lavaan syntax cheat sheet

Quick reference for =~, ~, , := and friends

Author

Affiliation

George Michaelides

Norwich Business School, University of East Anglia

Published

July 7, 2026

A one-page reference for the lavaan syntax used across this series. Grouped by category. For definitions of the terms, see the glossary; for the Greek symbols, see the notation key.

Model specification

Syntax	Name	Example	Notes
`=~`	“is measured by” — defines a latent variable	`pa =~ pa1 + pa2 + pa3`	The first indicator’s loading is fixed to 1 by default (marker-variable method)
`~`	“is regressed on” — defines a regression path	`creat ~ pa + con`	Used for structural paths and for `lm()`-style regressions
`~~`	“is correlated with” — covariance	`pa ~~ na`	Default between exogenous variables; can also free residual covariances
`~ 1`	intercept / mean	`pa ~ 1`	Usually estimated automatically for observed variables; freed for latents with `meanstructure = TRUE`
`1 *`	fix a parameter to 1	`pa =~ 1 * pa1`	Explicit form of the marker-variable default
`0 *`	fix a parameter to 0	`pa ~~ 0 * na`	Explicitly constrain a covariance to zero
`n *`	fix a parameter to a numeric value	`x ~ 0.5 * y`	Rarely needed; used for a priori constraints
`start() *`	set a starting value	`pa =~ start(1.2) * pa1`	Helps with convergence problems
`label *`	label a parameter (for constraints or `:=`)	`creat ~ b * pa + c * con`	Two parameters with the same label are constrained equal
`c(a, b) *`	group-specific parameter	`pa ~ c(a1, a2) * con`	Used in multigroup SEM; `a1` for group 1, `a2` for group 2
`:=`	define a new (derived) parameter	`indirect := a * b`	Operates on labelled parameters; used for indirect effects

Estimation options

Pass these arguments to cfa(), sem(), or lavaan():

Argument	Effect	Example
`estimator = "MLR"`	Robust maximum likelihood (Satorra–Bentler). Our default.	`cfa(model, data = df, estimator = "MLR")`
`estimator = "ML"`	Plain maximum likelihood. Required when bootstrapping.	`sem(model, data = df, estimator = "ML", se = "boot")`
`se = "boot"`	Bootstrap standard errors	`sem(model, data = df, se = "boot", bootstrap = 1000)`
`bootstrap = N`	Number of bootstrap replications	`bootstrap = 1000`
`std.lv = TRUE`	Set latent variances to 1; freely estimate all loadings	`cfa(model, data = df, std.lv = TRUE)`
`orthogonal = TRUE`	Force all latent covariances to zero	`cfa(model, data = df, orthogonal = TRUE)`
`missing = "ml"`	Full-information maximum likelihood for missing data (default)	`sem(model, data = df, missing = "ml")`
`missing = "listwise"`	Listwise deletion	`sem(model, data = df, missing = "listwise")`
`meanstructure = TRUE`	Estimate intercepts and latent means	`cfa(model, data = df, meanstructure = TRUE)`
`group = "gender"`	Multigroup analysis	`cfa(model, data = df, group = "gender")`

Entry-point functions

Function	Use	Example
`cfa()`	Confirmatory factor analysis (measurement model only)	`fit <- cfa(model, data = df)`
`sem()`	Structural equation model (measurement + structural)	`fit <- sem(model, data = df)`
`lavaan()`	The general function; `cfa()` and `sem()` are wrappers	`fit <- lavaan(model, data = df)`
`growth()`	Latent growth curve model	`fit <- growth(model, data = df)`

Reading output

Function	What it returns	Example
`summary(fit)`	A compact summary of parameter estimates	`summary(fit)`
`summary(fit, standardized = TRUE)`	Adds the `std.all`, `std.lv`, `std.nox` columns	`summary(fit, standardized = TRUE)`
`summary(fit, fit.measures = TRUE)`	Adds the fit indices section at the top	`summary(fit, fit.measures = TRUE)`
`summary(fit, rsquare = TRUE)`	Adds an $R^2$ row for each dependent variable	`summary(fit, rsquare = TRUE)`
`parameterEstimates(fit)`	Parameter estimates as a data frame (one row per parameter)	`parameterEstimates(fit)`
`parameterEstimates(fit, standardized = TRUE)`	Same, with standardised columns	`parameterEstimates(fit, standardized = TRUE)`
`parameterEstimates(fit, boot.ci.type = "bca.simple")`	BCa bootstrap confidence intervals	Use after `se = "boot"`
`standardizedSolution(fit)`	Tidy data frame of standardised parameters only	`standardizedSolution(fit)`
`fitMeasures(fit)`	Named vector of ~40 fit indices	`fitMeasures(fit)`
`fitMeasures(fit, c(...))`	Selected fit indices	`fitMeasures(fit, c("chisq","df","pvalue","cfi","tli","rmsea","srmr"))`
`coef(fit)`	Just the parameter estimates as a named vector	`coef(fit)`
`confint(fit)`	Confidence intervals for each parameter	`confint(fit, level = 0.95)`
`fitted(fit)`	The model-implied covariance matrix $\hat{\Sigma}(\theta)$	`fitted(fit)`
`resid(fit)`	Residual covariance matrix $S - \hat{\Sigma}(\theta)$	`resid(fit)`
`lavInspect(fit, "rsquare")`	$R^2$ for each observed and latent dependent variable	`lavInspect(fit, "rsquare")`
`lavInspect(fit, "sampstat")`	The sample covariance matrix $S$	`lavInspect(fit, "sampstat")`

Diagnostics and respecification

Function	What it returns	Example
`modindices(fit)`	All modification indices	`modindices(fit)`
`modindices(fit, minimum.value = 3.84)`	Only MIs above 3.84 ($\alpha = .05$)	`modindices(fit, minimum.value = 3.84)`
`modindices(fit, sort. = TRUE)`	Sorted by MI, largest first	`modindices(fit, minimum.value = 3.84, sort. = TRUE)`
`modindices(fit, op = "==~")`	Only MIs for factor loadings	`modindices(fit, op = "==~")`
`anova(fit1, fit2)`	Likelihood-ratio test between nested models	`anova(fit1, fit2)`
`lavTestScore(fit)`	Score test for freeing fixed parameters	`lavTestScore(fit)`

Multigroup and measurement invariance

Fitting a model in several groups at once and testing whether parameters are equal across them. Used both for measurement invariance testing (Tutorial 17) and for moderation by a categorical variable (Tutorial 16).

Argument / function	Effect	Example
`group = "gender"`	Fit the model separately in each group, freely by default	`cfa(model, data = df, group = "gender")`
`group.equal = "loadings"`	Constrain factor loadings equal across groups (metric / weak invariance)	`cfa(model, data = df, group = "g", group.equal = "loadings")`
`group.equal = c("loadings", "intercepts")`	Add equal item intercepts (scalar / strong invariance)	`cfa(model, data = df, group = "g", group.equal = c("loadings", "intercepts"))`
`group.equal = c("loadings", "intercepts", "residuals")`	Add equal residual variances (strict invariance)	`cfa(model, data = df, group = "g", group.equal = c("loadings", "intercepts", "residuals"))`
`group.partial = c("PA =~ pa3")`	Release specific equality constraints (partial invariance)	`cfa(model, data = df, group = "g", group.equal = "loadings", group.partial = c("PA =~ pa3"))`
`meanstructure = TRUE`	Estimate intercepts and latent means (required for scalar invariance and latent-mean comparison)	`cfa(model, data = df, group = "g", group.equal = c("loadings","intercepts"), meanstructure = TRUE)`
`lavTestLRT(fit1, fit2)`	Scaled $\chi^2$ difference test between nested multigroup models	`lavTestLRT(fit_config, fit_metric)`
`lavTestScore(fit)$uni`	Univariate score tests: which equality constraints to release for partial invariance	`lavTestScore(fit_metric)$uni`

The invariance hierarchy, tested in order:

fit_config <- cfa(model, data = df, group = "g", estimator = "MLR")              # 1. configural
fit_metric <- cfa(model, data = df, group = "g", group.equal = "loadings",       # 2. metric (weak)
                  estimator = "MLR")
fit_scalar <- cfa(model, data = df, group = "g",                                  # 3. scalar (strong)
                  group.equal = c("loadings", "intercepts"), estimator = "MLR")
lavTestLRT(fit_config, fit_metric)   # non-sig => metric invariance holds
lavTestLRT(fit_metric, fit_scalar)   # non-sig => scalar invariance holds

Supplement each LRT with fit-index change criteria (Chen (2007)): $\Delta$CFI $\leq .010$ and $\Delta$RMSEA $\leq .015$ indicate the constraint does not meaningfully worsen fit.

Tables and figures

Function	What it does	Example
`texreg::screenreg(fit)`	Print a regression-style table to the screen	`texreg::screenreg(fit)`
`texreg::htmlreg(fit, file = "table.html")`	Write a table to an HTML file	`texreg::htmlreg(fit, file = "tab.html")`
`texreg::texreg(fit, file = "table.tex")`	Write a table to a LaTeX file	`texreg::texreg(fit, file = "tab.tex")`
`semPlot::semPaths(fit)`	Legacy path-diagram plot	`semPlot::semPaths(fit, whatLabels = "std")`
`tidySEM::graph_sem(fit)`	Modern path diagram from a fitted lavaan object	`tidySEM::graph_sem(fit)`
`tidySEM::prepare_graph(fit)`	Customisable graph object (edit before rendering)	`tidySEM::prepare_graph(fit) \\|> tidySEM::edit_graph(...)`

A complete worked example

Putting it all together — the two-factor CFA we walk through in Tutorial 07:

library(lavaan)

model <- '
  NA =~ na1 + na2 + na3
  PA =~ pa1 + pa2 + pa3
  NA ~~ PA
'

fit <- cfa(model, data = ps, estimator = "MLR")
summary(fit, standardized = TRUE, fit.measures = TRUE)
fitMeasures(fit, c("chisq", "df", "pvalue",
                   "cfi", "tli",
                   "rmsea", "rmsea.ci.lower", "rmsea.ci.upper",
                   "srmr"))
modindices(fit, minimum.value = 3.84, sort. = TRUE)
tidySEM::graph_sem(fit)

References

Chen, F. F. (2007). Sensitivity of goodness of fit indexes to lack of measurement invariance. Structural Equation Modeling: A Multidisciplinary Journal, 14(3), 464–504. https://doi.org/10.1080/10705510701301834