mirt (version 0.4.0)

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 univariate and multivariate 1-4PL, graded, (generalized) partial credit, nominal, multiple choice, and partially compensatory 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. See confmirt for appropriate methods to be used on the objects returned from the estimation.

Usage

bfactor(data, specific, itemtype = NULL, guess = 0, upper
    = 1, SE = FALSE, free.start = NULL, startvalues = NULL,
    constrain = NULL, freepars = NULL, parprior = NULL,
    prev.cor = NULL, quadpts = 20, verbose = FALSE, debug =
    FALSE, technical = list(), ...)

Arguments

data

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

specific

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 is

itemtype

type of items to be modeled, declared as a vector for each item or a single value which will be repeated globally. The NULL default assumes that the items are ordinal or 2PL, however they may be changed to the following: 'Rasch', '1PL', '2PL', '3P

guess

fixed pseudo-guessing parameter. Can be entered as a single value to assign a global value or may be entered as a numeric vector for each item of length ncol(data).

upper

fixed upper bound parameters for 4-PL model. Can be entered as a single value to assign a global guessing parameter or may be entered as a numeric vector corresponding to each item

free.start

a list containing the start value and logical indicating whether a given parameter is to be freely estimated. Each element of the list consists of three components, the parameter number, the starting (or fixed) value, and a logical to indicate whe

SE

logical, estimate the standard errors? Calls the MHRM subroutine for a stochastic approximation

constrain

a list of user declared equality constraints. To see how to define the parameters correctly use constrain = 'index' initially to see how the parameters are labeled. To constrain parameters to be equal create a list with separate conca

parprior

a list of user declared prior item probabilities. To see how to define the parameters correctly use parprior = 'index' initially to see how the parameters are labeled. Can define either normal (normally for slopes and intercepts) or b

freepars

a list of user declared logical values indicating which parameters to estimate. To see how to define the parameters correctly use freepars = 'index' initially to see how the parameters are labeled. These values may be modified and inp

startvalues

a list of user declared start values for parameters. To see how to define the parameters correctly use startvalues = 'index' initially to see what the defaults would noramlly be. These values may be modified and input back into the fu

prev.cor

uses a previously computed correlation matrix to be used to estimate starting values for the EM estimation

quadpts

number of quadrature points per dimension.

verbose

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

debug

logical; turn on debugging features?

technical

a list containing lower level technical parameters for estimation [object Object],[object Object],[object Object],[object Object]

...

additional arguments to be passed

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, fscores, multipleGroup, wald

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)
coef(mod1)

###Try with fixed guessing parameters added
guess <- rep(.1,32)
mod2 <- bfactor(data, specific, guess = guess)
coef(mod2)

#########
#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)