In doomlab/learnSEM: Learning Tutorials for Structural Equation Modeling
library(learnr)
library(learnSEM)
knitr::opts_chunk$set(echo = FALSE)
library(lavaan)
library(semPlot)
data(caafidata)
Confirmatory Factor Analysis
This section of the course expands your knowledge of structural equation modeling and lavaan by covering confirmatory factor analysis models (CFA). CFA models are often described as the measurement model, as they are comprised of one of more latent variables and their indicators. You will learn how to create latent variables, analyze using the cfa() function, and summarize those models. You will also be able to compare and decide which models is a better representation of the data. The learning outcomes are:
- Build, analyze, summarize, and diagram a CFA model
- Explore parameter estimates and modification indices
- Compare two nested CFA models
- Learn how to tidy the output from a
lavaan model
CFA Videos
You can use vignette("lecture_cfa", "learnSEM") to view these notes in R.
Exercises
In this next section, you will answer questions using the R code blocks provided. Be sure to use the solution option to see the answer if you need it!
Please enter your name for submission. If you do not need to submit, just type anything you'd like in this box.
question_text(
"Student Name:",
answer("Your Name", correct = TRUE),
incorrect = "Thanks!",
try_again_button = "Modify your answer",
allow_retry = TRUE
)
The Data
The data is provided for you as caafidata, and it has been loaded for you in the background, along with the lavaan and semPlot libraries. The CAAFI was a questionnaire that examined the anxiety, attitudes, and familiarity surrounding computers.
To learn more about the questionnaire, use ?caafidata to bring up the description of the data.
?caafidata
Specify Your Model
In this section, we will specify two models. First, we will create a one-factor model of the CAAFI as a comparison for our theoretical model. The one-factor model includes all items on one latent variable, which would represent "computers" or a basic response to computers.
Create the lavaan model code for the one-factor model below, and name it one.model. While we have used ~ for regressions, remember that latent variables are created with =~. You should call your latent variable computer to match the solution. You can put the items in any order for the code, and the solution organizes them by proposed factor for the three-factor solution.
one.model <- '
computer =~ q3 + q13 + q14 + q16 + q20 + q21 + q22 + q23 + q27 + q30 + q1 + q2 + q4 + q5 + q8 + q11 + q18 + q19 + q28 + q29 + q6 + q7 + q9 + q10 + q12 + q15 + q17 + q24 + q25 + q26
'
Next, we will create the model for the three-factor solution. In this model, we propose that there are three facets to interacting with computers (albeit, this scale is nearly 20 years old!): anxiety, attitudes, and familiarity. Here's how the scale should break down:
- Computer Familiarity: Items 3, 13-14, 16, 20-23, 27, and 30.
- Computer Attitudes: Items 1-2, 4-5, 8, 11, 18-19, and 28-29.
- Computer Aversion: Items 6-7, 9-10, 12, 15, 17, and 24-26.
Below, create the three.model code. You should name your three factors: familiar, attitudes, and aversion to match the solution. You can put the latent variables and items in any order, as long as they match up to the right latent variable!
three.model <- '
familiar =~ q3 + q13 + q14 + q16 + q20 + q21 + q22 + q23 + q27 + q30
attitudes =~ q1 + q2 + q4 + q5 + q8 + q11 + q18 + q19 + q28 + q29
aversion =~ q6 + q7 + q9 + q10 + q12 + q15 + q17 + q24 + q25 + q26
'
Analyze the Model
Analyze your one-factor model using the cfa() function, and name the output one.fit. In this same exercise, analyze your three-factor model, and name the output three.fit.
one.model <- '
computer =~ q3 + q13 + q14 + q16 + q20 + q21 + q22 + q23 + q27 + q30 + q1 + q2 + q4 + q5 + q8 + q11 + q18 + q19 + q28 + q29 + q6 + q7 + q9 + q10 + q12 + q15 + q17 + q24 + q25 + q26
'
three.model <- '
familiar =~ q3 + q13 + q14 + q16 + q20 + q21 + q22 + q23 + q27 + q30
attitudes =~ q1 + q2 + q4 + q5 + q8 + q11 + q18 + q19 + q28 + q29
aversion =~ q6 + q7 + q9 + q10 + q12 + q15 + q17 + q24 + q25 + q26
'
one.fit <- cfa(one.model, data = caafidata)
three.fit <- cfa(three.model, data = caafidata)
Summarize Your Model
Let's summarize the two models you just created. Use the summary() function on both models with the standardized solution, rsquare values, and fit.measures all included.
You will see a lot of output! We will learn in a few exercises how to "tidy" that output and examine some of the individual pages separately. This exercise is just a reminder of the steps: build, analyze, summarize, and ... diagram is next.
one.model <- '
computer =~ q3 + q13 + q14 + q16 + q20 + q21 + q22 + q23 + q27 + q30 + q1 + q2 + q4 + q5 + q8 + q11 + q18 + q19 + q28 + q29 + q6 + q7 + q9 + q10 + q12 + q15 + q17 + q24 + q25 + q26
'
three.model <- '
familiar =~ q3 + q13 + q14 + q16 + q20 + q21 + q22 + q23 + q27 + q30
attitudes =~ q1 + q2 + q4 + q5 + q8 + q11 + q18 + q19 + q28 + q29
aversion =~ q6 + q7 + q9 + q10 + q12 + q15 + q17 + q24 + q25 + q26
'
one.fit <- cfa(one.model, data = caafidata)
three.fit <- cfa(three.model, data = caafidata)
summary(one.fit,
standardized = TRUE,
rsquare = TRUE,
fit.measures = TRUE)
summary(three.fit,
standardized = TRUE,
rsquare = TRUE,
fit.measures = TRUE)
Create a Picture
Use semPaths() to create a picture of your three-factor model. Use std for the whatLabels argument, any layout you would like, and edge.label.cex = 1 to increase the font size. We will also add the what and edge.color arguments to help us understand how to visually depict the strengths of the loadings for the model.
one.model <- '
computer =~ q3 + q13 + q14 + q16 + q20 + q21 + q22 + q23 + q27 + q30 + q1 + q2 + q4 + q5 + q8 + q11 + q18 + q19 + q28 + q29 + q6 + q7 + q9 + q10 + q12 + q15 + q17 + q24 + q25 + q26
'
three.model <- '
familiar =~ q3 + q13 + q14 + q16 + q20 + q21 + q22 + q23 + q27 + q30
attitudes =~ q1 + q2 + q4 + q5 + q8 + q11 + q18 + q19 + q28 + q29
aversion =~ q6 + q7 + q9 + q10 + q12 + q15 + q17 + q24 + q25 + q26
'
one.fit <- cfa(one.model, data = caafidata)
three.fit <- cfa(three.model, data = caafidata)
semPaths(three.fit,
whatLabels = "std",
layout = "spring",
edge.label.cex = 1,
what = "std",
edge.color = "blue")
Model Comparison
Use the anova() function to compare the models directly using the chi-square difference test. Include the fitmeasures() of aic and ecvi to show the non-nested model comparison.
one.model <- '
computer =~ q3 + q13 + q14 + q16 + q20 + q21 + q22 + q23 + q27 + q30 + q1 + q2 + q4 + q5 + q8 + q11 + q18 + q19 + q28 + q29 + q6 + q7 + q9 + q10 + q12 + q15 + q17 + q24 + q25 + q26
'
three.model <- '
familiar =~ q3 + q13 + q14 + q16 + q20 + q21 + q22 + q23 + q27 + q30
attitudes =~ q1 + q2 + q4 + q5 + q8 + q11 + q18 + q19 + q28 + q29
aversion =~ q6 + q7 + q9 + q10 + q12 + q15 + q17 + q24 + q25 + q26
'
one.fit <- cfa(one.model, data = caafidata)
three.fit <- cfa(three.model, data = caafidata)
anova(one.fit, three.fit)
fitmeasures(one.fit, c("aic", "ecvi"))
fitmeasures(three.fit, c("aic", "ecvi"))
question_text(
"Which model is better? ",
answer("The three factor model.", correct = TRUE),
incorrect = "You should find the model with the lower AIC and ECVI (three-factor).",
try_again_button = "Modify your answer",
allow_retry = TRUE
)
Clean Output
We can use parameterestimates() to create a data frame of the parameter estimates and their confidence intervals. However, there are a few other packages that also make cleaning up parameters and fit indices easy.
In this exercise, load the parameters library. Use the model_parameters() function to print out the standardized estimates for the three-factor model. In this exercise, it will print as a nice table, but if you use this code in a markdown document, it will automatically format the parameters as a table in markdown style.
If you like tibbles better than data frames, you can use the broom library to print out the parameter estimates using the tidy() function. Each are equally useful, as it may depend on what you would like do with the parameters which one you want to use. The parameters library output may be a bit easier to read for the open questions below.
one.model <- '
computer =~ q3 + q13 + q14 + q16 + q20 + q21 + q22 + q23 + q27 + q30 + q1 + q2 + q4 + q5 + q8 + q11 + q18 + q19 + q28 + q29 + q6 + q7 + q9 + q10 + q12 + q15 + q17 + q24 + q25 + q26
'
three.model <- '
familiar =~ q3 + q13 + q14 + q16 + q20 + q21 + q22 + q23 + q27 + q30
attitudes =~ q1 + q2 + q4 + q5 + q8 + q11 + q18 + q19 + q28 + q29
aversion =~ q6 + q7 + q9 + q10 + q12 + q15 + q17 + q24 + q25 + q26
'
one.fit <- cfa(one.model, data = caafidata)
three.fit <- cfa(three.model, data = caafidata)
library(parameters)
model_parameters(three.fit, standardize = TRUE)
#or
library(broom)
tidy(three.fit)
question_text(
"Look at the parameters shown in your table. Which item has the lowest relationship to its latent variable using the standardized solution?",
answer("Question 19", correct = TRUE),
incorrect = "Question 19 on our attitudes scale is the lowest at .37.",
try_again_button = "Modify your answer",
allow_retry = TRUE
)
question_text(
"Looking at the correlation table, do you think these are three separate factors?",
answer("The correlation between attitudes and aversion is high at .74 but otherwise these seem separate from familarity.", correct = TRUE),
incorrect = "The correlation between attitudes and aversion is high at .74 but otherwise these seem separate from familarity.",
try_again_button = "Modify your answer",
allow_retry = TRUE
)
Modifications
Now that we've decided the three-factor model is a better model, let's examine for potential modification indices. Be sure to use the sort option to see the strongest modification indices.
one.model <- '
computer =~ q3 + q13 + q14 + q16 + q20 + q21 + q22 + q23 + q27 + q30 + q1 + q2 + q4 + q5 + q8 + q11 + q18 + q19 + q28 + q29 + q6 + q7 + q9 + q10 + q12 + q15 + q17 + q24 + q25 + q26
'
three.model <- '
familiar =~ q3 + q13 + q14 + q16 + q20 + q21 + q22 + q23 + q27 + q30
attitudes =~ q1 + q2 + q4 + q5 + q8 + q11 + q18 + q19 + q28 + q29
aversion =~ q6 + q7 + q9 + q10 + q12 + q15 + q17 + q24 + q25 + q26
'
one.fit <- cfa(one.model, data = caafidata)
three.fit <- cfa(three.model, data = caafidata)
modificationindices(three.fit, sort = T)
- Computer Familiarity: Items 3, 13-14, 16, 20-23, 27, and 30.
- Computer Attitudes: Items 1-2, 4-5, 8, 11, 18-19, and 28-29.
- Computer Aversion: Items 6-7, 9-10, 12, 15, 17, and 24-26.
question_text(
"Given the relationship between the latent variables and the measured variables, which modification might you suggest adding?",
answer("Question 14 and 23 are the highest modification, and they are both on the familiarity scale.", correct = TRUE),
incorrect = "Question 14 and 23 are the highest modification, and they are both on the familiarity scale.",
try_again_button = "Modify your answer",
allow_retry = TRUE
)
Submit
On this page, you will create the submission for your instructor (if necessary). Please copy this report and submit using a Word document or paste into the text window of your submission page. Click "Generate Submission" to get your work!
encoder_logic()
encoder_ui()
doomlab/learnSEM documentation built on Jan. 25, 2024, 2 p.m.
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
library(learnr) library(learnSEM) knitr::opts_chunk$set(echo = FALSE) library(lavaan) library(semPlot) data(caafidata)
Confirmatory Factor Analysis
This section of the course expands your knowledge of structural equation modeling and lavaan by covering confirmatory factor analysis models (CFA). CFA models are often described as the measurement model, as they are comprised of one of more latent variables and their indicators. You will learn how to create latent variables, analyze using the cfa() function, and summarize those models. You will also be able to compare and decide which models is a better representation of the data. The learning outcomes are:
- Build, analyze, summarize, and diagram a CFA model
- Explore parameter estimates and modification indices
- Compare two nested CFA models
- Learn how to tidy the output from a
lavaanmodel
CFA Videos
You can use vignette("lecture_cfa", "learnSEM") to view these notes in R.
Exercises
In this next section, you will answer questions using the R code blocks provided. Be sure to use the solution option to see the answer if you need it!
Please enter your name for submission. If you do not need to submit, just type anything you'd like in this box.
question_text( "Student Name:", answer("Your Name", correct = TRUE), incorrect = "Thanks!", try_again_button = "Modify your answer", allow_retry = TRUE )
The Data
The data is provided for you as caafidata, and it has been loaded for you in the background, along with the lavaan and semPlot libraries. The CAAFI was a questionnaire that examined the anxiety, attitudes, and familiarity surrounding computers.
To learn more about the questionnaire, use ?caafidata to bring up the description of the data.
?caafidata
Specify Your Model
In this section, we will specify two models. First, we will create a one-factor model of the CAAFI as a comparison for our theoretical model. The one-factor model includes all items on one latent variable, which would represent "computers" or a basic response to computers.
Create the lavaan model code for the one-factor model below, and name it one.model. While we have used ~ for regressions, remember that latent variables are created with =~. You should call your latent variable computer to match the solution. You can put the items in any order for the code, and the solution organizes them by proposed factor for the three-factor solution.
one.model <- ' computer =~ q3 + q13 + q14 + q16 + q20 + q21 + q22 + q23 + q27 + q30 + q1 + q2 + q4 + q5 + q8 + q11 + q18 + q19 + q28 + q29 + q6 + q7 + q9 + q10 + q12 + q15 + q17 + q24 + q25 + q26 '
Next, we will create the model for the three-factor solution. In this model, we propose that there are three facets to interacting with computers (albeit, this scale is nearly 20 years old!): anxiety, attitudes, and familiarity. Here's how the scale should break down:
- Computer Familiarity: Items 3, 13-14, 16, 20-23, 27, and 30.
- Computer Attitudes: Items 1-2, 4-5, 8, 11, 18-19, and 28-29.
- Computer Aversion: Items 6-7, 9-10, 12, 15, 17, and 24-26.
Below, create the three.model code. You should name your three factors: familiar, attitudes, and aversion to match the solution. You can put the latent variables and items in any order, as long as they match up to the right latent variable!
three.model <- ' familiar =~ q3 + q13 + q14 + q16 + q20 + q21 + q22 + q23 + q27 + q30 attitudes =~ q1 + q2 + q4 + q5 + q8 + q11 + q18 + q19 + q28 + q29 aversion =~ q6 + q7 + q9 + q10 + q12 + q15 + q17 + q24 + q25 + q26 '
Analyze the Model
Analyze your one-factor model using the cfa() function, and name the output one.fit. In this same exercise, analyze your three-factor model, and name the output three.fit.
one.model <- ' computer =~ q3 + q13 + q14 + q16 + q20 + q21 + q22 + q23 + q27 + q30 + q1 + q2 + q4 + q5 + q8 + q11 + q18 + q19 + q28 + q29 + q6 + q7 + q9 + q10 + q12 + q15 + q17 + q24 + q25 + q26 ' three.model <- ' familiar =~ q3 + q13 + q14 + q16 + q20 + q21 + q22 + q23 + q27 + q30 attitudes =~ q1 + q2 + q4 + q5 + q8 + q11 + q18 + q19 + q28 + q29 aversion =~ q6 + q7 + q9 + q10 + q12 + q15 + q17 + q24 + q25 + q26 '
one.fit <- cfa(one.model, data = caafidata) three.fit <- cfa(three.model, data = caafidata)
Summarize Your Model
Let's summarize the two models you just created. Use the summary() function on both models with the standardized solution, rsquare values, and fit.measures all included.
You will see a lot of output! We will learn in a few exercises how to "tidy" that output and examine some of the individual pages separately. This exercise is just a reminder of the steps: build, analyze, summarize, and ... diagram is next.
one.model <- ' computer =~ q3 + q13 + q14 + q16 + q20 + q21 + q22 + q23 + q27 + q30 + q1 + q2 + q4 + q5 + q8 + q11 + q18 + q19 + q28 + q29 + q6 + q7 + q9 + q10 + q12 + q15 + q17 + q24 + q25 + q26 ' three.model <- ' familiar =~ q3 + q13 + q14 + q16 + q20 + q21 + q22 + q23 + q27 + q30 attitudes =~ q1 + q2 + q4 + q5 + q8 + q11 + q18 + q19 + q28 + q29 aversion =~ q6 + q7 + q9 + q10 + q12 + q15 + q17 + q24 + q25 + q26 ' one.fit <- cfa(one.model, data = caafidata) three.fit <- cfa(three.model, data = caafidata)
summary(one.fit, standardized = TRUE, rsquare = TRUE, fit.measures = TRUE) summary(three.fit, standardized = TRUE, rsquare = TRUE, fit.measures = TRUE)
Create a Picture
Use semPaths() to create a picture of your three-factor model. Use std for the whatLabels argument, any layout you would like, and edge.label.cex = 1 to increase the font size. We will also add the what and edge.color arguments to help us understand how to visually depict the strengths of the loadings for the model.
one.model <- ' computer =~ q3 + q13 + q14 + q16 + q20 + q21 + q22 + q23 + q27 + q30 + q1 + q2 + q4 + q5 + q8 + q11 + q18 + q19 + q28 + q29 + q6 + q7 + q9 + q10 + q12 + q15 + q17 + q24 + q25 + q26 ' three.model <- ' familiar =~ q3 + q13 + q14 + q16 + q20 + q21 + q22 + q23 + q27 + q30 attitudes =~ q1 + q2 + q4 + q5 + q8 + q11 + q18 + q19 + q28 + q29 aversion =~ q6 + q7 + q9 + q10 + q12 + q15 + q17 + q24 + q25 + q26 ' one.fit <- cfa(one.model, data = caafidata) three.fit <- cfa(three.model, data = caafidata)
semPaths(three.fit, whatLabels = "std", layout = "spring", edge.label.cex = 1, what = "std", edge.color = "blue")
Model Comparison
Use the anova() function to compare the models directly using the chi-square difference test. Include the fitmeasures() of aic and ecvi to show the non-nested model comparison.
one.model <- ' computer =~ q3 + q13 + q14 + q16 + q20 + q21 + q22 + q23 + q27 + q30 + q1 + q2 + q4 + q5 + q8 + q11 + q18 + q19 + q28 + q29 + q6 + q7 + q9 + q10 + q12 + q15 + q17 + q24 + q25 + q26 ' three.model <- ' familiar =~ q3 + q13 + q14 + q16 + q20 + q21 + q22 + q23 + q27 + q30 attitudes =~ q1 + q2 + q4 + q5 + q8 + q11 + q18 + q19 + q28 + q29 aversion =~ q6 + q7 + q9 + q10 + q12 + q15 + q17 + q24 + q25 + q26 ' one.fit <- cfa(one.model, data = caafidata) three.fit <- cfa(three.model, data = caafidata)
anova(one.fit, three.fit) fitmeasures(one.fit, c("aic", "ecvi")) fitmeasures(three.fit, c("aic", "ecvi"))
question_text( "Which model is better? ", answer("The three factor model.", correct = TRUE), incorrect = "You should find the model with the lower AIC and ECVI (three-factor).", try_again_button = "Modify your answer", allow_retry = TRUE )
Clean Output
We can use parameterestimates() to create a data frame of the parameter estimates and their confidence intervals. However, there are a few other packages that also make cleaning up parameters and fit indices easy.
In this exercise, load the parameters library. Use the model_parameters() function to print out the standardized estimates for the three-factor model. In this exercise, it will print as a nice table, but if you use this code in a markdown document, it will automatically format the parameters as a table in markdown style.
If you like tibbles better than data frames, you can use the broom library to print out the parameter estimates using the tidy() function. Each are equally useful, as it may depend on what you would like do with the parameters which one you want to use. The parameters library output may be a bit easier to read for the open questions below.
one.model <- ' computer =~ q3 + q13 + q14 + q16 + q20 + q21 + q22 + q23 + q27 + q30 + q1 + q2 + q4 + q5 + q8 + q11 + q18 + q19 + q28 + q29 + q6 + q7 + q9 + q10 + q12 + q15 + q17 + q24 + q25 + q26 ' three.model <- ' familiar =~ q3 + q13 + q14 + q16 + q20 + q21 + q22 + q23 + q27 + q30 attitudes =~ q1 + q2 + q4 + q5 + q8 + q11 + q18 + q19 + q28 + q29 aversion =~ q6 + q7 + q9 + q10 + q12 + q15 + q17 + q24 + q25 + q26 ' one.fit <- cfa(one.model, data = caafidata) three.fit <- cfa(three.model, data = caafidata)
library(parameters) model_parameters(three.fit, standardize = TRUE) #or library(broom) tidy(three.fit)
question_text( "Look at the parameters shown in your table. Which item has the lowest relationship to its latent variable using the standardized solution?", answer("Question 19", correct = TRUE), incorrect = "Question 19 on our attitudes scale is the lowest at .37.", try_again_button = "Modify your answer", allow_retry = TRUE )
question_text( "Looking at the correlation table, do you think these are three separate factors?", answer("The correlation between attitudes and aversion is high at .74 but otherwise these seem separate from familarity.", correct = TRUE), incorrect = "The correlation between attitudes and aversion is high at .74 but otherwise these seem separate from familarity.", try_again_button = "Modify your answer", allow_retry = TRUE )
Modifications
Now that we've decided the three-factor model is a better model, let's examine for potential modification indices. Be sure to use the sort option to see the strongest modification indices.
one.model <- ' computer =~ q3 + q13 + q14 + q16 + q20 + q21 + q22 + q23 + q27 + q30 + q1 + q2 + q4 + q5 + q8 + q11 + q18 + q19 + q28 + q29 + q6 + q7 + q9 + q10 + q12 + q15 + q17 + q24 + q25 + q26 ' three.model <- ' familiar =~ q3 + q13 + q14 + q16 + q20 + q21 + q22 + q23 + q27 + q30 attitudes =~ q1 + q2 + q4 + q5 + q8 + q11 + q18 + q19 + q28 + q29 aversion =~ q6 + q7 + q9 + q10 + q12 + q15 + q17 + q24 + q25 + q26 ' one.fit <- cfa(one.model, data = caafidata) three.fit <- cfa(three.model, data = caafidata)
modificationindices(three.fit, sort = T)
- Computer Familiarity: Items 3, 13-14, 16, 20-23, 27, and 30.
- Computer Attitudes: Items 1-2, 4-5, 8, 11, 18-19, and 28-29.
- Computer Aversion: Items 6-7, 9-10, 12, 15, 17, and 24-26.
question_text( "Given the relationship between the latent variables and the measured variables, which modification might you suggest adding?", answer("Question 14 and 23 are the highest modification, and they are both on the familiarity scale.", correct = TRUE), incorrect = "Question 14 and 23 are the highest modification, and they are both on the familiarity scale.", try_again_button = "Modify your answer", allow_retry = TRUE )
Submit
On this page, you will create the submission for your instructor (if necessary). Please copy this report and submit using a Word document or paste into the text window of your submission page. Click "Generate Submission" to get your work!
encoder_logic()
encoder_ui()
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