In doomlab/learnSEM: Learning Tutorials for Structural Equation Modeling
library(learnr)
library(learnSEM)
knitr::opts_chunk$set(echo = FALSE)
library(lavaan)
library(semPlot)
university.cov <- lav_matrix_lower2full(
c(169.00,
73.710, 182.2500,
73.229, 88.4250, 171.6100,
63.375, 72.5625, 127.7250, 156.2500,
42.120, 67.4325, 122.0265, 123.1875, 182.2500,
57.226, 63.2610, 117.1926, 154.4250, 138.0240, 201.6400,
30.875, 32.0625, 60.9805, 62.9375, 76.9500, 79.5910, 90.2500,
36.075, 38.9610, 61.0722, 58.2750, 65.9340, 70.9290, 81.1965, 123.2100,
18.096, 21.1410, 26.2131, 39.1500, 44.6310, 46.9452, 48.7635, 56.0106, 75.6900))
rownames(university.cov) <-
colnames(university.cov) <-
c("class", "social", "learn", "chronic", "physical", "sex",
"depression", "anxiety", "stress")
Full Structural Equation Models
This section of the course increases your skills by expanding from measurement models and CFA to full structural models. We will begin to use the latent variables to predict each other or add other covariates to predict the measurement models. You will use the sem() function and learn more about how to write lavaan code for composite variables. The learning outcomes are:
- Build, analyze, summarize, and diagram a full structural equation model
- Learn specific composite variable code
- Troubleshoot Heywood cases in these models
Full SEM Videos
You can use vignette("lecture_sem", "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 below, and it has been loaded for you in the background, along with the lavaan and semPlot libraries. The data contains:
- University composite (formative):
- Class - perception of the way school work, classes, grades, and other related academic goals are going for a student.
- Social - perception of social networks, friendships, support systems, and connectedness on campus.
- Learning - perception of student's happiness with the learning environment on campus (professors, academic support, fit with major, etc.).
- Psychological factor (reflexive):
- Depression
- Anxiety
- Stress
- Health factor (reflexive):
- Chronic health issues
- Physical fitness and active health
- Sexual health
The data is called university.cov, and we will use n = 300 for our model.
university.cov <- lav_matrix_lower2full(
c(169.00,
73.710, 182.2500,
73.229, 88.4250, 171.6100,
63.375, 72.5625, 127.7250, 156.2500,
42.120, 67.4325, 122.0265, 123.1875, 182.2500,
57.226, 63.2610, 117.1926, 154.4250, 138.0240, 201.6400,
30.875, 32.0625, 60.9805, 62.9375, 76.9500, 79.5910, 90.2500,
36.075, 38.9610, 61.0722, 58.2750, 65.9340, 70.9290, 81.1965, 123.2100,
18.096, 21.1410, 26.2131, 39.1500, 44.6310, 46.9452, 48.7635, 56.0106, 75.6900))
rownames(university.cov) <-
colnames(university.cov) <-
c("class", "social", "learn", "chronic", "physical", "sex",
"depression", "anxiety", "stress")
Specify Your Model
In this section, we will specific our overall composite.model by creating three latent variables for our measurement model:
University: class, social, learn as a composite variableHealth: chronic, physical, sex as a reflexive variablePsychology: depression, anxiety, stress as a reflexive variable
The structural model should include the university composite predicting both the psychological and health factors. We expect that as university perception changes, changes in mental and physical health symptoms should exist as well. Note: all variables have been scaled so that high scores are negative indicators.
composite.model <- '
University <~ class + social + learn
Health =~ chronic + physical + sex
Psychology =~ depression + anxiety + stress
Psychology ~ University
Health ~ University
'
Analyze the Model
Analyze your composite.model using the sem() function, and name the output composite.fit. There are 300 participants in the dataset. Remember the data name is university.cov, which is a covariance table.
composite.model <- '
University <~ class + social + learn
Health =~ chronic + physical + sex
Psychology =~ depression + anxiety + stress
Psychology ~ University
Health ~ University
'
composite.fit <- sem(model = composite.model,
sample.cov = university.cov,
sample.nobs = 300)
Oh no! Your model says it is not identified. What should you do? In this case, we have to remember that the entire model has to be identified. Let's look at a picture to see where that might be:
composite.model <- '
University <~ class + social + learn
Health =~ chronic + physical + sex
Psychology =~ depression + anxiety + stress
Psychology ~ University
Health ~ University
'
composite.fit <- sem(model = composite.model,
sample.cov = university.cov,
sample.nobs = 300)
semPaths(composite.fit,
whatLabels = "std",
layout = "spring",
edge.label.cex = 1)
Because University is predicting only Psychology and Health, we have two regression paths that act like a small measurement model for University. The identification for this section is not met, so we need to set them equal to each other or create a marker variable to control for these paths. The easiest solution is to set University =~ Psychology + Health rather than set two separate regressions. Rerun your composite.fit to make sure you do not get an error.
composite.model <- '
University <~ class + social + learn
Health =~ chronic + physical + sex
Psychology =~ depression + anxiety + stress
University =~ Psychology + Health
'
composite.model <- '
University <~ class + social + learn
Health =~ chronic + physical + sex
Psychology =~ depression + anxiety + stress
University =~ Psychology + Health
'
composite.fit <- sem(model = composite.model,
sample.cov = university.cov,
sample.nobs = 300)
Summarize Your Model
Let's summarize the final model you just created. Use the summary() function on both models with the standardized solution, r-square values, and fit.measures all included.
composite.model <- '
University <~ class + social + learn
Health =~ chronic + physical + sex
Psychology =~ depression + anxiety + stress
University =~ Psychology + Health
'
composite.fit <- sem(model = composite.model,
sample.cov = university.cov,
sample.nobs = 300)
summary(composite.fit,
standardized = TRUE,
rsquare = TRUE,
fit.measures = TRUE)
question_text(
"Look at the solution of the final model and describe that model. Do all of the items load with their latent variable? Does university appear to predict psychological and health factors?",
answer("Lots of right answers.", correct = TRUE),
incorrect = "Be sure to detail your answer! It appears that psychological and health items load on their latent, but the university latent is not a very good composite. Additionally, the university variable does predict the other two latents but it's likely driven by the learning environment which is related to the university variable.",
try_again_button = "Modify your answer",
allow_retry = TRUE
)
Create a Picture
Use semPaths() to create a picture of your full structural model. Use std for the whatLabels argument, any layout you would like, and edge.label.cex = 1 to increase the font size.
composite.model <- '
University <~ class + social + learn
Health =~ chronic + physical + sex
Psychology =~ depression + anxiety + stress
University =~ Psychology + Health
'
composite.fit <- sem(model = composite.model,
sample.cov = university.cov,
sample.nobs = 300)
semPaths(composite.fit,
whatLabels = "std",
layout = "spring",
edge.label.cex = 1)
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) university.cov <- lav_matrix_lower2full( c(169.00, 73.710, 182.2500, 73.229, 88.4250, 171.6100, 63.375, 72.5625, 127.7250, 156.2500, 42.120, 67.4325, 122.0265, 123.1875, 182.2500, 57.226, 63.2610, 117.1926, 154.4250, 138.0240, 201.6400, 30.875, 32.0625, 60.9805, 62.9375, 76.9500, 79.5910, 90.2500, 36.075, 38.9610, 61.0722, 58.2750, 65.9340, 70.9290, 81.1965, 123.2100, 18.096, 21.1410, 26.2131, 39.1500, 44.6310, 46.9452, 48.7635, 56.0106, 75.6900)) rownames(university.cov) <- colnames(university.cov) <- c("class", "social", "learn", "chronic", "physical", "sex", "depression", "anxiety", "stress")
Full Structural Equation Models
This section of the course increases your skills by expanding from measurement models and CFA to full structural models. We will begin to use the latent variables to predict each other or add other covariates to predict the measurement models. You will use the sem() function and learn more about how to write lavaan code for composite variables. The learning outcomes are:
- Build, analyze, summarize, and diagram a full structural equation model
- Learn specific composite variable code
- Troubleshoot Heywood cases in these models
Full SEM Videos
You can use vignette("lecture_sem", "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 below, and it has been loaded for you in the background, along with the lavaan and semPlot libraries. The data contains:
- University composite (formative):
- Class - perception of the way school work, classes, grades, and other related academic goals are going for a student.
- Social - perception of social networks, friendships, support systems, and connectedness on campus.
- Learning - perception of student's happiness with the learning environment on campus (professors, academic support, fit with major, etc.).
- Psychological factor (reflexive):
- Depression
- Anxiety
- Stress
- Health factor (reflexive):
- Chronic health issues
- Physical fitness and active health
- Sexual health
The data is called university.cov, and we will use n = 300 for our model.
university.cov <- lav_matrix_lower2full( c(169.00, 73.710, 182.2500, 73.229, 88.4250, 171.6100, 63.375, 72.5625, 127.7250, 156.2500, 42.120, 67.4325, 122.0265, 123.1875, 182.2500, 57.226, 63.2610, 117.1926, 154.4250, 138.0240, 201.6400, 30.875, 32.0625, 60.9805, 62.9375, 76.9500, 79.5910, 90.2500, 36.075, 38.9610, 61.0722, 58.2750, 65.9340, 70.9290, 81.1965, 123.2100, 18.096, 21.1410, 26.2131, 39.1500, 44.6310, 46.9452, 48.7635, 56.0106, 75.6900)) rownames(university.cov) <- colnames(university.cov) <- c("class", "social", "learn", "chronic", "physical", "sex", "depression", "anxiety", "stress")
Specify Your Model
In this section, we will specific our overall composite.model by creating three latent variables for our measurement model:
University: class, social, learn as a composite variableHealth: chronic, physical, sex as a reflexive variablePsychology: depression, anxiety, stress as a reflexive variable
The structural model should include the university composite predicting both the psychological and health factors. We expect that as university perception changes, changes in mental and physical health symptoms should exist as well. Note: all variables have been scaled so that high scores are negative indicators.
composite.model <- ' University <~ class + social + learn Health =~ chronic + physical + sex Psychology =~ depression + anxiety + stress Psychology ~ University Health ~ University '
Analyze the Model
Analyze your composite.model using the sem() function, and name the output composite.fit. There are 300 participants in the dataset. Remember the data name is university.cov, which is a covariance table.
composite.model <- ' University <~ class + social + learn Health =~ chronic + physical + sex Psychology =~ depression + anxiety + stress Psychology ~ University Health ~ University '
composite.fit <- sem(model = composite.model, sample.cov = university.cov, sample.nobs = 300)
Oh no! Your model says it is not identified. What should you do? In this case, we have to remember that the entire model has to be identified. Let's look at a picture to see where that might be:
composite.model <- ' University <~ class + social + learn Health =~ chronic + physical + sex Psychology =~ depression + anxiety + stress Psychology ~ University Health ~ University ' composite.fit <- sem(model = composite.model, sample.cov = university.cov, sample.nobs = 300) semPaths(composite.fit, whatLabels = "std", layout = "spring", edge.label.cex = 1)
Because University is predicting only Psychology and Health, we have two regression paths that act like a small measurement model for University. The identification for this section is not met, so we need to set them equal to each other or create a marker variable to control for these paths. The easiest solution is to set University =~ Psychology + Health rather than set two separate regressions. Rerun your composite.fit to make sure you do not get an error.
composite.model <- ' University <~ class + social + learn Health =~ chronic + physical + sex Psychology =~ depression + anxiety + stress University =~ Psychology + Health '
composite.model <- ' University <~ class + social + learn Health =~ chronic + physical + sex Psychology =~ depression + anxiety + stress University =~ Psychology + Health '
composite.fit <- sem(model = composite.model, sample.cov = university.cov, sample.nobs = 300)
Summarize Your Model
Let's summarize the final model you just created. Use the summary() function on both models with the standardized solution, r-square values, and fit.measures all included.
composite.model <- ' University <~ class + social + learn Health =~ chronic + physical + sex Psychology =~ depression + anxiety + stress University =~ Psychology + Health ' composite.fit <- sem(model = composite.model, sample.cov = university.cov, sample.nobs = 300)
summary(composite.fit, standardized = TRUE, rsquare = TRUE, fit.measures = TRUE)
question_text( "Look at the solution of the final model and describe that model. Do all of the items load with their latent variable? Does university appear to predict psychological and health factors?", answer("Lots of right answers.", correct = TRUE), incorrect = "Be sure to detail your answer! It appears that psychological and health items load on their latent, but the university latent is not a very good composite. Additionally, the university variable does predict the other two latents but it's likely driven by the learning environment which is related to the university variable.", try_again_button = "Modify your answer", allow_retry = TRUE )
Create a Picture
Use semPaths() to create a picture of your full structural model. Use std for the whatLabels argument, any layout you would like, and edge.label.cex = 1 to increase the font size.
composite.model <- ' University <~ class + social + learn Health =~ chronic + physical + sex Psychology =~ depression + anxiety + stress University =~ Psychology + Health ' composite.fit <- sem(model = composite.model, sample.cov = university.cov, sample.nobs = 300)
semPaths(composite.fit, whatLabels = "std", layout = "spring", edge.label.cex = 1)
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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