lavaan Syntax, with Focus on Item Response Modelslavaanify.IRT.RdThis 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)A model in lavaan syntax plus the additional
operators ?=g1, ?=s1, __ and nonlinear terms.
Optional vector of item names
Optional data frame with item responses
Optional logical indicating whether residual variances should be processed such that they are freely estimated.
Optional logical indicating whether lavmodel
should be parsed for DO statements.
A list with following entries
A lavaan parameter table
Processed syntax for lavaan package
Data frame with renamed and original nonlinear factor specifications
Data frame with original and modified syntax if nonlinear factors are used.
See sirt::tam2mirt for
converting objects of class tam into mirt
objects.
See sirt::lavaan2mirt
for estimating models in the mirt package using lavaan syntax.
See doparse for the DO and DO2 statements.
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