mirt (version 0.2.6)

bfactor: Full-Information Item Bifactor Analysis

Description

bfactor fits a confirmatory maximum likelihood bifactor model to dichotomous and polychotomous data under the item response theory paradigm. Pseudo-guessing parameters may be included but must be declared as constant.

Usage

bfactor(data, specific, guess = 0, upper = 1, SE = FALSE,
    prev.cor = NULL, par.prior = FALSE, startvalues = NULL,
    quadpts = 15, verbose = FALSE, debug = FALSE, technical
    = list(), ...)

  ## S3 method for class 'bfactor':
summary(object, digits = 3, ...)

  ## S3 method for class 'bfactor':
coef(object, digits = 3, ...)

  ## S3 method for class 'bfactor':
fitted(object, digits = 3, ...)

  ## S3 method for class 'bfactor':
residuals(object, restype = 'LD',
    digits = 3, printvalue = NULL, ...)

Arguments

data

a complete matrix or data.frame of item responses that consists of only 0, 1, and NA values to be factor analyzed. If scores have been recorded by the response pattern then they can be recoded to dichotom

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 i

printvalue

a numeric value to be specified when using the res='exp' option. Only prints patterns that have standardized residuals greater than abs(printvalue). The default (NULL) prints all response patterns

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

SE

logical; estimate parameter standard errors?

prev.cor

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

par.prior

a list declaring which items should have assumed priors distributions, and what these prior weights are. Elements are slope and int to specify the coefficients beta prior for the slopes and normal prior for the interc

startvalues

user declared start values for parameters

quadpts

number of quadrature points per dimension.

object

a model estimated from bfactor of class bfactorClass

restype

type of residuals to be displayed. Can be either 'LD' for a local dependence matrix (Chen & Thissen, 1997) or 'exp' for the expected values for the frequencies of every response pattern

digits

number of significant digits to be rounded

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],[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); note that this only makes sense when comparing class bfactorClass models to class mirtClass or polymirtClass. The general equation used for item bifactor analysis in this package is in the logistic form with a scaling correction of 1.702. This correction is applied to allow comparison to mainstream programs such as TESTFACT 4 (2003) and POLYFACT. Unlike TESTFACT 4 (2003) initial start values are computed by using information from a quasi-tetrachoric correlation matrix, potentially with Carroll's (1945) adjustment for chance responses. To begin, a MINRES factor analysis with one factor is extracted, and the transformed loadings and intercepts (see mirt for more details) are used as starting values for the general factor loadings and item intercepts. Values for the specific factor loadings are taken to be half the magnitude of the extracted general factor loadings. Note that while the sign of the loading may be incorrect for specific factors (and possibly for some of the general factor loadings) the intercepts and general factor loadings will be relatively close to the final solution. These initial values should be an improvement over the TESTFACT initial starting values of 1.414 for all the general factor slopes, 1 for all the specific factor slopes, and 0 for all the intercepts. Factor scores are estimated assuming a normal prior distribution and can be appended to the input data matrix (full.scores = TRUE) or displayed in a summary table for all the unique response patterns. Fitted and residual values can be observed by using the fitted and residuals functions. To examine individuals item plots use itemplot which will also plot information and surface functions. Residuals are computed using the LD statistic (Chen & Thissen, 1997) in the lower diagonal of the matrix returned by residuals, and Cramer's V above the diagonal.

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 Carroll, J. B. (1945). The effect of difficulty and chance success on correlations between items and between tests. Psychometrika, 26, 347-372. Wood, R., Wilson, D. T., Gibbons, R. D., Schilling, S. G., Muraki, E., & Bock, R. D. (2003). TESTFACT 4 for Windows: Test Scoring, Item Statistics, and Full-information Item Factor Analysis [Computer software]. Lincolnwood, IL: Scientific Software International.

See Also

expand.table, key2binary, confmirt, fscores

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 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,
1.0,NA,NA),ncol=3,byrow=TRUE)

sigma <- diag(3)
dataset <- simdata(a,d,2000,sigma)

specific <- c(rep(1,7),rep(2,7))
simmod <- bfactor(dataset, specific)
coef(simmod)