M2: Compute M2 statistic

Description

Computes the M2 (Maydeu-Olivares & Joe, 2006) statistic for dichotomous data and the M2* statistic for polytomous data (collapsing over response categories for better stability; see Cai and Hansen, 2013), as well as associated fit indices that are based on fitting the null model.

Usage

M2(obj, calcNull = TRUE, quadpts = NULL, Theta = NULL, impute = 0,
  CI = 0.9, residmat = FALSE, QMC = FALSE, ...)

Arguments

obj

an estimated model object from the mirt package

calcNull

logical; calculate statistics for the null model as well? Allows for statistics such as the limited information TLI and CFI

quadpts

number of quadrature points to use during estimation. If NULL, a suitable value will be chosen based on the rubric found in fscores

Theta

a matrix of factor scores for each person used for imputation

impute

a number indicating how many imputations to perform (passed to imputeMissing) when there are missing data present. This requires a precomputed Theta input. Will return a data.frame object

numeric value from 0 to 1 indicating the range of the confidence interval for RMSEA. Default returns the 90% interval

residmat

logical; return the residual matrix used to compute the SRMSR statistic?

QMC

logical; use quasi-Monte Carlo integration? Useful for higher dimensional models. If quadpts not specified, 2000 nodes are used by default

...

additional arguments to pass

Value

Returns a data.frame object with the M2 statistic, along with the degrees of freedom, p-value, RMSEA (with 90% confidence interval), SRMSR if all items were ordinal, and optionally the TLI and CFI model fit statistics

References

Cai, L. & Hansen, M. (2013). Limited-information goodness-of-fit testing of hierarchical item factor models. British Journal of Mathematical and Statistical Psychology, 66, 245-276.

Maydeu-Olivares, A. & Joe, H. (2006). Limited information goodness-of-fit testing in multidimensional contingency tables Psychometrika, 71, 713-732.

Examples

Run this code

dat <- expand.table(LSAT7)
(mod1 <- mirt(dat, 1))
M2(mod1)

#M2 imputed with missing data present (run in parallel)
dat[sample(1:prod(dim(dat)), 250)] <- NA
mod2 <- mirt(dat, 1)
mirtCluster()
Theta <- fscores(mod2, full.scores=TRUE)
M2(mod2, Theta=Theta, impute = 10)