mirt (version 0.8.0)

bfactor: Full-Information Item Bi-factor Analysis

Description

bfactor fits a confirmatory maximum likelihood bi-factor model to dichotomous and polytomous data under the item response theory paradigm. Fits the IRT models using a dimensional reduction EM algorithm so that regardless of the number of specific factors estimated the model only uses a two-dimensional quadrature grid for integration (hence the maximum number of factors in estimation is only 2). See confmirt for appropriate methods to be used on the objects returned from the estimation.

Usage

bfactor(data, model, SE = FALSE, SE.type = 'SEM', verbose
    = TRUE, ...)

Arguments

data

a matrix or data.frame that consists of numerically ordered data, with missing data coded as NA

model

a numeric vector specifying which factor loads on which item. For example, if for a 4 item test with two specific factors, the first specific factor loads on the first two items and the second specific factor on the last two, then the vector i

SE

logical; calculate information matrix and standard errors?

SE.type

type of standard errors to calculate. See mirt for details

verbose

logical; print observed log-likelihood value at each iteration?

...

additional arguments to be passed to the main estimation function. See mirt for more details

Details

bfactor follows the item factor analysis strategy explicated by Gibbons and Hedeker (1992) and Gibbons et al. (2007). 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.

References

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

See Also

expand.table, key2binary, confmirt.model, mirt, confmirt, bfactor, multipleGroup, mixedmirt, wald, itemplot, fscores, fitIndices, extract.item, iteminfo, testinfo, probtrace, boot.mirt, imputeMissing, itemfit, mod2values, read.mirt, simdata, createItem

Examples

###load SAT12 and compute bifactor model with 3 specific factors
data(SAT12)
data <- key2binary(SAT12,
  key = c(1,4,5,2,3,1,2,1,3,1,2,4,2,1,5,3,4,4,1,4,3,3,4,1,3,5,1,3,1,5,4,5))
specific <- c(2,3,2,3,3,2,1,2,1,1,1,3,1,3,1,2,1,1,3,3,1,1,3,1,3,3,1,3,2,3,1,2)
mod1 <- bfactor(data, specific)
summary(mod1)
itemplot(mod1, 18, drop.zeros = TRUE) #drop the zero slopes to allow plotting

###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, and use estimated mod1 as starting values
sv <- mod2values(mod1)
sv$value[220] <- 0
sv$est[220] <- FALSE
mod3 <- bfactor(data, specific, pars = sv) #with excellent starting values

#without using starting values (required if SE.type = 'SEM')
specific[32] <- NA
mod3 <- bfactor(data, specific)
anova(mod1, mod3)


#########
#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)