mirt fits an unconditional maximum likelihood factor analysis model to dichotomous data under the item response theory paradigm. Pseudo-guessing parameters may be included but must be declared as constant, since the estimation of these parameters often leads to unacceptable solutions.mirt(fulldata, nfact, guess = 0, prev.cor = NULL, par.prior = FALSE,
startvalues = NULL, quadpts = NULL, ncycles = 300, tol = .001, nowarn = TRUE,
debug = FALSE, ...)
## S3 method for class 'mirt':
summary(object, rotate='varimax', suppress = 0, digits = 3, ...)
## S3 method for class 'mirt':
coef(object, digits = 3, ...)
## S3 method for class 'mirt':
anova(object, object2, ...)
## S3 method for class 'mirt':
fitted(object, digits = 3, ...)
## S3 method for class 'mirt':
plot(x, type = 'info', npts = 50, rot = list(x = -70, y = 30, z = 10), ...)
## S3 method for class 'mirt':
residuals(object, digits = 3, ...)matrix or data.frame 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 dichotomous format using the slope and int to specify the coefficients beta prior for the slopes and normal prior for the intercepts, and mirt to be plotted or printedmirt of class mirtmirt of class mirt with more estimated parameters than object'curve' for the total test score as a function of two dimensions, or 'info' to show the test information function for two dimensionsmirt returns an object of class mirt, with the following elements:X2df and X2ncycles if the tolerance is reachedc(1,0,0), indicating no influence on the parameterscoef since these will be helpful in determining whether a guessing parameter should be removed (item facility value is too close to the guessing parameter) or if an item should be constrained or removed entirely (values too close to 0 or 1). As a general rule, items with facilities greater than .95, or items that are only .05 greater than the guessing parameter, should be considered for removal from the analysis. It is also important to pay attention to the log-likelihood values printed after the model is estimated, since if these values do not increase then there likely is a problem with the estimation. Also, increasing the number of quadrature points per dimension may help to stabilize the estimation process.mirt follows the item factor analysis strategy by marginal maximum likelihood estimation (MML) that is outlined in Bock and Aiken (1981) and Bock, Gibbons and Muraki (1988). Nested models may be compared via the approximate chi-squared difference test or by a reduction in AIC (accessible via anova). 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). The target equation is
$$P(X | \theta; \bold{a}_i; d_i; g_i) = g_i + (1 - g_i) * 1.702(\bold{a}_i' \bold{a}_i + d_i)/ (1 + 1.702(\bold{a}_i' \bold{a}_i + d_i))$$
where i is the item index, $\bold{a}_i$ is the vector of discrimination parameters (i.e. slopes), $d_i$ is the intercept, and $g_i$ is the pseudo-guessing parameter. To avoid estimation difficulties the $g_i$'s must be specified by the user.
Estimation of the model begins with computing a matrix of tetrachoric correlations, potentially with Carroll's (1945) adjustment for chance responds. A MINRES factor analysis with nfact is then extracted and item parameters are estimated by $a_{ij} = f_{ij}/u_i$, where $f_{ij}$ is the factor loading for the ith item on the jth factor, and $u_i$ is the square root of the factor uniqueness, $\sqrt{1 - h_i^2}$. The initially intercept parameters are determined by calculating the inverse normal of the item facility (i.e., item easiness), $q_i$, to obtain $d_i = q_i / u_i$. Following these initial estimates the model is iterated using the EM estimation strategy with non-adaptive quadrature points. Implicit equation accelerations (described in Ramsey (1975)) are also added to facilitate parameter convergence speed, and this is adjusted every third cycle.
Factor scores are estimated assuming a normal prior distribution and can be appended to the input data matrix (full.data = TRUE) or displayed in a summary table for all the unique response patterns. summary allows for various rotations available from the GPArotation package. These are:
[object Object],[object Object]
Using plot will plot the either the test surface function or 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. 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.expand.table,key2binary#load LSAT section 7 data and compute 1 and 2 factor models
data(LSAT7)
fulldata <- expand.table(LSAT7)
(mod1 <- mirt(fulldata, 1))
summary(mod1)
residuals(mod1)
plot(mod1) #test information function
(mod2 <- mirt(fulldata, 2))
summary(mod2)
coef(mod2)
residuals(mod2)
anova(mod1, mod2) #compare the two models
scores <- fscores(mod2) #save factor score table
###########
data(SAT12)
fulldata <- 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))
#without guessing scree(tmat) #looks like a 2 factor solution
mod1 <- mirt(fulldata, 1)
mod2 <- mirt(fulldata, 2)
mod3 <- mirt(fulldata, 3)
anova(mod1,mod2)
anova(mod2, mod3) #negative AIC, 2 factors probably best
#with guessing
mod1g <- mirt(fulldata, 1, guess = .1)
coef(mod1g)
mod2g <- mirt(fulldata, 2, guess = .1)
coef(mod2g)
anova(mod1g, mod2g)
summary(mod2g, rotate='promax')Run the code above in your browser using DataLab