In this tutorial, we are going to use lavaan for a
multiple linear regression path analysis.
library(lavaan)For this example, our data is a variance-covariance matrix for three observed variables: ReadSC1, MathSC1, Goals2. For more information about the data, please refer back to the course slides.
We use the following code to read the variance-covariance matrix into
R. We first create an object called mlr.lower which
contains the lower diagonal elements of the covariance matrix. We then
use the getCov() function in lavaan to convert
the matrix to a \(3\times3\) full
symmetric covariance matrix with variable names. If you have a full
covariance matrix to begin with, you can directly import the matrix
without the need to convert it.
mlr.lower <- '
1.623
-.308 1.951
.198 .290 1.627'
(mlr.cov <- getCov(mlr.lower, names = c("ReadSC1", "MathSC1", "Goals2")))## ReadSC1 MathSC1 Goals2
## ReadSC1 1.623 -0.308 0.198
## MathSC1 -0.308 1.951 0.290
## Goals2 0.198 0.290 1.627In order for lavaan to fit a model to the data, you need
to tell lavaan what the model is. To communicate with
lavaan, you would need to speak its language – the
lavaan model syntax. The model syntax describes the model
to be estimated. It usually consists of multiple formulas. Depending on
the operator being used, different formulas carry different meanings. In
this example, we use the tilde ~ to tell
lavaan that we wish to regress Goals2 on ReadSC1 and
MathSC1. We then use the double tilde ~~ to tell
lavaan that we wish to estimate the variances of the
independent variables and the residual variance of the outcome variable.
We also allow the two independent variables to covary.
mlr.model <- '
# regression
Goals2 ~ ReadSC1 + MathSC1
# variance and covariances
Goals2 ~~ Goals2
ReadSC1 ~~ ReadSC1
MathSC1 ~~ MathSC1
ReadSC1 ~~ MathSC1
'After you specify the model syntax, you can fit the model to the
variance-covariance matrix using the sem() function. In
this function, we first specify the model syntax. Then we tell
lavaan that our data is a variance-covariance matrix using
the sample.cov = argument. We also tell lavaan
that our sample size is 1000.
mlr.fit <- sem(mlr.model, sample.cov = mlr.cov, sample.nobs = 1000)Next you can summarize the results using the
summary()function. To get more info on the model fit
measures, you can use the optional argument
fit.measures = TRUE. To take a look at the standardzied
parameter estimates, you can use the optional argument
standardized = TRUE. Unstandardized solutions are displayed
in the column labled “Estimate”. The standardized solutions are listed
in the column labeled “Std.all”.
summary(mlr.fit, fit.measures = T, standardized = T)## lavaan 0.6.15 ended normally after 16 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 6
##
## Number of observations 1000
##
## Model Test User Model:
##
## Test statistic 0.000
## Degrees of freedom 0
##
## Model Test Baseline Model:
##
## Test statistic 81.389
## Degrees of freedom 3
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000
## Tucker-Lewis Index (TLI) 1.000
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -5034.298
## Loglikelihood unrestricted model (H1) -5034.298
##
## Akaike (AIC) 10080.597
## Bayesian (BIC) 10110.043
## Sample-size adjusted Bayesian (SABIC) 10090.987
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.000
## P-value H_0: RMSEA <= 0.050 NA
## P-value H_0: RMSEA >= 0.080 NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.000
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Goals2 ~
## ReadSC1 0.155 0.031 4.941 0.000 0.155 0.155
## MathSC1 0.173 0.029 6.056 0.000 0.173 0.190
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## ReadSC1 ~~
## MathSC1 -0.308 0.057 -5.393 0.000 -0.308 -0.173
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Goals2 1.545 0.069 22.361 0.000 1.545 0.950
## ReadSC1 1.621 0.073 22.361 0.000 1.621 1.000
## MathSC1 1.949 0.087 22.361 0.000 1.949 1.000