0.626
PathogenDsgst2 0.972 0.092 10.592 0.000 1.061 0.690
PathogenDsgst3 1.079 0.108 10.004 0.000 1.178 0.733
PathogenDsgst4 0.567 0.073 7.770 0.000 0.618 0.471
PathogenDsgst5 1.043 0.101 10.284 0.000 1.139 0.642
PathogenDsgst6 0.825 0.092 8.956 0.000 0.900 0.479
PathogenDsgst7 1.194 0.120 9.913 0.000 1.303 0.696
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.PathogenDsgst1 1.848 0.163 11.350 0.000 1.848 0.608
.PathogenDsgst2 1.241 0.128 9.682 0.000 1.241 0.525
.PathogenDsgst3 1.197 0.139 8.619 0.000 1.197 0.463
.PathogenDsgst4 1.341 0.107 12.590 0.000 1.341 0.778
.PathogenDsgst5 1.854 0.168 11.030 0.000 1.854 0.588
.PathogenDsgst6 2.724 0.192 14.185 0.000 2.724 0.771
.PathogenDsgst7 1.808 0.198 9.139 0.000 1.808 0.516
PatDis 1.191 0.189 6.294 0.000 1.000 1.000
CFA first 6 Modification Indices:
lhs op rhs mi epc sepc.lv sepc.all sepc.nox
24 PathogenDisgust2 ~~ PathogenDisgust5 18.698 -0.441 -0.441 -0.291 -0.291
22 PathogenDisgust2 ~~ PathogenDisgust3 18.652 0.397 0.397 0.325 0.325
32 PathogenDisgust4 ~~ PathogenDisgust6 13.850 0.400 0.400 0.209 0.209
35 PathogenDisgust5 ~~ PathogenDisgust7 13.463 0.455 0.455 0.248 0.248
29 PathogenDisgust3 ~~ PathogenDisgust6 9.379 -0.355 -0.355 -0.196 -0.196
20 PathogenDisgust1 ~~ PathogenDisgust6 8.496 0.386 0.386 0.172 0.172Subscale Germ Aversion
regEx <- "^GermAversion"
nameVariable <- "GermAv"
sum(str_detect(string = colnames(dat), pattern = regEx))[1] 8tmp_dat <- na.omit(dat[,str_detect(string = colnames(dat), pattern = regEx)])
tmp <- CFAstats(dataset = tmp_dat, regularExp = regEx, labelLatent = str_remove(string = nameVariable, pattern = "mean_"),
showPlots = TRUE,
computeEFA = TRUE,
computeCFA = TRUE,
computeCFAMplus = FALSE)
descriptive statistics:
Mean SD Median CoeffofVariation Minimum Maximun
GermAversion-1 4.28 1.85 4 0.43 1 7
GermAversion-2 3.51 1.92 4 0.55 1 7
GermAversion-3 5.04 1.77 5 0.35 1 7
GermAversion-4 3.89 2.12 4 0.54 1 7
GermAversion-5r 3.90 2.05 4 0.52 1 7
GermAversion-6 5.98 1.36 6 0.23 1 7
GermAversion-7r 4.23 1.84 5 0.44 1 7
GermAversion-8r 4.03 2.07 4 0.51 1 7
Lower Quantile Upper Quantile Skewness Kurtosis(-3) KS-Test
GermAversion-1 1 7 -0.21 -1.02 0
GermAversion-2 1 7 0.24 -1.08 0
GermAversion-3 1 7 -0.69 -0.50 0
GermAversion-4 1 7 0.10 -1.40 0
GermAversion-5r 1 7 0.22 -1.33 0
GermAversion-6 1 7 -1.63 2.43 0
GermAversion-7r 1 7 -0.14 -1.15 0
GermAversion-8r 1 7 -0.03 -1.37 0
variables under investigation: GermAversion1 GermAversion2 GermAversion3 GermAversion4 GermAversion5r GermAversion6 GermAversion7r GermAversion8r
Cronbachs Alpha: 0.74 
Parallel analysis suggests that the number of factors = 3 and the number of components = 1
GermAv
Number of components: 1
EFA factor loadings (1 factor solution):
Loadings:
MR1
GermAversion1 0.705
GermAversion2 0.737
GermAversion3 0.518
GermAversion4 0.412
GermAversion5r 0.496
GermAversion6 0.563
GermAversion7r 0.466
GermAversion8r 0.537
MR1
SS loadings 2.548
Proportion Var 0.319
CFA summary and fit statistics:
lavaan 0.6-19 ended normally after 32 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 16
Number of observations 363
Model Test User Model:
Standard Scaled
Test Statistic 73.743 66.968
Degrees of freedom 20 20
P-value (Chi-square) 0.000 0.000
Scaling correction factor 1.101
Yuan-Bentler correction (Mplus variant)
Model Test Baseline Model:
Test statistic 527.189 461.027
Degrees of freedom 28 28
P-value 0.000 0.000
Scaling correction factor 1.144
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.892 0.892
Tucker-Lewis Index (TLI) 0.849 0.848
Robust Comparative Fit Index (CFI) 0.896
Robust Tucker-Lewis Index (TLI) 0.854
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -5686.341 -5686.341
Scaling correction factor 0.955
for the MLR correction
Loglikelihood unrestricted model (H1) -5649.469 -5649.469
Scaling correction factor 1.036
for the MLR correction
Akaike (AIC) 11404.682 11404.682
Bayesian (BIC) 11466.992 11466.992
Sample-size adjusted Bayesian (SABIC) 11416.231 11416.231
Root Mean Square Error of Approximation:
RMSEA 0.086 0.080
90 Percent confidence interval - lower 0.066 0.061
90 Percent confidence interval - upper 0.107 0.101
P-value H_0: RMSEA <= 0.050 0.003 0.007
P-value H_0: RMSEA >= 0.080 0.703 0.538
Robust RMSEA 0.084
90 Percent confidence interval - lower 0.063
90 Percent confidence interval - upper 0.107
P-value H_0: Robust RMSEA <= 0.050 0.006
P-value H_0: Robust RMSEA >= 0.080 0.651
Standardized Root Mean Square Residual:
SRMR 0.058 0.058
Parameter Estimates:
Standard errors Sandwich
Information bread Observed
Observed information based on Hessian
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
GermAv =~
GermAversion1 1.000 1.272 0.690
GermAversion2 1.098 0.085 12.958 0.000 1.397 0.729
GermAversion3 0.642 0.090 7.154 0.000 0.817 0.461
GermAversion4 0.707 0.105 6.712 0.000 0.899 0.425
GermAversion5r 0.711 0.112 6.319 0.000 0.904 0.442
GermAversion6 0.496 0.068 7.330 0.000 0.631 0.464
GermAversion7r 0.601 0.103 5.831 0.000 0.764 0.416
GermAversion8r 0.801 0.106 7.571 0.000 1.019 0.494
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.GermAversion1 1.784 0.184 9.695 0.000 1.784 0.525
.GermAversion2 1.721 0.192 8.976 0.000 1.721 0.469
.GermAversion3 2.469 0.200 12.357 0.000 2.469 0.787
.GermAversion4 3.663 0.269 13.637 0.000 3.663 0.819
.GermAversion5r 3.370 0.254 13.277 0.000 3.370 0.805
.GermAversion6 1.447 0.163 8.856 0.000 1.447 0.784
.GermAversion7r 2.792 0.208 13.415 0.000 2.792 0.827
.GermAversion8r 3.223 0.253 12.763 0.000 3.223 0.756
GermAv 1.617 0.230 7.027 0.000 1.000 1.000
CFA first 6 Modification Indices:
lhs op rhs mi epc sepc.lv sepc.all sepc.nox
39 GermAversion4 ~~ GermAversion8r 15.625 -0.781 -0.781 -0.227 -0.227
27 GermAversion2 ~~ GermAversion5r 9.777 -0.527 -0.527 -0.219 -0.219
23 GermAversion1 ~~ GermAversion7r 8.630 -0.428 -0.428 -0.192 -0.192
45 GermAversion7r ~~ GermAversion8r 8.214 0.493 0.493 0.164 0.164
18 GermAversion1 ~~ GermAversion2 7.753 0.470 0.470 0.268 0.268
31 GermAversion3 ~~ GermAversion4 7.114 0.457 0.457 0.152 0.152item 4
Beliefs About Obese Persons Scale
regEx <- "^BeliefsAboutObesePersons"
nameVariable <- "BelAbObPe"
sum(str_detect(string = colnames(dat), pattern = regEx))[1] 8tmp_dat <- na.omit(dat[,str_detect(string = colnames(dat), pattern = regEx)])
tmp <- CFAstats(dataset = tmp_dat, regularExp = regEx, labelLatent = str_remove(string = nameVariable, pattern = "mean_"),
showPlots = TRUE,
computeEFA = TRUE,
computeCFA = TRUE,
computeCFAMplus = FALSE)
descriptive statistics:
Mean SD Median CoeffofVariation Minimum Maximun
BeliefsAboutObesePersons-1r 2.64 1.26 2 0.47 1 6
BeliefsAboutObesePersons-2 3.55 1.30 4 0.36 1 6
BeliefsAboutObesePersons-3r 2.20 1.19 2 0.54 1 6
BeliefsAboutObesePersons-4r 2.70 1.33 2 0.49 1 6
BeliefsAboutObesePersons-5r 2.09 1.22 2 0.58 1 6
BeliefsAboutObesePersons-6r 2.12 1.11 2 0.53 1 6
BeliefsAboutObesePersons-7 3.03 1.37 3 0.45 1 6
BeliefsAboutObesePersons-8r 1.85 0.94 2 0.51 1 5
Lower Quantile Upper Quantile Skewness Kurtosis(-3)
BeliefsAboutObesePersons-1r 1 6 0.70 0.12
BeliefsAboutObesePersons-2 1 6 -0.21 -0.60
BeliefsAboutObesePersons-3r 1 6 1.26 1.61
BeliefsAboutObesePersons-4r 1 6 0.75 -0.03
BeliefsAboutObesePersons-5r 1 6 1.33 1.39
BeliefsAboutObesePersons-6r 1 6 1.09 1.14
BeliefsAboutObesePersons-7 1 6 0.33 -0.78
BeliefsAboutObesePersons-8r 1 5 1.13 1.10
KS-Test
BeliefsAboutObesePersons-1r 0
BeliefsAboutObesePersons-2 0
BeliefsAboutObesePersons-3r 0
BeliefsAboutObesePersons-4r 0
BeliefsAboutObesePersons-5r 0
BeliefsAboutObesePersons-6r 0
BeliefsAboutObesePersons-7 0
BeliefsAboutObesePersons-8r 0
variables under investigation: BeliefsAboutObesePersons1r BeliefsAboutObesePersons2 BeliefsAboutObesePersons3r BeliefsAboutObesePersons4r BeliefsAboutObesePersons5r BeliefsAboutObesePersons6r BeliefsAboutObesePersons7 BeliefsAboutObesePersons8r
Cronbachs Alpha: 0.74 Error in if (any(lower > upper)) stop("lower>upper integration limits") :
Fehlender Wert, wo TRUE/FALSE nötig ist
[1] "use instead of polychoric correlations pearson correlations"
Parallel analysis suggests that the number of factors = 2 and the number of components = 2
BelAbObPe
Number of components: 2 KMO criteria is to low (< .6) for:
BeliefsAboutObesePersons2
mean KMO: 0.84
EFA factor loadings (1 factor solution):
Loadings:
MR1
BeliefsAboutObesePersons1r 0.587
BeliefsAboutObesePersons2 0.168
BeliefsAboutObesePersons3r 0.831
BeliefsAboutObesePersons4r 0.587
BeliefsAboutObesePersons5r 0.767
BeliefsAboutObesePersons6r 0.807
BeliefsAboutObesePersons7 0.235
BeliefsAboutObesePersons8r 0.484
MR1
SS loadings 2.936
Proportion Var 0.367
CFA summary and fit statistics:
lavaan 0.6-19 ended normally after 27 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 16
Number of observations 363
Model Test User Model:
Standard Scaled
Test Statistic 81.590 62.545
Degrees of freedom 20 20
P-value (Chi-square) 0.000 0.000
Scaling correction factor 1.305
Yuan-Bentler correction (Mplus variant)
Model Test Baseline Model:
Test statistic 707.340 486.290
Degrees of freedom 28 28
P-value 0.000 0.000
Scaling correction factor 1.455
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.909 0.907
Tucker-Lewis Index (TLI) 0.873 0.870
Robust Comparative Fit Index (CFI) 0.917
Robust Tucker-Lewis Index (TLI) 0.883
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -4348.755 -4348.755
Scaling correction factor 1.538
for the MLR correction
Loglikelihood unrestricted model (H1) -4307.960 -4307.960
Scaling correction factor 1.408
for the MLR correction
Akaike (AIC) 8729.510 8729.510
Bayesian (BIC) 8791.820 8791.820
Sample-size adjusted Bayesian (SABIC) 8741.059 8741.059
Root Mean Square Error of Approximation:
RMSEA 0.092 0.077
90 Percent confidence interval - lower 0.072 0.058
90 Percent confidence interval - upper 0.113 0.096
P-value H_0: RMSEA <= 0.050 0.001 0.010
P-value H_0: RMSEA >= 0.080 0.844 0.402
Robust RMSEA 0.087
90 Percent confidence interval - lower 0.063
90 Percent confidence interval - upper 0.112
P-value H_0: Robust RMSEA <= 0.050 0.006
P-value H_0: Robust RMSEA >= 0.080 0.713
Standardized Root Mean Square Residual:
SRMR 0.069 0.069
Parameter Estimates:
Standard errors Sandwich
Information bread Observed
Observed information based on Hessian
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
BelAbObPe =~
BlfsAbtObsPrs1 1.000 0.681 0.543
BlfsAbtObsPrs2 0.269 0.120 2.244 0.025 0.183 0.142
BlfsAbtObsPrs3 1.392 0.160 8.703 0.000 0.947 0.795
BlfsAbtObsPrs4 1.157 0.154 7.494 0.000 0.788 0.594
BlfsAbtObsPrs5 1.254 0.159 7.884 0.000 0.854 0.701
BlfsAbtObsPrs6 1.226 0.168 7.296 0.000 0.834 0.750
BlfsAbtObsPrs7 0.367 0.133 2.756 0.006 0.249 0.183
BlfsAbtObsPrs8 0.602 0.115 5.245 0.000 0.410 0.437
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.BlfsAbtObsPrs1 1.110 0.106 10.495 0.000 1.110 0.706
.BlfsAbtObsPrs2 1.640 0.105 15.666 0.000 1.640 0.980
.BlfsAbtObsPrs3 0.523 0.087 5.983 0.000 0.523 0.368
.BlfsAbtObsPrs4 1.137 0.123 9.225 0.000 1.137 0.647
.BlfsAbtObsPrs5 0.755 0.128 5.888 0.000 0.755 0.509
.BlfsAbtObsPrs6 0.542 0.085 6.335 0.000 0.542 0.438
.BlfsAbtObsPrs7 1.796 0.117 15.300 0.000 1.796 0.967
.BlfsAbtObsPrs8 0.710 0.067 10.614 0.000 0.710 0.809
BelAbObPe 0.463 0.094 4.929 0.000 1.000 1.000
CFA first 6 Modification Indices:
lhs op rhs mi epc
29 BeliefsAboutObesePersons2 ~~ BeliefsAboutObesePersons7 47.115 0.622
38 BeliefsAboutObesePersons4r ~~ BeliefsAboutObesePersons7 5.861 -0.193
23 BeliefsAboutObesePersons1r ~~ BeliefsAboutObesePersons7 5.405 -0.180
22 BeliefsAboutObesePersons1r ~~ BeliefsAboutObesePersons6r 5.108 -0.117
26 BeliefsAboutObesePersons2 ~~ BeliefsAboutObesePersons4r 3.610 -0.144
43 BeliefsAboutObesePersons6r ~~ BeliefsAboutObesePersons7 3.477 0.112
sepc.lv sepc.all sepc.nox
29 0.622 0.362 0.362
38 -0.193 -0.135 -0.135
23 -0.180 -0.128 -0.128
22 -0.117 -0.151 -0.151
26 -0.144 -0.106 -0.106
43 0.112 0.114 0.114item 2
Attitude Towards Obese People Scale
regEx <- "^AttitudeTowardsObesePeople"
nameVariable <- "AttTowObPe"
sum(str_detect(string = colnames(dat), pattern = regEx))[1] 20tmp_dat <- na.omit(dat[,str_detect(string = colnames(dat), pattern = regEx)])
tmp <- CFAstats(dataset = tmp_dat, regularExp = regEx, labelLatent = str_remove(string = nameVariable, pattern = "mean_"),
showPlots = TRUE,
computeEFA = TRUE,
computeCFA = TRUE,
computeCFAMplus = FALSE)
descriptive statistics:
Mean SD Median CoeffofVariation Minimum
AttitudeTowardsObesePeople-1 3.37 1.35 3 0.40 1
AttitudeTowardsObesePeople-10r 3.76 1.37 4 0.37 1
AttitudeTowardsObesePeople-11r 3.81 1.34 4 0.35 1
AttitudeTowardsObesePeople-12r 3.90 1.35 4 0.34 1
AttitudeTowardsObesePeople-13 2.78 1.37 3 0.49 1
AttitudeTowardsObesePeople-14r 3.93 1.36 4 0.35 1
AttitudeTowardsObesePeople-15r 3.77 1.35 4 0.36 1
AttitudeTowardsObesePeople-16r 4.09 1.50 4 0.37 1
AttitudeTowardsObesePeople-17 2.20 1.31 2 0.60 1
AttitudeTowardsObesePeople-18 2.73 1.49 3 0.55 1
AttitudeTowardsObesePeople-19r 3.75 1.27 4 0.34 1
AttitudeTowardsObesePeople-20r 3.48 1.53 3 0.44 1
AttitudeTowardsObesePeople-2r 2.92 1.25 3 0.43 1
AttitudeTowardsObesePeople-3r 2.79 1.30 3 0.47 1
AttitudeTowardsObesePeople-4r 4.02 1.51 4 0.38 1
AttitudeTowardsObesePeople-5r 3.11 1.46 3 0.47 1
AttitudeTowardsObesePeople-6r 3.35 1.53 3 0.46 1
AttitudeTowardsObesePeople-7 3.76 1.25 4 0.33 1
AttitudeTowardsObesePeople-8 2.89 1.31 3 0.45 1
AttitudeTowardsObesePeople-9 3.20 1.31 3 0.41 1
Maximun Lower Quantile Upper Quantile Skewness
AttitudeTowardsObesePeople-1 6 1 6 -0.02
AttitudeTowardsObesePeople-10r 6 1 6 -0.02
AttitudeTowardsObesePeople-11r 6 1 6 -0.14
AttitudeTowardsObesePeople-12r 6 1 6 -0.10
AttitudeTowardsObesePeople-13 6 1 6 0.58
AttitudeTowardsObesePeople-14r 6 1 6 -0.16
AttitudeTowardsObesePeople-15r 6 1 6 -0.05
AttitudeTowardsObesePeople-16r 6 1 6 -0.26
AttitudeTowardsObesePeople-17 6 1 6 1.02
AttitudeTowardsObesePeople-18 6 1 6 0.46
AttitudeTowardsObesePeople-19r 6 1 6 -0.02
AttitudeTowardsObesePeople-20r 6 1 6 0.10
AttitudeTowardsObesePeople-2r 6 1 6 0.44
AttitudeTowardsObesePeople-3r 6 1 6 0.52
AttitudeTowardsObesePeople-4r 6 1 6 -0.34
AttitudeTowardsObesePeople-5r 6 1 6 0.30
AttitudeTowardsObesePeople-6r 6 1 6 0.19
AttitudeTowardsObesePeople-7 6 1 6 -0.21
AttitudeTowardsObesePeople-8 6 1 6 0.35
AttitudeTowardsObesePeople-9 6 1 6 0.19
Kurtosis(-3) KS-Test
AttitudeTowardsObesePeople-1 -0.70 0
AttitudeTowardsObesePeople-10r -0.82 0
AttitudeTowardsObesePeople-11r -0.68 0
AttitudeTowardsObesePeople-12r -0.78 0
AttitudeTowardsObesePeople-13 -0.44 0
AttitudeTowardsObesePeople-14r -0.86 0
AttitudeTowardsObesePeople-15r -0.65 0
AttitudeTowardsObesePeople-16r -1.06 0
AttitudeTowardsObesePeople-17 0.28 0
AttitudeTowardsObesePeople-18 -0.80 0
AttitudeTowardsObesePeople-19r -0.60 0
AttitudeTowardsObesePeople-20r -1.00 0
AttitudeTowardsObesePeople-2r -0.23 0
AttitudeTowardsObesePeople-3r -0.42 0
AttitudeTowardsObesePeople-4r -0.92 0
AttitudeTowardsObesePeople-5r -0.77 0
AttitudeTowardsObesePeople-6r -1.05 0
AttitudeTowardsObesePeople-7 -0.48 0
AttitudeTowardsObesePeople-8 -0.66 0
AttitudeTowardsObesePeople-9 -0.51 0
variables under investigation: AttitudeTowardsObesePeople1 AttitudeTowardsObesePeople10r AttitudeTowardsObesePeople11r AttitudeTowardsObesePeople12r AttitudeTowardsObesePeople13 AttitudeTowardsObesePeople14r AttitudeTowardsObesePeople15r AttitudeTowardsObesePeople16r AttitudeTowardsObesePeople17 AttitudeTowardsObesePeople18 AttitudeTowardsObesePeople19r AttitudeTowardsObesePeople20r AttitudeTowardsObesePeople2r AttitudeTowardsObesePeople3r AttitudeTowardsObesePeople4r AttitudeTowardsObesePeople5r AttitudeTowardsObesePeople6r AttitudeTowardsObesePeople7 AttitudeTowardsObesePeople8 AttitudeTowardsObesePeople9
Cronbachs Alpha: 0.83 
Parallel analysis suggests that the number of factors = 4 and the number of components = 3
AttTowObPe
Number of components: 3
EFA factor loadings (1 factor solution):
Loadings:
MR1
AttitudeTowardsObesePeople1 0.556
AttitudeTowardsObesePeople10r 0.546
AttitudeTowardsObesePeople11r 0.174
AttitudeTowardsObesePeople12r 0.409
AttitudeTowardsObesePeople13 0.185
AttitudeTowardsObesePeople14r 0.425
AttitudeTowardsObesePeople15r 0.385
AttitudeTowardsObesePeople16r 0.529
AttitudeTowardsObesePeople17 0.419
AttitudeTowardsObesePeople18 0.539
AttitudeTowardsObesePeople19r 0.548
AttitudeTowardsObesePeople20r 0.577
AttitudeTowardsObesePeople2r 0.625
AttitudeTowardsObesePeople3r 0.265
AttitudeTowardsObesePeople4r 0.515
AttitudeTowardsObesePeople5r 0.671
AttitudeTowardsObesePeople6r 0.645
AttitudeTowardsObesePeople7 0.427
AttitudeTowardsObesePeople8 0.336
AttitudeTowardsObesePeople9 0.564
MR1
SS loadings 4.751
Proportion Var 0.238
CFA summary and fit statistics:
lavaan 0.6-19 ended normally after 39 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 40
Number of observations 363
Model Test User Model:
Standard Scaled
Test Statistic 904.749 776.411
Degrees of freedom 170 170
P-value (Chi-square) 0.000 0.000
Scaling correction factor 1.165
Yuan-Bentler correction (Mplus variant)
Model Test Baseline Model:
Test statistic 2012.252 1657.521
Degrees of freedom 190 190
P-value 0.000 0.000
Scaling correction factor 1.214
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.597 0.587
Tucker-Lewis Index (TLI) 0.549 0.538
Robust Comparative Fit Index (CFI) 0.603
Robust Tucker-Lewis Index (TLI) 0.557
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -12035.010 -12035.010
Scaling correction factor 1.149
for the MLR correction
Loglikelihood unrestricted model (H1) -11582.636 -11582.636
Scaling correction factor 1.162
for the MLR correction
Akaike (AIC) 24150.021 24150.021
Bayesian (BIC) 24305.797 24305.797
Sample-size adjusted Bayesian (SABIC) 24178.894 24178.894
Root Mean Square Error of Approximation:
RMSEA 0.109 0.099
90 Percent confidence interval - lower 0.102 0.093
90 Percent confidence interval - upper 0.116 0.106
P-value H_0: RMSEA <= 0.050 0.000 0.000
P-value H_0: RMSEA >= 0.080 1.000 1.000
Robust RMSEA 0.107
90 Percent confidence interval - lower 0.099
90 Percent confidence interval - upper 0.115
P-value H_0: Robust RMSEA <= 0.050 0.000
P-value H_0: Robust RMSEA >= 0.080 1.000
Standardized Root Mean Square Residual:
SRMR 0.113 0.113
Parameter Estimates:
Standard errors Sandwich
Information bread Observed
Observed information based on Hessian
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
AttTowObPe =~
AtttdTwrdsObP1 1.000 0.667 0.495
AtttdTwrdsOP10 1.129 0.254 4.453 0.000 0.753 0.549
AtttdTwrdsOP11 0.403 0.208 1.934 0.053 0.269 0.201
AtttdTwrdsOP12 0.870 0.249 3.498 0.000 0.580 0.432
AtttdTwrdsOP13 0.187 0.167 1.121 0.262 0.125 0.092
AtttdTwrdsOP14 0.883 0.213 4.142 0.000 0.589 0.434
AtttdTwrdsOP15 0.802 0.227 3.537 0.000 0.535 0.397
AtttdTwrdsOP16 1.135 0.230 4.942 0.000 0.757 0.507
AtttdTwrdsOP17 0.635 0.121 5.230 0.000 0.424 0.324
AtttdTwrdsOP18 1.037 0.129 8.016 0.000 0.692 0.466
AtttdTwrdsOP19 1.034 0.218 4.740 0.000 0.690 0.542
AtttdTwrdsOP20 1.271 0.247 5.146 0.000 0.848 0.557
AtttdTwrdsObP2 1.080 0.162 6.651 0.000 0.720 0.576
AtttdTwrdsObP3 0.427 0.128 3.327 0.001 0.285 0.219
AtttdTwrdsObP4 1.170 0.280 4.182 0.000 0.781 0.517
AtttdTwrdsObP5 1.429 0.240 5.965 0.000 0.954 0.652
AtttdTwrdsObP6 1.445 0.289 4.998 0.000 0.964 0.633
AtttdTwrdsObP7 0.722 0.114 6.316 0.000 0.481 0.387
AtttdTwrdsObP8 0.517 0.136 3.815 0.000 0.345 0.263
AtttdTwrdsObP9 0.971 0.110 8.795 0.000 0.648 0.493
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.AtttdTwrdsObP1 1.368 0.148 9.219 0.000 1.368 0.755
.AtttdTwrdsOP10 1.313 0.124 10.582 0.000 1.313 0.698
.AtttdTwrdsOP11 1.707 0.116 14.700 0.000 1.707 0.959
.AtttdTwrdsOP12 1.469 0.127 11.537 0.000 1.469 0.814
.AtttdTwrdsOP13 1.848 0.132 14.010 0.000 1.848 0.992
.AtttdTwrdsOP14 1.494 0.107 13.963 0.000 1.494 0.811
.AtttdTwrdsOP15 1.528 0.129 11.857 0.000 1.528 0.842
.AtttdTwrdsOP16 1.661 0.145 11.491 0.000 1.661 0.743
.AtttdTwrdsOP17 1.532 0.165 9.261 0.000 1.532 0.895
.AtttdTwrdsOP18 1.729 0.193 8.973 0.000 1.729 0.783
.AtttdTwrdsOP19 1.142 0.100 11.452 0.000 1.142 0.706
.AtttdTwrdsOP20 1.602 0.132 12.131 0.000 1.602 0.690
.AtttdTwrdsObP2 1.045 0.090 11.625 0.000 1.045 0.668
.AtttdTwrdsObP3 1.614 0.113 14.257 0.000 1.614 0.952
.AtttdTwrdsObP4 1.671 0.173 9.687 0.000 1.671 0.733
.AtttdTwrdsObP5 1.229 0.104 11.867 0.000 1.229 0.575
.AtttdTwrdsObP6 1.391 0.143 9.705 0.000 1.391 0.599
.AtttdTwrdsObP7 1.317 0.115 11.479 0.000 1.317 0.850
.AtttdTwrdsObP8 1.597 0.135 11.839 0.000 1.597 0.931
.AtttdTwrdsObP9 1.304 0.147 8.879 0.000 1.304 0.756
AttTowObPe 0.445 0.141 3.156 0.002 1.000 1.000
CFA first 6 Modification Indices:
lhs op rhs mi epc
166 AttitudeTowardsObesePeople17 ~~ AttitudeTowardsObesePeople18 70.741 0.744
125 AttitudeTowardsObesePeople13 ~~ AttitudeTowardsObesePeople8 64.390 0.728
231 AttitudeTowardsObesePeople8 ~~ AttitudeTowardsObesePeople9 48.891 0.549
58 AttitudeTowardsObesePeople1 ~~ AttitudeTowardsObesePeople7 47.464 0.508
82 AttitudeTowardsObesePeople11r ~~ AttitudeTowardsObesePeople15r 40.876 0.553
175 AttitudeTowardsObesePeople17 ~~ AttitudeTowardsObesePeople8 34.677 0.491
sepc.lv sepc.all sepc.nox
166 0.744 0.457 0.457
125 0.728 0.424 0.424
231 0.549 0.380 0.380
58 0.508 0.379 0.379
82 0.553 0.342 0.342
175 0.491 0.314 0.314Perceived Causes of Obesity Questionnaires
regEx <- "^PerceivedCausesofObesity"
nameVariable <- "PerCaOb"
sum(str_detect(string = colnames(dat), pattern = regEx))[1] 14tmp_dat <- na.omit(dat[,str_detect(string = colnames(dat), pattern = regEx)])
tmp <- CFAstats(dataset = tmp_dat, regularExp = regEx, labelLatent = str_remove(string = nameVariable, pattern = "mean_"),
showPlots = TRUE,
computeEFA = TRUE,
computeCFA = TRUE,
computeCFAMplus = FALSE)
descriptive statistics:
Mean SD Median CoeffofVariation Minimum Maximun
PerceivedCausesofObesity-1 4.19 0.92 4 0.22 1 5
PerceivedCausesofObesity-10 3.45 1.02 3 0.30 1 5
PerceivedCausesofObesity-11 3.20 1.08 3 0.34 1 5
PerceivedCausesofObesity-12 3.08 1.25 3 0.41 1 5
PerceivedCausesofObesity-13 3.32 1.22 3 0.37 1 5
PerceivedCausesofObesity-14 4.01 1.01 4 0.25 1 5
PerceivedCausesofObesity-2 4.20 0.95 4 0.23 1 5
PerceivedCausesofObesity-3 3.83 1.15 4 0.30 1 5
PerceivedCausesofObesity-4 3.52 1.08 4 0.31 1 5
PerceivedCausesofObesity-5 3.90 1.07 4 0.27 1 5
PerceivedCausesofObesity-6 3.80 1.00 4 0.26 1 5
PerceivedCausesofObesity-7 3.28 1.03 3 0.31 1 5
PerceivedCausesofObesity-8 2.61 1.13 2 0.43 1 5
PerceivedCausesofObesity-9 3.69 1.04 4 0.28 1 5
Lower Quantile Upper Quantile Skewness Kurtosis(-3)
PerceivedCausesofObesity-1 1 5 -1.16 1.10
PerceivedCausesofObesity-10 1 5 -0.26 -0.43
PerceivedCausesofObesity-11 1 5 -0.05 -0.58
PerceivedCausesofObesity-12 1 5 -0.05 -1.05
PerceivedCausesofObesity-13 1 5 -0.35 -0.79
PerceivedCausesofObesity-14 1 5 -0.94 0.37
PerceivedCausesofObesity-2 1 5 -1.26 1.29
PerceivedCausesofObesity-3 1 5 -0.96 0.17
PerceivedCausesofObesity-4 1 5 -0.21 -0.85
PerceivedCausesofObesity-5 1 5 -0.82 -0.06
PerceivedCausesofObesity-6 1 5 -0.54 -0.27
PerceivedCausesofObesity-7 1 5 -0.21 -0.49
PerceivedCausesofObesity-8 1 5 0.40 -0.60
PerceivedCausesofObesity-9 1 5 -0.54 -0.29
KS-Test
PerceivedCausesofObesity-1 0
PerceivedCausesofObesity-10 0
PerceivedCausesofObesity-11 0
PerceivedCausesofObesity-12 0
PerceivedCausesofObesity-13 0
PerceivedCausesofObesity-14 0
PerceivedCausesofObesity-2 0
PerceivedCausesofObesity-3 0
PerceivedCausesofObesity-4 0
PerceivedCausesofObesity-5 0
PerceivedCausesofObesity-6 0
PerceivedCausesofObesity-7 0
PerceivedCausesofObesity-8 0
PerceivedCausesofObesity-9 0
variables under investigation: PerceivedCausesofObesity1 PerceivedCausesofObesity10 PerceivedCausesofObesity11 PerceivedCausesofObesity12 PerceivedCausesofObesity13 PerceivedCausesofObesity14 PerceivedCausesofObesity2 PerceivedCausesofObesity3 PerceivedCausesofObesity4 PerceivedCausesofObesity5 PerceivedCausesofObesity6 PerceivedCausesofObesity7 PerceivedCausesofObesity8 PerceivedCausesofObesity9
Cronbachs Alpha: 0.83 
Parallel analysis suggests that the number of factors = 3 and the number of components = 3
PerCaOb
Number of components: 3
EFA factor loadings (1 factor solution):
Loadings:
MR1
PerceivedCausesofObesity1 0.618
PerceivedCausesofObesity10 0.567
PerceivedCausesofObesity11 0.648
PerceivedCausesofObesity12 0.325
PerceivedCausesofObesity13 0.487
PerceivedCausesofObesity14 0.652
PerceivedCausesofObesity2 0.654
PerceivedCausesofObesity3 0.521
PerceivedCausesofObesity4 0.476
PerceivedCausesofObesity5 0.698
PerceivedCausesofObesity6 0.685
PerceivedCausesofObesity7 0.460
PerceivedCausesofObesity8 0.278
PerceivedCausesofObesity9 0.481
MR1
SS loadings 4.293
Proportion Var 0.307
CFA summary and fit statistics:
lavaan 0.6-19 ended normally after 32 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 28
Number of observations 363
Model Test User Model:
Standard Scaled
Test Statistic 409.044 356.998
Degrees of freedom 77 77
P-value (Chi-square) 0.000 0.000
Scaling correction factor 1.146
Yuan-Bentler correction (Mplus variant)
Model Test Baseline Model:
Test statistic 1361.134 1149.916
Degrees of freedom 91 91
P-value 0.000 0.000
Scaling correction factor 1.184
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.739 0.736
Tucker-Lewis Index (TLI) 0.691 0.688
Robust Comparative Fit Index (CFI) 0.744
Robust Tucker-Lewis Index (TLI) 0.698
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -7044.793 -7044.793
Scaling correction factor 1.152
for the MLR correction
Loglikelihood unrestricted model (H1) -6840.271 -6840.271
Scaling correction factor 1.147
for the MLR correction
Akaike (AIC) 14145.585 14145.585
Bayesian (BIC) 14254.628 14254.628
Sample-size adjusted Bayesian (SABIC) 14165.797 14165.797
Root Mean Square Error of Approximation:
RMSEA 0.109 0.100
90 Percent confidence interval - lower 0.099 0.090
90 Percent confidence interval - upper 0.120 0.110
P-value H_0: RMSEA <= 0.050 0.000 0.000
P-value H_0: RMSEA >= 0.080 1.000 1.000
Robust RMSEA 0.107
90 Percent confidence interval - lower 0.096
90 Percent confidence interval - upper 0.118
P-value H_0: Robust RMSEA <= 0.050 0.000
P-value H_0: Robust RMSEA >= 0.080 1.000
Standardized Root Mean Square Residual:
SRMR 0.086 0.086
Parameter Estimates:
Standard errors Sandwich
Information bread Observed
Observed information based on Hessian
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
PerCaOb =~
PrcvdCssfObst1 1.000 0.535 0.582
PrcvdCssfObs10 1.028 0.218 4.720 0.000 0.550 0.541
PrcvdCssfObs11 1.230 0.222 5.534 0.000 0.658 0.612
PrcvdCssfObs12 0.694 0.189 3.670 0.000 0.371 0.297
PrcvdCssfObs13 1.051 0.168 6.249 0.000 0.563 0.462
PrcvdCssfObs14 1.142 0.138 8.279 0.000 0.611 0.609
PrcvdCssfObst2 1.084 0.114 9.476 0.000 0.580 0.610
PrcvdCssfObst3 0.997 0.117 8.491 0.000 0.533 0.465
PrcvdCssfObst4 0.888 0.236 3.763 0.000 0.475 0.441
PrcvdCssfObst5 1.288 0.169 7.632 0.000 0.689 0.644
PrcvdCssfObst6 1.195 0.172 6.954 0.000 0.640 0.640
PrcvdCssfObst7 0.810 0.176 4.592 0.000 0.433 0.421
PrcvdCssfObst8 0.499 0.159 3.144 0.002 0.267 0.237
PrcvdCssfObst9 0.895 0.095 9.411 0.000 0.479 0.460
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.PrcvdCssfObst1 0.560 0.058 9.731 0.000 0.560 0.662
.PrcvdCssfObs10 0.733 0.072 10.192 0.000 0.733 0.708
.PrcvdCssfObs11 0.725 0.070 10.284 0.000 0.725 0.626
.PrcvdCssfObs12 1.429 0.085 16.791 0.000 1.429 0.912
.PrcvdCssfObs13 1.169 0.089 13.132 0.000 1.169 0.787
.PrcvdCssfObs14 0.635 0.065 9.741 0.000 0.635 0.629
.PrcvdCssfObst2 0.569 0.065 8.718 0.000 0.569 0.628
.PrcvdCssfObst3 1.031 0.104 9.879 0.000 1.031 0.784
.PrcvdCssfObst4 0.933 0.079 11.776 0.000 0.933 0.805
.PrcvdCssfObst5 0.669 0.072 9.259 0.000 0.669 0.585
.PrcvdCssfObst6 0.591 0.054 10.930 0.000 0.591 0.591
.PrcvdCssfObst7 0.871 0.067 12.938 0.000 0.871 0.823
.PrcvdCssfObst8 1.203 0.074 16.359 0.000 1.203 0.944
.PrcvdCssfObst9 0.856 0.076 11.340 0.000 0.856 0.789
PerCaOb 0.286 0.080 3.586 0.000 1.000 1.000
CFA first 6 Modification Indices:
lhs op rhs mi epc
49 PerceivedCausesofObesity10 ~~ PerceivedCausesofObesity4 68.894 0.385
43 PerceivedCausesofObesity10 ~~ PerceivedCausesofObesity11 45.571 0.289
110 PerceivedCausesofObesity4 ~~ PerceivedCausesofObesity9 34.651 -0.291
60 PerceivedCausesofObesity11 ~~ PerceivedCausesofObesity4 29.961 0.258
35 PerceivedCausesofObesity1 ~~ PerceivedCausesofObesity2 25.994 0.171
66 PerceivedCausesofObesity12 ~~ PerceivedCausesofObesity13 21.731 0.328
sepc.lv sepc.all sepc.nox
49 0.385 0.466 0.466
43 0.289 0.396 0.396
110 -0.291 -0.325 -0.325
60 0.258 0.314 0.314
35 0.171 0.303 0.303
66 0.328 0.253 0.253Item Response Theory for “Attitude Towards Obese People Scale”
Factor Loadings (F1) indicate how strongly each item is associated with the latent trait, rule of thumb:
- 0.70 = strong
- 0.40–0.69 = moderate
- < 0.40 = weak
Communality (h²) is the proportion of variance in each item explained by the factor, rule of thumb: + h² > 0.40 → item is well represented + h² < 0.30 → potentially problematic item
# regular expression
regEx <- "^AttitudeTowardsObesePeople"
# Filter variables matching the pattern
irt_items <- dat[, str_detect(colnames(dat), pattern = regEx)]
# Drop rows with missing data (mirt requires complete cases)
irt_items <- na.omit(irt_items)
# Ensure all items are treated as ordered factors
irt_items[] <- lapply(irt_items, function(x) as.numeric(as.character(x)))
# Fit Graded Response Model (1-factor)
mod_grm_1f <- mirt(data = irt_items, model = 1, itemtype = "graded", verbose = FALSE)
# Summarize model
summary(mod_grm_1f) F1 h2
AttitudeTowardsObesePeople-1 0.573 0.3287
AttitudeTowardsObesePeople-10r 0.595 0.3545
AttitudeTowardsObesePeople-11r 0.246 0.0604
AttitudeTowardsObesePeople-12r 0.475 0.2260
AttitudeTowardsObesePeople-13 0.196 0.0383
AttitudeTowardsObesePeople-14r 0.472 0.2223
AttitudeTowardsObesePeople-15r 0.451 0.2034
AttitudeTowardsObesePeople-16r 0.566 0.3209
AttitudeTowardsObesePeople-17 0.423 0.1790
AttitudeTowardsObesePeople-18 0.564 0.3177
AttitudeTowardsObesePeople-19r 0.592 0.3503
AttitudeTowardsObesePeople-20r 0.623 0.3877
AttitudeTowardsObesePeople-2r 0.642 0.4119
AttitudeTowardsObesePeople-3r 0.294 0.0862
AttitudeTowardsObesePeople-4r 0.582 0.3391
AttitudeTowardsObesePeople-5r 0.697 0.4864
AttitudeTowardsObesePeople-6r 0.685 0.4693
AttitudeTowardsObesePeople-7 0.449 0.2017
AttitudeTowardsObesePeople-8 0.351 0.1230
AttitudeTowardsObesePeople-9 0.587 0.3450
SS loadings: 5.451
Proportion Var: 0.273
Factor correlations:
F1
F1 1# Plot Item Characteristic Curves (ICCs) for all items
plot(mod_grm_1f, type = "trace", facet_items = TRUE, main = "Item Characteristic Curves")
# Plot Test Information Curve
plot(mod_grm_1f, type = "info", main = "Test Information Curve: Individualism–Communitarianism")
### compare results to:
cor.plot(r = cor(irt_items))
some items are uninformative (see ICCs)
Compare 1-Factor vs. 2-Factor Models vs. 3-Factor Models:
# mod_grm_2f <- mirt(data = irt_items, model = 2, itemtype = "graded", verbose = FALSE)
# mod_grm_3f <- mirt(data = irt_items, model = 2, itemtype = "graded", verbose = FALSE)
# anova(mod_grm_1f, mod_grm_2f, mod_grm_3f)
# summary(mod_grm_3f)significant p-value (e.g., < .05) supports the X-factor model.
latent class analysis for factor scores
Remark: after scale purification (setting up final CFAs), we could rerun this analyses to get interpretable results
tmp_EFA_overall[[1]]$scores
# options(Mplus_command = "C:/Program Files/Mplus/Mplus.exe")
# getOption("Mplus_command")
## run LCA
setwd("outputs/LCA_factorScores")
if(runMplusLCA){
## add factor scores
dat_with_scores <- cbind(
dat,
tmp_EFA_overall[[1]]$scores
)
LCA_dat <- dat_with_scores[, c("PROLIFIC_PID",
str_subset(string = colnames(dat_with_scores), pattern = "^MR"))]
tmp <- str_subset(string = colnames(LCA_dat), pattern = "^MR")
# tmp <- str_remove_all(string = tmp, pattern = "^A_")
# cat(tmp)
# cat(paste0(tmp, "(", 1:length(tmp), ")"))
colnames(LCA_dat) <- c("ID", tmp)
# prepareMplusData(df = LCA_dat, filename = "LCA_dat.dat")
l = 1
list_lca <- list()
for(i in 2:LCArunsDef){
print(i)
numClasses <- i
LCA_mplus <- mplusObject(
TITLE = paste0("Latent Class Analysis Factor Scores", " c=", numClasses),
VARIABLE =paste0("
usevariables = MR1 MR3 MR8 MR2 MR6 MR5 MR7 MR4;
classes = c(", numClasses, ")"),
ANALYSIS =
"
Type=mixture; ! LCA analysis
STARTS= 500 100;
!LRTstarts=0 0 300 20;
",
PLOT =
"
type = plot3;
series is MR1(1) MR3(2) MR8(3) MR2(4) MR6(5) MR5(6) MR7(7) MR4(8);
",
SAVEDATA = paste0("file = lca_", numClasses, ".txt ;
save = cprob;
format = free;
"),
OUTPUT = "tech11 tech14;", rdata = LCA_dat)
list_lca[[l]] <- mplusModeler(LCA_mplus,
modelout = paste0("lca_FCs", numClasses, ".inp"),
run = 1L)
l = l + 1
}
# comment out to avoid overwriting LCA outputs
saveRDS(list_lca, file="list_lca.rds")
}else{
list_lca <- readRDS("list_lca.rds" )
}get fit statistics LCA:
getLCAfitstatistics(listMplusOutput = list_lca)
Classes LL AIC BIC SABIC CAIC BLRTp VLMRLRTp Entropy
1 2 -3740.371 7530.742 7628.102 7548.788 7653.102 0 0.0000 0.719
2 3 -3673.231 7414.463 7546.872 7439.005 7580.872 0 0.0177 0.812
3 4 -3630.904 7347.809 7515.268 7378.848 7558.267 0 0.4933 0.757
4 5 -3584.367 7272.733 7475.242 7310.269 7527.243 0 0.1766 0.802
5 6 -3553.187 7228.374 7465.933 7272.406 7526.933 0 0.1083 0.832get profile plot:
### number of classes
num_classes <- 5 # index - 1
# Step 1: Extract means
params <- list_lca[[num_classes]]$results$parameters$unstandardized
means_df <- params %>%
filter(paramHeader == "Means" & !grepl("^C#\\d$", param))
# Step 2: Get class proportions
class_counts <- table(list_lca[[num_classes]]$results$savedata$C)
total_n <- sum(class_counts)
class_props <- round(100 * class_counts / total_n, 1)
# Create descriptive labels
class_labels <- paste0("Class ", names(class_counts), " (", class_props, "%)")
# Map class numbers to labels
class_label_map <- setNames(class_labels, paste0("Class ", names(class_counts)))
# Step 3: Prepare data for plotting
means_long <- means_df %>%
mutate(Indicator = param,
Class = paste0("Class ", LatentClass)) %>%
select(Indicator, Class, est) %>%
pivot_wider(names_from = Class, values_from = est) %>%
pivot_longer(cols = starts_with("Class"), names_to = "Class", values_to = "Mean")
# Apply the new labels
means_long$Class <- class_label_map[means_long$Class]
# Optional: Set indicator order
means_long$Indicator <- factor(means_long$Indicator)
# Step 4: Plot
ggplot(means_long, aes(x = Indicator, y = Mean, group = Class, color = Class)) +
geom_line(size = 1) +
geom_point(size = 2) +
theme_minimal() +
labs(title = "Latent Class Profile Plot",
x = "Items",
y = "Estimated Means") +
theme(text = element_text(size = 14),
axis.text.x = element_text(angle = 45, hjust = 1),
legend.title = element_blank())Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
ℹ Please use `linewidth` instead.
class_counts
1 2 3 4 5 6
17 24 139 104 43 36 References
Peng, Roger D., and Elizabeth Matsui. 2016. The Art of Data Science: A Guide for Anyone Who Works with Data. Lulu.com. https://bookdown.org/rdpeng/artofdatascience/.
Wickham, Hadley, and Garrett Grolemund. 2017. R for Data Science: Import, Tidy, Transform, Visualize, and Model Data. "O’Reilly Media, Inc.". https://r4ds.had.co.nz/.
Xie, Yihui, J. J. Allaire, and Garrett Grolemund. 2018. R Markdown: The Definitive Guide. New York: Chapman; Hall/CRC. https://doi.org/10.1201/9781138359444.