polymirt: Full-Information Item Factor Analysis for Mixed Data Formats

Description

polymirt fits an unconditional full-information maximum-likelihood factor analysis model to dichotomous and polychotomous data under the item response theory paradigm using Cai's (2010) Metropolis-Hastings Robbins-Monro algorithm.

Usage

polymirt(data, nfact, guess = 0, prev.cor = NULL,
	ncycles = 2000, burnin = 100, SEM.cycles = 50, kdraws = 1,
    tol = .001, printcycles = TRUE, calcLL = TRUE, draws = 2000,
    debug = FALSE, ...)

## S3 method for class 'polymirt':
summary(object, rotate='varimax', suppress = 0, digits = 3, ...)

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

## S3 method for class 'polymirt':
plot(x, npts = 50, rot = list(x = -70, y = 30, z = 10), ...)

## S3 method for class 'polymirt':
residuals(object, digits = 3, ...)

## S3 method for class 'polymirt':
anova(object, object2, ...)

Arguments

data

a matrix or data.frame that consists of numerically ordered data

nfact

number of factors to be extracted

guess

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

prev.cor

use a previously computed correlation matrix to be used to estimate starting values the estimation. The input could be any correlation matrix, but it is advised to use a matrix of polychoric correlations.

rotate

type of rotation to perform after the initial orthogonal parameters have been extracted. See mirt for a list of possible rotations

ncycles

the maximum number of iterations to be performed

burnin

number of burn-in cycles to perform before beginning the SEM stage

SEM.cycles

number of stochastic EM cycles to perform before beginning the MH-RM algorithm

kdraws

number of Metropolis-Hastings imputations of the factor scores at each iteration. Default is 1

tol

tolerance that will terminate the model estimation; must occur in 3 consecutive iterations

logical; display the standard errors?

an object of class polymirt to be plotted or printed

object

a model estimated from polymirt of class polymirt

object2

a model estimated from polymirt of class polymirt

suppress

a numeric value indicating which (possibly rotated) factor loadings should be suppressed. Typical values are around .3 in most statistical software

digits

the number of significant digits to be rounded

npts

number of quadrature points to be used for plotting features. Larger values make plots look smoother

rot

allows rotation of the 3D graphics

printcycles

logical; display iteration history during estimation?

calcLL

logical; calculate the log-likelihood?

draws

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

debug

logical; turn on debugging features?

...

additional arguments to be passed

Details

polymirt follows the item factor analysis strategy by a stochastic version of maximum likelihood estimation described by Cai (2010). The general equation used for multidimensional item response theory 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 (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. Use of plot will display the test information function for 1 and 2 dimensional solutions. To examine individuals item plots use itemplot (although the plink package is much more suitable for IRT graphics) which will also plot information and surface functions. coef displays the item parameters with their associated standard errors, while use of summary transforms the slopes into a factor loadings metric. Also, factor loading values below a specified constant can be also be suppressed in summary to allow better visual clarity. Models may be compared by using the anova function, where a Chi-squared difference test and AIC difference values are displayed.

References

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

Examples

Run this code

#load LSAT section 7 data and compute 1 and 2 factor models
data(LSAT7)
fulldata <- expand.table(LSAT7)

(mod1 <- polymirt(fulldata, 1))
summary(mod1)
residuals(mod1)

(mod2 <- polymirt(fulldata, 2))
summary(mod2)
coef(mod2)
anova(mod1,mod2)

###########
#data from the 'ltm' package in numeric format
data(Science)
(mod1 <- polymirt(Science,1))
summary(mod1)
residuals(mod1)
coef(mod1)

(mod2 <- polymirt(Science,2, calcLL = FALSE)) #don't calculate log-likelihood
mod2 <- logLik(mod2,5000) #calc log-likelihood here with more draws
summary(mod2, 'promax', suppress = .3)
coef(mod2)
anova(mod1,mod2)