mirt (version 0.3.0)

confmirt: Confirmatory Full-Information Item Factor Analysis

Description

confmirt fits a conditional (i.e., confirmatory) full-information maximum-likelihood factor analysis model to dichotomous and polytomous data under the item response theory paradigm using Cai's (2010) Metropolis-Hastings Robbins-Monro algorithm. Fits univariate and multivariate Rasch, 1-4PL, graded, (generalized) partial credit, nominal, multiple choice, and partially-compensatory models, potentially with polynomial and product constructed latent traits.

Usage

confmirt(data, model, itemtype = NULL, guess = 0, upper =
    1, startvalues = NULL, constrain = NULL, freepars =
    NULL, parprior = NULL, verbose = TRUE, calcLL = TRUE,
    draws = 2000, debug = FALSE, rotate = 'varimax', Target
    = NULL, technical = list(), ...)
  ## S3 method for class 'confmirt':
coef(object, rotate = '', Target =
    NULL, allpars = FALSE, digits = 3, ...)
  ## S3 method for class 'confmirt':
summary(object, digits = 3, ...)
  ## S3 method for class 'confmirt':
residuals(object, restype = 'LD',
    digits = 3, printvalue = NULL, ...)
  ## S3 method for class 'confmirt':
anova(object, object2, ...)
  ## S3 method for class 'confmirt':
fitted(object, digits = 3, ...)

Arguments

data

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

model

an object returned from confmirt.model() declaring how the factor model is to be estimated, or a single numeric value indicating the number of exploratory factors to estimate. See confmirt.

guess

initial (or fixed) values for the pseudo-guessing parameter. Can be entered as a single value to assign a global guessing parameter or may be entered as a numeric vector for each item

upper

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

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

verbose

logical; display iteration history during estimation?

calcLL

logical; calculate the log-likelihood via Monte Carlo integration?

draws

the number of Monte Carlo draws to estimate the log-likelihood

allpars

logical; print all the item parameters instead of just the slopes?

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

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

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

debug

logical; turn on debugging features?

object

an object of class confmirtClass

object2

an object of class confmirtClass

digits

the number of significant digits to be rounded

rotate

if model is numeric (indicating an exploratory item FA) then this rotation is used. Default is 'varimax'

Target

a dummy variable matrix indicting a target rotation pattern

technical

list specifying subtle parameters that can be adjusted. These values are [object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

...

additional arguments to be passed

Confirmatory IRT

Specification of the confirmatory item factor analysis model follows many of the rules in the SEM framework for confirmatory factor analysis. The variances of the latent factors are automatically fixed to 1 to help facilitate model identification. All parameters may be fixed to constant values or set equal to other parameters using the appropriate declarations.

Exploratory IRT

Specifying a number as the second input to confmirt an exploratory IRT model is estimated and can be viewed as a stochastic analogue of mirt, with much of the same behaviour and specifications. Rotation and target matrix options will be used in this subroutine and will be passed to the returned object for use in generic functions such as summary() and fscores. Again, factor means and variances are fixed to ensure proper identification. See mirt for more details.

Details

confmirt follows a confirmatory and exploratory item factor analysis strategy that uses a stochastic version of maximum likelihood estimation described by Cai (2010a, 2010b). The general equation used for multidimensional item response theory in this function 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 (2003) and POLYFACT. Missing data are treated as 'missing at random' so that each response vector is included in the estimation (i.e., full-information). 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. For computing the log-likelihood more accurately see logLik.

coef displays the item parameters with their associated standard errors, while use of summary transforms the slopes into a factor loadings metric and if the model is exploratory allows for rotating the parameters. Also, nested models may be compared by using the anova function, where a Chi-squared difference test and AIC/BIC difference values are displayed.

References

Cai, L. (2010a). High-Dimensional exploratory item factor analysis by a Metropolis-Hastings Robbins-Monro algorithm. Psychometrika, 75, 33-57.

Cai, L. (2010b). Metropolis-Hastings Robbins-Monro algorithm for confirmatory item factor analysis. Journal of Educational and Behavioral Statistics, 35, 307-335.

Chalmers, R., P. (2012). mirt: A Multidimensional Item Response Theory Package for the R Environment. Journal of Statistical Software, 48(6), 1-29.

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, simdata, fscores, confmirt.model

Examples

#Exploratory model estimation, similar to mirt()
data(LSAT7)
fulldata <- expand.table(LSAT7)
(mod1 <- confmirt(fulldata, 1))

#Confirmatory models

#simulate data
a <- matrix(c(
1.5,NA,
0.5,NA,
1.0,NA,
1.0,0.5,
 NA,1.5,
 NA,0.5,
 NA,1.0,
 NA,1.0),ncol=2,byrow=TRUE)

d <- matrix(c(
-1.0,NA,NA,
-1.5,NA,NA,
 1.5,NA,NA,
 0.0,NA,NA,
3.0,2.0,-0.5,
2.5,1.0,-1,
2.0,0.0,NA,
1.0,NA,NA),ncol=3,byrow=TRUE)

sigma <- diag(2)
sigma[1,2] <- sigma[2,1] <- .4
items <- c(rep('dich',4), rep('graded',3), 'dich')
dataset <- simdata(a,d,2000,items,sigma)

#analyses
#CIFA for 2 factor crossed structure

model.1 <- confmirt.model()
  F1 = 1-4
  F2 = 4-8
  COV = F1*F2


mod1 <- confmirt(dataset,model.1)
coef(mod1)
summary(mod1)
residuals(mod1)

#####
#bifactor
model.3 <- confmirt.model()
  G = 1-8
  F1 = 1-4
  F2 = 5-8


mod3 <- confmirt(dataset,model.3)
coef(mod3)
summary(mod3)
residuals(mod3)
anova(mod1,mod3)

#####
#polynomial/combinations
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))

model.quad <- confmirt.model()
       F1 = 1-32
  (F1*F1) = 1-32


model.combo <- confmirt.model()
       F1 = 1-16
       F2 = 17-32
  (F1*F2) = 1-8


(mod.quad <- confmirt(data, model.quad))
(mod.combo <- confmirt(data, model.combo))
anova(mod.quad, mod.combo)