auxiliary: Analyzing data with full-information maximum likelihood with auxiliary variables

Description

Analyzing data with full-information maximum likelihood with auxiliary variables. The techniques used to account for auxiliary variables are both extra-dependent-variables and saturated-correlates approaches (Enders, 2008). The extra-dependent-variables approach is used for exogenous varibles in the model (see fixed.x attribute when fitting the lavaan model). For other variables, the saturated-correlates approach is used. WARNINGS: this function does not work for all models. See the examples below.

Usage

auxiliary(object, aux, ...)

Arguments

object

The lavaan object or the parameter table

aux

The list of auxiliary variable

...

The additional arguments in the lavaan function.

Value

The lavaanStar object which contains the original lavaan object and the additional values of the null model, which need to be adjusted to account for auxiliary variables.

References

Enders, C. K. (2008). A note of the use of missing auxiliary variables in full information maximum likelihood-based structural equation models. Structural Equation Modeling, 15, 434-448.

Examples

Run this code

# Example of confirmatory factor analysis

HS.model <- ' visual  =~ x1 + x2 + x3
              textual =~ x4 + x5 + x6
              speed   =~ x7 + x8 + x9 '
			  
dat <- data.frame(HolzingerSwineford1939, z=rnorm(nrow(HolzingerSwineford1939), 0, 1))
			  
fit <- cfa(HS.model, data=dat) #, group="sex", meanstructure=TRUE)
fitaux <- auxiliary(fit, aux="z", data=dat)

# Example of multiple groups confirmatory factor analysis

fitgroup <- cfa(HS.model, data=dat, group="school")
fitgroupaux <- auxiliary(fitgroup, aux="z", data=dat, group="school")

# Example of path analysis

mod <- ' x5 ~ x4
x4 ~ x3
x3 ~ x1 + x2'

fitpath <- sem(mod, data=dat)
fitpathaux <- auxiliary(fitpath, aux="z", data=dat)

# Example of full structural equation modeling

dat2 <- data.frame(PoliticalDemocracy, z=rnorm(nrow(PoliticalDemocracy), 0, 1))
model <- ' 
     ind60 =~ x1 + x2 + x3
     dem60 =~ y1 + a*y2 + b*y3 + c*y4
     dem65 =~ y5 + a*y6 + b*y7 + c*y8

    dem60 ~ ind60
    dem65 ~ ind60 + dem60

    y1 ~~ y5
    y2 ~~ y4 + y6
    y3 ~~ y7
    y4 ~~ y8
    y6 ~~ y8
'
fitsem <- sem(model, data=dat2, meanstructure=TRUE)
fitsemaux <- auxiliary(fitsem, aux="z", data=dat2, meanstructure=TRUE)

#########################################################
## These following codes show the models that do not work with the current function

##### 1. covariate at the factor level
## HS.model.cov <- ' visual  =~ x1 + x2 + x3
##              textual =~ x4 + x5 + x6
##             speed   =~ x7 + x8 + x9 
##			  visual ~ sex
##			  textual ~ sex
##			  speed ~ sex'
	  
## fitcov <- cfa(HS.model.cov, data=dat) 
## fitcovaux <- auxiliary(fitcov, aux="z", data=dat)

### The auxiliary code does not work when specifying manually.
## HS.model.covxx <- ' visual  =~ x1 + x2 + x3
##              textual =~ x4 + x5 + x6
##              speed   =~ x7 + x8 + x9 
##			  visual ~ sex
##			  textual ~ sex
##			  speed ~ sex
##			  z ~~ z
##			  z ~~ x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9
##			  z ~ sex'
	  
## fitcovxx <- cfa(HS.model.covxx, data=dat) 
## fitcovaux <- auxiliary(fitcov, aux="z", data=dat)

##### 2. Endogenous variable with single indicator 
## HS.model.cov2 <- ' visual  =~ x1 + x2 + x3
##               textual =~ x4 + x5 + x6
##               x7 ~ visual + textual'
## 	  
## fitcov2 <- sem (HS.model.cov2, data=dat, fixed.x=FALSE) #, group="sex", meanstructure=TRUE)
## fitcov2aux <- auxiliary(fitcov2, aux="z", data=dat)


### The auxiliary code does not work when specifying manually.
## HS.model.covyy <- ' visual  =~ x1 + x2 + x3
##               textual =~ x4 + x5 + x6
##               x7 ~ visual + textual
## 			  z ~~ x1 + x2 + x3 + x4 + x5 + x6 + x7'
## fitcovyy <- sem(HS.model.covyy, data=dat) #, group="sex", meanstructure=TRUE)