Slight Extension of the <code>lavaan</code> Syntax, with Focus on Item Response Models

This functions slightly extends the lavaan syntax implemented in the lavaan package (see lavaan::lavaanify).

Guessing and slipping parameters can be specified by using the operators ?=g1 and ?=s1, respectively.

The operator __ can be used for a convenient specification for groups of items. For example, I1__I5 refers to items I1,...,I5. The operator __ can also be used for item labels (see Example 2).

Nonlinear terms can also be specified for loadings (=~) and regressions (~) (see Example 3).

It is also possible to construct the syntax using a loop by making use of the DO statement, see doparse for specification.

The operators MEASERR1 and MEASERR0 can be used for model specification for variables which contains known measurement error (see Example 6). While MEASERR1 can be used for endogenous variables, MEASERR0 provides the specification for exogeneous variables.

lavaanify.IRT(lavmodel, items=NULL, data=NULL, include.residuals=TRUE,
    doparse=TRUE)

Arguments

lavmodel	A model in `lavaan` syntax plus the additional operators `?=g1`, `?=s1`, `__` and nonlinear terms.
items	Optional vector of item names
data	Optional data frame with item responses
include.residuals	Optional logical indicating whether residual variances should be processed such that they are freely estimated.
doparse	Optional logical indicating whether `lavmodel` should be parsed for `DO` statements.

Value

A list with following entries

lavpartable

A lavaan parameter table

lavaan.syntax

Processed syntax for lavaan package

nonlin_factors

Data frame with renamed and original nonlinear factor specifications

nonlin_syntable

Data frame with original and modified syntax if nonlinear factors are used.

Examples

library(lavaan)

#############################################################################
# EXAMPLE 1: lavaan syntax with guessing and slipping parameters
#############################################################################

# define model in lavaan
lavmodel <- "
    F=~ A1+c*A2+A3+A4
    # define slipping parameters for A1 and A2
    A1 + A2 ?=s1
    # joint guessing parameter for A1 and A2
    A1+A2 ?=c1*g1
    A3 | 0.75*t1
    # fix guessing parameter to .25 and
    # slipping parameter to .01 for item A3
    A3 ?=.25*g1+.01*s1
    A4 ?=c2*g1
    A1 | a*t1
    A2 | b*t1
      "

# process lavaan syntax
lavpartable <- TAM::lavaanify.IRT(lavmodel)$lavpartable
  ##     id lhs op rhs user group free ustart exo label eq.id unco
  ##  1   1   F=~  A1    1     1    1     NA   0           0    1
  ##  2   2   F=~  A2    1     1    2     NA   0     c     0    2
  ##  3   3   F=~  A3    1     1    3     NA   0           0    3
  ##  4   4   F=~  A4    1     1    4     NA   0           0    4
  ##  5   5  A3  |  t1    1     1    0   0.75   0           0    0
  ##  6   6  A1  |  t1    1     1    5     NA   0     a     0    5
  ##  7   7  A2  |  t1    1     1    6     NA   0     b     0    6
  ##  8   8  A1 ?=s1    1     1    7     NA   0           0    7
  ##  9   9  A2 ?=s1    1     1    8     NA   0           0    8
  ##  10 10  A1 ?=g1    1     1    9     NA   0    c1     1    9
  ##  11 11  A2 ?=g1    1     1    9     NA   0    c1     1   10
  ##  12 12  A3 ?=g1    1     1    0   0.25   0           0    0
  ##  13 13  A3 ?=s1    1     1    0   0.01   0           0    0
  ##  14 14  A4 ?=g1    1     1   10     NA   0    c2     0   11

if (FALSE) {
#############################################################################
# EXAMPLE 2: Usage of "__" and "?=" operators
#############################################################################

library(sirt)
data(data.read, package="sirt")
dat <- data.read
items <- colnames(dat)

lavmodel <- "
   F1=~ A1+A2+ A3+lam4*A4
   # equal item loadings for items B1 to B4
   F2=~ lam5*B1__B4
   # different labelled item loadings of items C1 to C4
   F3=~ lam9__lam12*C1__C4
   # item intercepts
   B1__B2 | -0.5*t1
   B3__C1 | int6*t1
   # guessing parameters
   C1__C3 ?=g1
   C4 + B1__B3 ?=0.2*g1
   # slipping parameters
   A1__B1 + B3__C2 ?=slip1*s1
   # residual variances
   B1__B3 ~~ errB*B1__B3
   A2__A4 ~~ erra1__erra3*A2__A4
    "
lav2 <- TAM::lavaanify.IRT( lavmodel, data=dat)
lav2$lavpartable
cat( lav2$lavaan.syntax )

#** simplified example
lavmodel <- "
   F1=~ A1+lam4*A2+A3+lam4*A4
   F2=~ lam5__lam8*B1__B4
   F1 ~~ F2
   F1 ~~ 1*F1
   F2 ~~ 1*F2
    "
lav3 <- TAM::lavaanify.IRT( lavmodel, data=dat)
lav3$lavpartable
cat( lav3$lavaan.syntax )

#############################################################################
# EXAMPLE 3: Nonlinear terms
#############################################################################

#*** define items
items <- paste0("I",1:12)

#*** define lavaan model
lavmodel <- "
   F1=~ I1__I5
   F2=~ I6__I9
   F3=~ I10__I12
   # I3, I4 and I7 load on interaction of F1 and F2
   I(F1*F2)=~ a*I3+a*I4
   I(F1*F2)=~ I7
   # I3 and I5 load on squared factor F1
   I(F1^2)=~ I3 + I5
   # I1 regression on B spline version of factor F1
   I( bs(F1,4) )=~ I1
   F2 ~ F1 + b*I(F1^2) + I(F1>0)
   F3 ~ F1 + F2 + 1.4*I(F1*F2) + b*I(F1^2) + I(F2^2 )
   # F3 ~ F2 + I(F2^2)      # this line is ignored in the lavaan model
   F1 ~~ 1*F1
    "

#*** process lavaan syntax
lav3 <- TAM::lavaanify.IRT( lavmodel, items=items)

#*** inspect results
lav3$lavpartable
cat( lav3$lavaan.syntax )
lav3$nonlin_syntable
lav3$nonlin_factors

#############################################################################
# EXAMPLE 4: Using lavaanify.IRT for estimation with lavaan
#############################################################################

data(data.big5, package="sirt")
# extract first 10 openness items
items <- which( substring( colnames(data.big5), 1, 1 )=="O"  )[1:10]
dat <- as.data.frame( data.big5[, items ] )
  ##   > colnames(dat)
  ##    [1] "O3"  "O8"  "O13" "O18" "O23" "O28" "O33" "O38" "O43" "O48"
apply(dat,2,var)  # variances

#*** Model 1: Confirmatory factor analysis with one factor
lavmodel <- "
   O=~ O3__O48   # convenient syntax for defining the factor for all items
   O ~~ 1*O
   "
# process lavaan syntax
res <- TAM::lavaanify.IRT( lavmodel, data=dat )
# estimate lavaan model
mod1 <- lavaan::lavaan( model=res$lavaan.syntax, data=dat)
summary(mod1, standardized=TRUE, fit.measures=TRUE, rsquare=TRUE )
}

#############################################################################
# EXAMPLE 5: lavaanify.IRT with do statements
#############################################################################

lavmodel <- "
  DO(1,6,1)
    F=~ I%
  DOEND
  DO(1,5,2)
    A=~ I%
  DOEND
  DO(2,6,2)
    B=~ I%
  DOEND
  F ~~ 1*F
  A ~~ 1*A
  B ~~ 1*B
  F ~~ 0*A
  F ~~ 0*B
  A ~~ 0*B
   "
res <- TAM::lavaanify.IRT( lavmodel, items=paste("I",1:6) )
cat(res$lavaan.syntax)

#############################################################################
# EXAMPLE 6: Single indicator models with measurement error (MEASERR operator)
#############################################################################

# define lavaan model
lavmodel <- "
  ytrue ~ xtrue + z
  # exogeneous variable error-prone y with error variance .20
  MEASERR1(ytrue,y,.20)
  # exogeneous variable error-prone x with error variance .35
  MEASERR0(xtrue,x,.35)
  ytrue ~~ ytrue
    "
# observed items
items <- c("y","x","z")
# lavaanify
res <- TAM::lavaanify.IRT( lavmodel, items )
cat(res$lavaan.syntax)
  ##   > cat(res$lavaan.syntax)
  ##   ytrue~xtrue
  ##   ytrue~z
  ##   ytrue=~1*y
  ##   y~~0.2*y
  ##   xtrue=~1*x
  ##   x~~0.35*x
  ##   xtrue~~xtrue
  ##   ytrue~~ytrue
  ##   z~~z

Slight Extension of the `lavaan` Syntax, with Focus on Item Response Models

Arguments

Value

See also

Examples

Slight Extension of the lavaan Syntax, with Focus on Item Response Models

Arguments

Value

See also

Examples

Slight Extension of the `lavaan` Syntax, with Focus on Item Response Models