Path Model Estimation

This function computes a path model. Predictors are allowed to possess measurement errors. Known measurement error variances (and covariances) or reliabilities can be specified by the user. Alternatively, a set of indicators can be defined for each latent variable, and for each imputed and replicated dataset the measurement error variance is determined by means of calculating the reliability Cronbachs alpha. Measurement errors are handled by adjusting covariance matrices (see Buonaccorsi, 2010, Ch. 5).

BIFIE.pathmodel( BIFIEobj, lavaan.model, reliability=NULL, group=NULL,
        group_values=NULL, se=TRUE )

# S3 method for BIFIE.pathmodel
summary(object,digits=4,...)

# S3 method for BIFIE.pathmodel
coef(object,...)

# S3 method for BIFIE.pathmodel
vcov(object,...)

Arguments

BIFIEobj

Object of class BIFIEdata

lavaan.model

String including the model specification in lavaan syntax. lavaan.model also allows the extended functionality in the TAM::lavaanify.IRT function.

reliability

Optional vector containing the reliabilities of each variable. This vector can also include only a subset of all variables.

group

Optional grouping variable(s)

group_values

Optional vector of grouping values. This can be omitted and grouping values will be determined automatically.

se

Optional logical indicating whether statistical inference based on replication should be employed.

object

Object of class BIFIE.pathmodel

digits

Number of digits for rounding output

...

Further arguments to be passed

Details

The following conventions are used as parameter labels in the output.

Y~X is the regression coefficient of the regression from \(Y\) on \(X\).

X->Z->Y denotes the path coefficient from \(X\) to \(Y\) passing the mediating variable \(Z\).

X-+>Y denotes the total effect (of all paths) from \(X\) to \(Y\).

X-~>Y denotes the sum of all indirect effects from \(X\) to \(Y\).

The parameter suffix _stand refers to parameters for which all variables are standardized.

Value

A list with following entries

stat

Data frame with unstandardized and standardized regression coefficients, path coefficients, total and indirect effects, residual variances, and \(R^2\)

output

Extensive output with all replicated statistics

...

More values

References

Buonaccorsi, J. P. (2010). Measurement error: Models, methods, and applications. CRC Press.

See also

See the lavaan and lavaan.survey package.

For the lavaan syntax, see lavaan::lavaanify and TAM::lavaanify.IRT

Examples

if (FALSE) {
#############################################################################
# EXAMPLE 1: Path model data.bifie01
#############################################################################

data(data.bifie01)
dat <- data.bifie01
# create dataset with replicate weights and plausible values
bifieobj <- BIFIEsurvey::BIFIE.data.jack( data=dat,  jktype="JK_TIMSS",
                jkzone="JKCZONE", jkrep="JKCREP", wgt="TOTWGT",
                pv_vars=c("ASMMAT","ASSSCI") )

#**************************************************************
#*** Model 1: Path model
lavmodel1 <- "
     ASMMAT ~ ASBG07A + ASBG07B  + ASBM03 + ASBM02A + ASBM02E
     # define latent variable with 2nd and 3rd item in reversed scoring
     ASBM03=~ 1*ASBM03A + (-1)*ASBM03B + (-1)*ASBM03C + 1*ASBM03D
     ASBG07A ~ ASBM02E
     ASBG07A ~~ .2*ASBG07A    # measurement error variance of .20
     ASBM02E ~~ .45*ASBM02E     # measurement error variance of .45
     ASBM02E ~ ASBM02A + ASBM02B
        "
#--- Model 1a: model calculated by gender
mod1a <- BIFIEsurvey::BIFIE.pathmodel( bifieobj, lavmodel1, group="female" )
summary(mod1a)

#--- Model 1b: Input of some known reliabilities
reliability <- c( "ASBM02B"=.6, "ASBM02A"=.8 )
mod1b <- BIFIEsurvey::BIFIE.pathmodel( bifieobj, lavmodel1, reliability=reliability)
summary(mod1b)

#**************************************************************
#*** Model 2: Linear regression with errors in predictors

# specify lavaan model
lavmodel2 <- "
     ASMMAT ~ ASBG07A + ASBG07B + ASBM03A
     ASBG07A ~~ .2*ASBG07A
        "
mod2 <- BIFIEsurvey::BIFIE.pathmodel( bifieobj, lavmodel2  )
summary(mod2)
}