CFA - Examples

# Load packages
library(tidyverse)

── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
✔ dplyr     1.2.0     ✔ readr     2.2.0
✔ forcats   1.0.1     ✔ stringr   1.6.0
✔ ggplot2   4.0.2     ✔ tibble    3.3.1
✔ lubridate 1.9.5     ✔ tidyr     1.3.2
✔ purrr     1.2.1     
── 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 errors

library(lavaan)

This is lavaan 0.6-21
lavaan is FREE software! Please report any bugs.

library(dynamic)

Beta version. Please report bugs: https://github.com/melissagwolf/dynamic/issues.

Rosenberg Self-Esteem Scale

The Rosenberg self-esteem scale (Rosenberg, 1989) is a unidimensional scale to assess global self-esteem. It is one of the most commonly used scales in psychology and could therefore serve as a nice illustration of how to assess whether the data fits a single factor model.

It should be noted, however, that apparently there is some controversy whether the scale is actually unifactorial (Donnellan et al., 2016).

The Data

# Load data
items <- read_csv("RSECSV.csv")

Rows: 1127 Columns: 10
── Column specification ────────────────────────────────────────────────────────
Delimiter: ","
dbl (10): R1, R2, R3, R4, R5, R6, R7, R8, R9, R10

ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

# Data preparation
# Replace all -9999 values with NA
items <- mutate(items, across(everything(), ~ na_if(.x, -9999)))

The data was taken from Donnellan et al. (2016), who conducted a study to assess the factorial structure of the RSE. The data consists of nrow(items) participants, who were college students at a public university in the Southwestern United States.

The Model

model <- "
  self_esteem =~ R1 + R2 + R3 + R4 + R5 + R6 + R7 + R8 + R9 + R10
"

fit <- cfa(model = model, data = items, estimator = "MLR")
fitmeasures(fit, 
  fit.measures = c("pvalue", "pvalue.scaled", "srmr", "rmsea", "cfi"))

       pvalue pvalue.scaled          srmr         rmsea           cfi 
        0.000         0.000         0.082         0.165         0.802 

#fit_cutoffs <- cfaOne(fit)

Marsh’s Self-Description Questionnaire

# Load data
marsh <- read_csv("marsh.csv")

Rows: 15661 Columns: 13
── Column specification ────────────────────────────────────────────────────────
Delimiter: ","
dbl (13): Eng1, Eng2, Eng3, Eng4, Math1, Math2, Math3, Math4, Par1, Par2, Pa...

ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

Data for this example is from 15,661 students in 10th grade who participated in the National Education Longitudinal Study of 1988. Items from this scale include:

Parents:

• My parents treat me fairly

• I do not like my parents very much

• I get along well with my parents

• My parents are usually unhappy or disappointed with what I do

• My parents understand me

English

• I learn things quickly in English classes

• English is one of my best subjects

• I get good marks in English

• I’m hopeless in English classes

Mathematics

• Mathematics is one of my best subjects

• I have always done well in mathematics

• I get good marks in mathematics

• I do badly in tests of mathematics

marsh_model <- "
  english =~ Eng1 + Eng2 + Eng3 + Eng4
  math    =~ Math1 + Math2 + Math3 + Math4
  parent  =~ Par1 + Par2 + Par3 + Par4 + Par5
"

marsh_fit <- cfa(model = marsh_model, data = marsh, estimator = "MLR")
fitmeasures(marsh_fit, 
  fit.measures = c("pvalue", "pvalue.scaled", "srmr", "rmsea", "cfi")
)

       pvalue pvalue.scaled          srmr         rmsea           cfi 
        0.000         0.000         0.051         0.083         0.935 

#marsh_fit_cutoffs <- cfaHB(marsh_fit)