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. Missing values are automatically assumed to be 0.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, restype = 'LD', 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 NULLslope 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 dimensions'LD' for a local dependence matrix (Chen & Thissen, 1997) or 'exp' for the expected values for the frequencies of every response patterncoef 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 or treated with prior distributions. Also, increasing the number of quadrature points per dimension may help to stabilize the estimation process.polymirt function, which can analyze mixed dichotomous and polytomous data formats as well as estimate the lower asymptote paramters. For a specialized bifactor model see bfactor, and for more general confirmatory item response modeling see the confmirt function.mirt follows the item factor analysis strategy by marginal maximum likelihood estimation (MML) 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/BIC values (comparison via anova). The general equation used for dichotomous multidimensional item response theory item is a logistic form with a scaling correction of 1.702. This correction is applied to allow comparison to mainstream programs such as TESTFACT (2003). The general IRT equation is
$$P(X | \theta; \bold{a}_i; d_i; g_i) = g_j + (1 - g_j) / (1 + exp(-1.702(\bold{a}_j' \theta + d_j)))$$
where j is the item index, $\bold{a}_j$ is the vector of discrimination parameters (i.e., slopes), $$\theta$$ is the vector of factor scores, $d_j$ is the intercept, and $g_j$ is the pseudo-guessing parameter. To avoid estimation difficulties the $g_j$'s must be specified by the user.
Estimation begins by computing a matrix of quasi-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 $a_{ij} = f_{ij}/u_j$, where $f_{ij}$ is the factor loading for the jth item on the ith factor, and $u_j$ is the square root of the factor uniqueness, $\sqrt{1 - h_j^2}$. The initial intercept parameters are determined by calculating the inverse normal of the item facility (i.e., item easiness), $q_j$, to obtain $d_j = q_j / u_j$. Following these initial estimates the model is iterated using the EM estimation strategy with fixed quadrature points. Implicit equation accelerations described by Ramsey (1975) are also added to facilitate parameter convergence speed, and these are 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 individual item plots use itemplot (although the plink package may be 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,polymirt,confmirt#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