# 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

 ```1 2``` ```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

`print.ppc` for summarizing the results and `ppc_resp_irtree` for summarizing posterior predictive response frequencies.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15``` ```## 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) ```