Explore Fit Indices

After reviewing the standardized loadings in the previous exercise, we found that several of the manifest variables may not represent our latent variable well. As a second measure of our model, you can examine the fit indices to see if the model appropriately fits the data. You can look at both the goodness of fit and badness of fit statistics using the fit.measures argument within the summary() function.

Remember that goodness of fit statistics, like the CFI and TLI, should be large (over .90) and close to one, while badness of fit measures like the RMSEA and SRMR should be small (less than .10) and close to zero.

This exercise is part of the course

Structural Equation Modeling with lavaan in R

Exercise instructions

Use the summary() function on your text.fit model.
Include the argument to view the fit indices.
Do not include the standardized loadings.

Hands-on interactive exercise

Have a go at this exercise by completing this sample code.

# Load the lavaan library
library(lavaan)

# Load the data and define model
data(HolzingerSwineford1939)
text.model <- 'textspeed =~ x4 + x5 + x6 + x7 + x8 + x9'

# Analyze the model with cfa()
text.fit <- cfa(model = text.model, data = HolzingerSwineford1939)

# Summarize the model

Edit and Run Code

This exercise is part of the course

Structural Equation Modeling with lavaan in R

AdvancedSkill Level

4.9+

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In this chapter, you will dive into creating your first structural equation model with lavaan. You will learn important terminology, how to build, and run models. You will create a one-factor model of mental test abilities using the classic Holzinger and Swineford (1939) dataset.

Exercise 1: Model Specification Exercise 2: Build Text Speed Model Exercise 3: Build Political Democracy Model Exercise 4: Model Analysis Exercise 5: Analyze Text Speed Model Exercise 6: Summarize Political Democracy Exercise 7: Model Assessment Exercise 8: Examine Standardized Loadings Exercise 9: Explore Fit Indices

Current Exercise

Exercise 10: Examine Political Democracy

In this chapter, you will expand your skills in lavaan to creating multi-factor models. We will improve the one-factor models from the last chapter by creating multiple latent variables in the classic Holzinger and Swineford (1939) dataset.

Exercise 1: Multifactor Specification Exercise 2: Create a Zero df Model Exercise 3: Fix the Zero df Model Exercise 4: Build a Multi-Factor Model Exercise 5: Summarize the Multi-Factor Model Exercise 6: Model Structure Exercise 7: Three-Factor Model with Zero Correlation Exercise 8: Create a Direct Path Exercise 9: Modification Indices Exercise 10: Check Model Variance Exercise 11: Examine Modification Indices Exercise 12: Model Comparison Exercise 13: Compare Two Models Exercise 14: Select Specific Fit Indices

Structural equation models do not always run smoothly, and in this chapter, you will learn how to troubleshoot Heywood cases which are common errors. You will also learn how to diagram your model in R using the semPlot library.

Exercise 1: Heywood Cases on the Latent Variable Exercise 2: Analyze a Latent Heywood Case Exercise 3: Fix the Latent Heywood Model Exercise 4: Heywood Cases on the Manifest Variables Exercise 5: Analyze a Manifest Heywood Case Exercise 6: Fix the Manifest Heywood Model Exercise 7: Create Diagrams with semPaths()Exercise 8: Basic SEM Diagram Exercise 9: Edit the Layout Exercise 10: Edit the Labels

This chapter examines the WAIS-III IQ Scale and its structural properties. You will use your skills from the first three chapters to create various models of the WAIS-III, troubleshoot errors in those models, and create diagrams of the final model.

Exercise 1: Model the WAIS-III IQ Scale Exercise 2: Create a Four-Factor Model Exercise 3: Update the Model Exercise 4: Diagram the Final Model Exercise 5: Update the WAIS-III Model Exercise 6: Add Paths to Improve Fit Exercise 7: Compare Models Exercise 8: A Hierarchical Model of IQ Exercise 9: Create a Hierarchical Model Exercise 10: Diagram the Hierarchical Model Exercise 11: Course Wrap Up