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Basic lavaan Syntax Guide

James B. Grace

Last modified: August 1, 2013

Contents: (Basic Topics Only)

a. Correlating Errors

c. Naming Parameters

d. Fixing Parameter Values to Specific Quantities

4. More Estimation Options

a. Estimating Intercepts

b. Obtaining Estimates of Correlations/Covariances Between Exogenous Variables

5. More Options for Extracting Results

a. Extracting the Parameter Estimates

b. Standardized Estimates

c. Model Fit Statistics

Adapted from Rosseel, Y. June 14, 2011. “Lavaan Introduction.pdf”

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1. Getting Started

A few basic points:

Lavaan is an R package for classical structural equation modeling (SEM).

An elementary introduction to SEM designed for those in the natural sciences can be found in

Grace (2006). Another treatment for biologists with slightly different emphases has been written

by Shipley (2000). For first time users in the social sciences, Kline’s (2010) book provides an

good entry-level treatment. Technical fundamentals for classic SEM are presented in Bollen

The lavaan package is currently still a beta-version package and not considered complete. That

said, it is approaching the functionality of some commercial packages.

One feature of lavaan is that it does not require you to be an expert in R. You do need to know

how to import datasets into R and how to execute commands. You also need to know how to

install and load packages. The lavaan syntax is simple and requires only general background

knowledge, not a deep familiarity with the R language.

The numerical results of the lavaan package are typically very close, if not identical, to the

results of the commercial package Mplus. If you wish to compare the results with those obtained

by other SEM packages, there are options available for doing so.

In this presentation, as is common in the biometric tradition of structural equations, the inclusion

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statements, (b) estimation statements, and (c) statements for extracting results. The reader should

be aware that there are additional steps in the SEM process, particularly leading from theory to

model specification and also following the extraction of results (Grace et al. 2010, Grace et al.

2012). Here is a preview of the three main lavaan commands, which will be explained

subsequently.

At the heart of the lavaan package is the model ‘syntax'. The model syntax is a description of the

model to be estimated. In this section, I briefly present the lavaan model syntax for modeling

with observed variables. More syntax will be introduced in later sections.

In the R environment, a regression formula has the following form:

y ~ x1 + x2

In lavaan, a typical model is simply a set (or system) of equations contained within quotation

marks. Here is a model (model.1) and its syntax:

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Note that the equations (there are two in this example) are “string literals”, i.e., by placing them

in quotes we make them essentially character statements. Lavaan interprets the statements in

their parts, recognizing that there are three variables (y1, x1, and x2) and two operators (~, +) in

the first literal and three variables (y2, y1, and x2) and two operators (~, +) in the second as

well. Also note exogenous variables are allowed to correlate by default in lavaan.

The four basic types of specification operators in lavaan are:

formula type operator operator stands for

b. Estimation/Fitting

Lavaan has command statements for estimating different types of models. The most basic

command is “sem”. Here I show how we can estimate the parameters in the above model.

Here, “model.1” refers to the model specification assigned to the object and “data.mod1” is the

name for the data object in R.

c. Extracting Results

There are a variety of ways of extracting results from the estimated object. Here is the most basic

extraction statement.

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lavaan (0.4-12) converged normally after 40 iterations

Number of observations 90

Estimator ML

Minimum Function Chi-square 23.222

Degrees of freedom 1

P-value 0.000

Parameter estimates:

Standard Errors Standard

y1 ~

x2 -0.083 0.019 -4.440 0.000

y2 ~

y1 9.910 5.083 1.950 0.051

x2 -2.531 0.976 -2.593 0.010

Variances:

y1 0.080 0.012

y2 187.212 27.908

3. More Specification Options

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It is important to note here the common convention that when a correlation is specified between

two endogenous variables, it is understood that the correlation is a residual correlation and

therefore, a correlation between their prediction errors (strictly speaking in causal modeling,

what statisticians would call prediction errors represent other factors affecting a variable).

Results presented below include a covariance between y1 and y2, which has now been requested.

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Standard Errors Standard

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In this model statement, x1 is pre-multiplied by zero to set its value to zero. We can also

accomplish this using a more elaborate and more flexible approach:

Now we have labeled the parameter “b1” and then assigned it a value of 0 in a separate

P-value 0.000

Parameter estimates:

Information Expected

Standard Errors Standard

Estimate Std.err Z-value P(>|z|)

Regressions:

y1 ~

y1 ~~

y2 (b4) 0.798 0.426 1.872 0.061

Variances:

y1 0.081 0.012

y2 195.119 29.087

Constraints: Slack (>=0)

b1 - 0 0.000

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4. More Estimation Options

a. Estimating Intercepts

By default, lavaan sets the scales for the variables to zero, placing the emphasis on the other

parameters (e.g., path coefficients). One advantage for this default (along with the default of not

estimating exogenous covariances) is that we don’t estimate as many parameters, which is

helpful when sample sizes are limited. However, there certainly are times when we want the

estimates for intercepts (e.g., for generating prediction equations). Obtaining these additional

parameters is easy, as it only requires overriding a default in the estimation statement. Here we

statement.

Both approaches produce the following results:

Estimate Std.err Z-value P(>|z|)

Regressions:

y1 ~

x2 -0.083 0.019 -4.440 0.000

Variances:

y1 0.080 0.012

y2 187.212 27.908

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e. Residual Covariances

In addition to looking at modification indices, it can be useful sometimes to look at residuals.

Here we are talking about residuals in the covariance matrix, not in the data values themselves (a

topic I deal with elsewhere). We can use the “resid” function for this purpose, which includes the

option of looking at the standardized residuals.

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Bollen, K. A. 1989. Structural equations with latent variables. John Wiley & Sons, New York,

K.M., and Schweiger, E.W. 2012. Guidelines for a graph-theoretic implementation of

structural equation modeling. Ecosphere 3(8): article 73 (44 pages).

(http://www.esajournals.org/doi/abs/10.1890/ES12-00048.1)

Kline, R.B. 2010. Principles and Practice of Structural Equation Modeling. Guilford Press, New

York, New York, USA.

Shipley, B. 2000. Cause and correlation in biology. Cambridge University Press, Cambridge,

UK.