TAM: tam.latreg – R documentation

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tam.latreg

Latent Regression Model

Description

This function fits a latent regression model \bold{θ}=\bold{Y} \bold{β} + \bold{\varepsilon}. Only the individual likelihood evaluated at a \bold{θ} grid is needed as the input. Like in tam.mml a multivariate normal distribution is posed on the residual distribution. Plausible values can be drawn by subsequent application of tam.pv (see Example 1).

Usage

tam.latreg(like, theta=NULL, Y=NULL, group=NULL, formulaY=NULL, dataY=NULL,
   beta.fixed=FALSE, beta.inits=NULL, variance.fixed=NULL,
   variance.inits=NULL, est.variance=TRUE, pweights=NULL, pid=NULL,
   userfct.variance=NULL, variance.Npars=NULL, verbose=TRUE, control=list())

## S3 method for class 'tam.latreg'
summary(object,file=NULL,...)

## S3 method for class 'tam.latreg'
print(x,...)

Arguments

`like`	Individual likelihood. This can be typically extracted from fitted item response models by making use of `IRT.likelihood`.
`theta`	Used \bold{θ} grid in the fitted IRT model. If `like` is generated by the `IRT.likelihood` function, then `theta` is automatically extracted as an attribute.
`Y`	A matrix of covariates in latent regression. Note that the intercept is automatically included as the first predictor.
`group`	An optional vector of group identifiers
`formulaY`	An R formula for latent regression. Transformations of predictors in Y (included in `dataY`) can be easily specified, e. g. `female*race` or `I(age^2)`.
`dataY`	An optional data frame with possible covariates Y in latent regression. This data frame will be used if an R formula in `formulaY` is specified.
`beta.fixed`	A matrix with three columns for fixing regression coefficients. 1st column: Index of Y value, 2nd column: dimension, 3rd column: fixed β value. If no constraints should be imposed on β, then set `beta.fixed=FALSE` (see Example 2, Model `2_4`) which is the default.
`beta.inits`	A matrix (same format as in `beta.fixed`) with initial β values
`variance.fixed`	An optional matrix with three columns for fixing entries in covariance matrix: 1st column: dimension 1, 2nd column: dimension 2, 3rd column: fixed value
`variance.inits`	Initial covariance matrix in estimation. All matrix entries have to be specified and this matrix is NOT in the same format like `variance.inits`.
`est.variance`	Should the covariance matrix be estimated? This argument applies to estimated item slopes in `tam.mml.2pl`. The default is `FALSE` which means that latent variables (in the first group) are standardized in 2PL estimation.
`pweights`	An optional vector of person weights
`pid`	An optional vector of person identifiers
`userfct.variance`	Optional user customized function for variance specification (See Simulated Example 17).
`variance.Npars`	Number of estimated parameters of variance matrix if a `userfct.variance` is provided.
`verbose`	Optional logical indicating whether iteration should be displayed.
`control`	List of control parameters, see `tam.mml` fro details.
`object`	Object of class `tam.latreg`
`file`	A file name in which the summary output will be written
`x`	Object of class `tam.latreg`
`...`	Further arguments to be passed

Value

Subset of values of tam.mml

Examples

## Not run: 
#############################################################################
# EXAMPLE 1: Unidimensional latent regression model with fitted IRT model in
#            sirt package
#############################################################################

library(sirt)
data(data.pisaRead, package="sirt")
dat <- data.pisaRead$data

items <- grep("R4", colnames(dat), value=TRUE )    # select test items from data
# define testlets
testlets <- substring( items, 1, 4 )
itemcluster <- match( testlets, unique(testlets) )
# fit Rasch copula model (only few iterations)
mod <- sirt::rasch.copula2( dat[,items], itemcluster=itemcluster, mmliter=5)
# extract individual likelihood
like1 <- IRT.likelihood( mod )
# fit latent regression model in TAM
Y <- dat[, c("migra", "hisei", "female") ]
mod2 <- TAM::tam.latreg( like1, theta=attr(like1, "theta"), Y=Y, pid=dat$idstud )
summary(mod2)
# plausible value imputation
pv2 <- TAM::tam.pv( mod2 )
# create list of imputed datasets
Y <- dat[, c("idstud", "idschool", "female", "hisei", "migra") ]
pvnames <- c("PVREAD")
datlist <- TAM::tampv2datalist( pv2, pvnames=pvnames, Y=Y, Y.pid="idstud")

#--- fit some models
library(mice)
library(miceadds)
# convert data list into a mice object
mids1 <- miceadds::datalist2mids( datlist )
# perform an ANOVA
mod3a <- with( mids1, stats::lm(PVREAD ~ hisei*migra) )
summary( pool( mod3a ))
mod3b <- miceadds::mi.anova( mids1, "PVREAD ~ hisei*migra" )

#############################################################################
# EXAMPLE 2: data.pisaRead - fitted IRT model in mirt package
#############################################################################

library(sirt)
library(mirt)

data(data.pisaRead, package="sirt")
dat <- data.pisaRead$data

# define dataset with item responses
items <- grep("R4", colnames(dat), value=TRUE )
resp <- dat[,items]
# define dataset with covariates
X <- dat[, c("female","hisei","migra") ]

# fit 2PL model in mirt
mod <- mirt::mirt( resp, 1, itemtype="2PL", verbose=TRUE)
print(mod)
# extract coefficients
sirt::mirt.wrapper.coef(mod)

# extract likelihood
like <- IRT.likelihood(mod)
str(like)

# fit latent regression model in TAM
mod2 <- TAM::tam.latreg( like, Y=X, pid=dat$idstud )
summary(mod2)
# plausible value imputation
pv2 <- TAM::tam.pv( mod2, samp.regr=TRUE, nplausible=5 )
# create list of imputed datasets
X <- dat[, c("idstud", "idschool", "female", "hisei", "migra") ]
pvnames <- c("PVREAD")
datlist <- TAM::tampv2datalist( pv2, pvnames=pvnames, Y=X, Y.pid="idstud")
str(datlist)

# regression using semTools package
library(semTools)
lavmodel <- "
   PVREAD ~ hisei + female
           "
mod1a <- semTools::sem.mi( lavmodel, datlist)
summary(mod1a, standardized=TRUE, rsquare=TRUE)

#############################################################################
# EXAMPLE 3: data.Students - fitted confirmatory factor analysis in lavaan
#############################################################################

library(CDM)
library(sirt)
library(lavaan)

data(data.Students, package="CDM")
dat <- data.Students
vars <- scan(what="character", nlines=1)
   urban female sc1 sc2 sc3 sc4 mj1 mj2 mj3 mj4
dat <- dat[, vars]
dat <- na.omit(dat)

# fit confirmatory factor analysis in lavaan
lavmodel <- "
   SC=~ sc1__sc4
   SC ~~ 1*SC
   MJ=~ mj1__mj4
   MJ ~~ 1*MJ
   SC ~~ MJ
        "
# process lavaan syntax
res <- TAM::lavaanify.IRT( lavmodel, dat )
# fit lavaan CFA model
mod1 <- lavaan::cfa( res$lavaan.syntax, dat, std.lv=TRUE)
summary(mod1, standardized=TRUE, fit.measures=TRUE )
# extract likelihood
like1 <- TAM::IRTLikelihood.cfa( dat, mod1 )
str(like1)
# fit latent regression model in TAM
X <- dat[, c("urban","female") ]
mod2 <- TAM::tam.latreg( like1, Y=X  )
summary(mod2)
# plausible value imputation
pv2 <- TAM::tam.pv( mod2, samp.regr=TRUE, normal.approx=TRUE )
# create list of imputed datasets
Y <- dat[, c("urban", "female" ) ]
pvnames <- c("PVSC", "PVMJ")
datlist <- TAM::tampv2datalist( pv2, pvnames=pvnames, Y=Y )
str(datlist)

## End(Not run)

TAM

Test Analysis Modules

v3.6-45

GPL (>= 2)

Authors

Alexander Robitzsch [aut,cre] (<https://orcid.org/0000-0002-8226-3132>), Thomas Kiefer [aut], Margaret Wu [aut]

Initial release

2021-04-22 14:35:52