Structural equation modeling (SEM) is a series of multivariate analyses (including factor analysis and path analysis) that allow complex relationships between one or more independent variables (IV) and one or more dependent variables (DV). More specifically, it examines variances and covariances to find interrelationships among latent and observed variables. SEM is similar to (but more powerful than) regression analyses, as it examines linear causal relationships among variables while simultaneously accounting for measurement error and testing theory validity.
Note: Latent variables are constructs used to explain observable variables (manifest or indicator). Latent variables cannot be directly observed or measured but rather are approximated through various measures. (Examples: conscientiousness, intelligence, extraversion, depression). Latent variables are represented by circles/ellipses in SEM diagrams, and "factors" in the analysis.
Observed/Manifest Variables: are constructs that are directly measured. They can be continuous (e.g., age, income) or categorical (e.g., gender, education level). If you ONLY have observed variables - path analysis will be used. Observed variables are represented by squares or rectangles in SEM diagrams.
When you have theoretical models with multiple latent variables (unobserved constructs) and observed variables (measured variables).
Can answer the questions about the validity of a proposed causal process (confirmatory), the appropriateness of your model, the amount of variance in both manifest & latent DVs accounted for by the IVs, the reliability of measured variables, and group differences.
Do NOT use SEM if: Your sample size is small (< 200), you are exploring relationships without a prior theoretical model → use EFA or regression instead, all your variables are directly observed with no latent constructs → use path analysis or multiple regression, you have no prior regression or factor analysis background (SEM builds on both; work through those first).
Before running a test, four assumptions should be met:
Large sample size: SEM requires a substantially larger sample than regression. A general rule of thumb is at least 10 observations per estimated parameter, with a minimum of N = 200 recommended for stable results.
Multivariate normality: The observed variables should be approximately normally distributed.
Theory-driven model: SEM is confirmatory, not exploratory. Your model should be based on an established theoretical framework before running the analysis. Testing multiple models on the same data until one fits ("fishing") inflates Type I error.
Sufficient indicators: Each latent variable should have at least 3 observed indicator variables for the model to be identified.
Check for normality
Click "Modules" in the upper right-hand corner
Click "jamovi library"
Search for "semlj - SEM" under the "Available" tab and click "Install"
Click "SEM"
Click "SEM - interactive"
Check "Path Diagram" and "Show residuals" in the "Path Diagram" menu
Move the DV into the "Endogenous Variables" box.
Move the IV into the "Exogenous Variables" box.
Parameter estimates: Coefficients that indicate the strength and direction of the relationships among the variables.
If estimate is negative, there is an inverse relationship between variables
If estimate is positive, there is a direct relationship between variables
If estimate is high, there is a strong relationship
If estimate is low, there is a weak relationship
p-value: The probability of detecting a meaningful relationship/difference when there is none. Looking for a small value (p < .05).
If p < .05, reject the null hypothesis. It IS a significant relationship.
If p > .05, accept the null hypothesis. It is NOT a significant relationship.
Confidence interval: A range of values that is likely to contain the true parameter estimate.
If the confidence interval is narrow, there are more precise estimates.
Chi-Square: A measure of model fit, testing the null hypothesis that the model fits the data well. RMSEA and CFI are reported alongside it.
If the Chi-Square value is low and high p-value (p > .05), there is a good fit.
If the Chi-Square value is high and low p-value (p < .05), there is a poor fit.
Root Mean Square Error of Approximation (RMSEA): A measure of how well the model, with unknown but optimally chosen parameter estimates, fits the population covariance matrix.
If RMSEA is < 0.05, there is a good fit.
If RMSEA is between 0.05 and 0.08, there is a reasonable fit.
If RMSEA is > 0.08, there is a poor fit.
Comparative Fit Index (CFI): Compares the fit of a target model to an independent model.
If CFI is > 0.95, there is a good fit.
If CFI is between 0.90 and 0.95, there is an acceptable fit.
If CFI is < 0.90, there is a poor fit.\
Tucker-Lewis Index (TLI): Similar to CFI, compares model fit relative to a null model while penalizing model complexity.
If TLI is > 0.95, there is a good fit.
If TLI is between 0.90 and 0.95, there is an acceptable fit.
If TLI is < 0.90, there is a poor fit.
Akaike Information Criterion (AIC): A measure used for model comparison
If AIC is lower, it is a better-fitting model.
Appropriate data visualization: Path diagram
Sample table: Example
Sample write-up: View results section