ppc_irtree: Posterior predicitve checks and p-values for several...

In hplieninger/mpt2irt: Bringing Multinomial Processing Tree Models To Item Response Theory To Investigate Response Styles

Description

This function takes posterior predictive probabilities (from post_prob_irtree), and compares—for several discrepency measures—observations and predictions both descriptively and via posterior predicitive p-values.

Usage

ppc_irtree(prob = NULL, statistics = c("item_cor", "OR", "Q3", "ISD",
  "resp"), fit = NULL, X = NULL, revItem = NULL, traitItem = NULL)

Arguments

prob	Numeric array of dimension R x N x J x 5 (for N persons, J items with 5 categories, and R iterations).
statistics	Character vector of length >= 1 specifying the discrepency measures to use.
fit	a fitted object from fit_irtree or preferably from summarize_irtree_fit.
X	Numeric matrix of dimension N x J containing the observed item responses. item_cor: Item-total correlation, i.e., polyserial correlation between response and total score. OR: Odds ratio for (dichotomized) pairs of items. Q3: Yen's Q3 statistic. ISD: Item-score-distribution, i.e., Pearson's X2 of residuals. resp: Observed responses (integer), predicted responses (integer), and expected responses (numeric).
revItem	vector of length J specifying reversed items (1=reversed, 0=regular)
traitItem	vector of length J specifying the underlying traits (e.g., indexed from 1...5). Standard: only a single trait is measured by all items. If the Big5 are measured, might be something like c(1,1,1,2,2,2,...,5,5,5,5)

Value

Returns an object of class ppc

References

Levy, R. (2011). Posterior predictive model checking for conjunctive multidimensionality in item response theory. Journal of Educational and Behavioral Statistics, 36, 672-694. doi:10.3102/1076998611410213

Li, T., Xie, C., & Jiao, H. (2017). Assessing fit of alternative unidimensional polytomous IRT models using posterior predictive model checking. Psychological Methods, 22, 397-408. doi:10.1037/met0000082

Sinharay, S., Johnson, M. S., & Stern, H. S. (2006). Posterior predictive assessment of item response theory models. Applied Psychological Measurement, 30, 298-321. doi:10.1177/0146621605285517

Zhu, X., & Stone, C. A. (2012). Bayesian comparison of alternative graded response models for performance assessment applications. Educational and Psychological Measurement, 72, 774-799. doi:10.1177/0013164411434638

See Also

print.ppc for summarizing the results and ppc_resp_irtree for summarizing posterior predictive response frequencies.

Examples

## Not run: 
J <- 10
betas <- cbind(rnorm(J, .5), rnorm(J, .5), rnorm(J, 1.5), rnorm(J, 0))
dat <- generate_irtree_ext(N = 20, J = J, betas = betas, beta_ARS_extreme = .5)

# fit model
res1 <- fit_irtree(dat$X, revItem = dat$revItem, M = 200)
res2 <- summarize_irtree_fit(res1)

# posterior predictive checking
res3 <- post_prob_irtree(res2)
res4 <- ppc_irtree(prob = res3, fit = res1)
res4

## End(Not run)

hplieninger/mpt2irt documentation built on May 17, 2019, 4:54 p.m.