bfactor fits a confirmatory maximum likelihood two-tier/bifactor model to
dichotomous and polytomous data under the item response theory paradigm.
The IRT models are fit using a dimensional reduction EM algorithm so that regardless
of the number of specific factors estimated the model only uses the number of
factors in the second-tier structure plus 1. For the bifactor model the maximum
number of dimensions is only 2 since the second-tier only consists of a
ubiquitous unidimensional factor. See mirt for appropriate methods to be used
on the objects returned from the estimation.bfactor(data, model, model2 = mirt.model(paste0("G = 1-", ncol(data))),
group = NULL, quadpts = 21, ...)matrix or data.frame that consists of
numerically ordered data, with missing data coded as NAc(1,mirt.model(). By default
the model will fit a unidimensional model in the second-tier, and therefore be equivalent to
the bifactor modelmirt
for more details and examplesConfirmatoryClass
(ConfirmatoryClass-class) or MultipleGroupClass(MultipleGroupClass-class).bfactor follows the item factor analysis strategy explicated by
Gibbons and Hedeker (1992), Gibbons et al. (2007), and Cai (2010).
Nested models may be compared via an approximate
chi-squared difference test or by a reduction in AIC or BIC (accessible via
anova). See mirt for more details regarding the
IRT estimation approach used in this package. The default is to use 21 quadrature
for each dimensions, but this can be over-written by passing a quadpts = #}
argument.Note: for multiple group two-tier analyses only the second-tier means and variances
should be freed since the specific factors are not treated independently due to the
dimension reduction technique.
###Try with fixed guessing parameters added guess <- rep(.1,32) mod2 <- bfactor(data, specific, guess = guess) coef(mod2) anova(mod1, mod2)
## don't estimate specific factor for item 32 specific[32] <- NA mod3 <- bfactor(data, specific) anova(mod1, mod3)
# same, but decalred manually (not run) #sv <- mod2values(mod1) #sv$value[220] <- 0 #parameter 220 is the 32 items specific slope #sv$est[220] <- FALSE #mod3 <- bfactor(data, specific, pars = sv) #with excellent starting values
######### # mixed itemtype example
#simulate data a <- matrix(c( 1,0.5,NA, 1,0.5,NA, 1,0.5,NA, 1,0.5,NA, 1,0.5,NA, 1,0.5,NA, 1,0.5,NA, 1,NA,0.5, 1,NA,0.5, 1,NA,0.5, 1,NA,0.5, 1,NA,0.5, 1,NA,0.5, 1,NA,0.5),ncol=3,byrow=TRUE)
d <- matrix(c( -1.0,NA,NA, -1.5,NA,NA, 1.5,NA,NA, 0.0,NA,NA, 2.5,1.0,-1, 3.0,2.0,-0.5, 3.0,2.0,-0.5, 3.0,2.0,-0.5, 2.5,1.0,-1, 2.0,0.0,NA, -1.0,NA,NA, -1.5,NA,NA, 1.5,NA,NA, 0.0,NA,NA),ncol=3,byrow=TRUE) items <- rep('dich', 14) items[5:10] <- 'graded'
sigma <- diag(3) dataset <- simdata(a,d,2000,itemtype=items,sigma=sigma)
specific <- c(rep(1,7),rep(2,7)) simmod <- bfactor(dataset, specific) coef(simmod)
######### # Two-tier model
#simulate data set.seed(1234) a <- matrix(c( 0,1,0.5,NA,NA, 0,1,0.5,NA,NA, 0,1,0.5,NA,NA, 0,1,0.5,NA,NA, 0,1,0.5,NA,NA, 0,1,NA,0.5,NA, 0,1,NA,0.5,NA, 0,1,NA,0.5,NA, 1,0,NA,0.5,NA, 1,0,NA,0.5,NA, 1,0,NA,0.5,NA, 1,0,NA,NA,0.5, 1,0,NA,NA,0.5, 1,0,NA,NA,0.5, 1,0,NA,NA,0.5, 1,0,NA,NA,0.5),ncol=5,byrow=TRUE)
d <- matrix(rnorm(16)) items <- rep('dich', 16)
sigma <- diag(5) sigma[1,2] <- sigma[2,1] <- .4 dataset <- simdata(a,d,2000,itemtype=items,sigma=sigma)
specific <- c(rep(1,5),rep(2,6),rep(3,5)) model <- mirt.model(' G1 = 1-8 G2 = 9-16 COV = G1*G2')
#quadpts dropped for faster estimation, but not as precise simmod <- bfactor(dataset, specific, model, quadpts = 9, TOL = 1e-3) coef(simmod) summary(simmod) itemfit(simmod, QMC=TRUE) M2(simmod)
Chalmers, R., P. (2012). mirt: A Multidimensional Item Response Theory Package for the R Environment. Journal of Statistical Software, 48(6), 1-29.
Gibbons, R. D., & Hedeker, D. R. (1992). Full-information Item Bi-Factor Analysis. Psychometrika, 57, 423-436.
Gibbons, R. D., Darrell, R. B., Hedeker, D., Weiss, D. J., Segawa, E., Bhaumik, D. K., Kupfer, D. J., Frank, E., Grochocinski, V. J., & Stover, A. (2007). Full-Information item bifactor analysis of graded response data. Applied Psychological Measurement, 31, 4-19.
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