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Add model evaluation metrics model objects

Source: R/add-model-evaluation.R
model_evaluation.Rd

Add model evaluation metrics to fitted model objects. These functions are wrappers around other functions that compute the metrics. The benefit of using these wrappers is that the model evaluation metrics are saved as part of the model object so that time-intensive calculations do not need to be repeated. See Details for specifics.

Usage

add_criterion(
  x,
  criterion = c("loo", "waic", "aic", "bic"),
  overwrite = FALSE,
  save = TRUE,
  ...,
  r_eff = NA
)

add_reliability(x, overwrite = FALSE, save = TRUE, ...)

add_fit(
  x,
  method = c("m2", "ppmc"),
  overwrite = FALSE,
  save = TRUE,
  ...,
  ci = 0.9
)

add_respondent_estimates(
  x,
  probs = c(0.025, 0.975),
  overwrite = FALSE,
  save = TRUE
)

Arguments

x

A measrdcm object.

criterion

A vector of information criteria to calculate and add to the model object. Must be "loo" or "waic" for models estimated with MCMC, or "aic" or "bic" for models estimated with the optimizer.

overwrite

Logical. Indicates whether specified elements that have already been added to the estimated model should be overwritten. Default is FALSE.

save

Logical. Only relevant if a file was specified in the measrdcm object passed to x. If TRUE (the default), the model is re-saved to the specified file when new criteria are added to the R object. If FALSE, the new criteria will be added to the R object, but the saved file will not be updated.

...

Arguments passed on to fit_ppmc

model_fit

The posterior predictive model checks to compute for an evaluation of model-level fit. If NULL, no model-level checks are computed. See details.

item_fit

The posterior predictive model checks to compute for an evaluation of item-level fit. If NULL, no item-level checks are computed. See details.

r_eff

Vector of relative effective sample size estimates for the likelihood (exp(log_lik)) of each observation. This is related to the relative efficiency of estimating the normalizing term in self-normalized importance sampling when using posterior draws obtained with MCMC. If MCMC draws are used and r_eff is not provided then the reported PSIS effective sample sizes and Monte Carlo error estimates can be over-optimistic. If the posterior draws are (near) independent then r_eff=1 can be used. r_eff has to be a scalar (same value is used for all observations) or a vector with length equal to the number of observations. The default value is 1. See the relative_eff() helper functions for help computing r_eff.

method

A vector of model fit methods to evaluate and add to the model object.

ci

The confidence interval for the RMSEA, computed from the M2

probs

The percentiles to be computed by the stats::quantile() function. Only relevant if the model was estimated with method = "mcmc". Only used if summary is TRUE.

Value

A modified measrdcm object with the corresponding slot populated with the specified information.

Details

For add_respondent_estimates(), estimated person parameters are added to the $respondent_estimates element of the fitted model.

For add_fit(), model and item fit information are added to the $fit element of the fitted model. This function wraps fit_m2() to calculate the M2 statistic (Hansen et al., 2016; Liu et al., 2016) and/or fit_ppmc() to calculate posterior predictive model checks (Park et al., 2015; Sinharay & Almond, 2007; Sinharay et al., 2006; Thompson, 2019), depending on which methods are specified.

For add_criterion(), relative fit criteria are added to the $criteria element of the fitted model. This function wraps loo() or waic() to calculate the LOO-CV (Vehtari et al., 2017) or WAIC (Watanabe, 2010), respectively, for models estimated with MCMC. For models estimated with the optimizer, this wraps aic() or bic() to estimate the AIC (Akaike, 1973) or BIC (Schwarz, 1978), respectively.

For add_reliability(), reliability information is added to the $reliability element of the fitted model. Pattern level reliability is described by Cui et al. (2012). Classification reliability and posterior probability reliability are described by Johnson & Sinharay (2018, 2020), respectively. This function wraps reliability(). Arguments supplied to ... are passed to reliability().

References

Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. In B. N. Petrov & F. Csáki (Eds.), Proceedings of the Second International Symposium on Information Theory (pp. 267-281). Akademiai Kiado.

Cui, Y., Gierl, M. J., & Chang, H.-H. (2012). Estimating classification consistency and accuracy for cognitive diagnostic assessment. Journal of Educational Measurement, 49(1), 19-38. doi:10.1111/j.1745-3984.2011.00158.x

Hansen, M., Cai, L., Monroe, S., & Li, Z. (2016). Limited-information goodness-of-fit testing of diagnostic classification item response models. British Journal of Mathematical and Statistical Psychology, 69(3), 225-252. doi:10.1111/bmsp.12074

Johnson, M. S., & Sinharay, S. (2018). Measures of agreement to assess attribute-level classification accuracy and consistency for cognitive diagnostic assessments. Journal of Educational Measurement, 55(4), 635-664. doi:10.1111/jedm.12196

Johnson, M. S., & Sinharay, S. (2020). The reliability of the posterior probability of skill attainment in diagnostic classification models. Journal of Educational and Behavioral Statistics, 45(1), 5-31. doi:10.3102/1076998619864550

Liu, Y., Tian, W., & Xin, T. (2016). An application of M2 statistic to evaluate the fit of cognitive diagnostic models. Journal of Educational and Behavioral Statistics, 41(1), 3-26. doi:10.3102/1076998615621293

Park, J. Y., Johnson, M. S., Lee, Y-S. (2015). Posterior predictive model checks for cognitive diagnostic models. International Journal of Quantitative Research in Education, 2(3-4), 244-264. doi:10.1504/IJQRE.2015.071738

Schwarz, G. (1978). Estimating the dimension of a model. The Annals of Statistics, 6(2), 461–464. doi:10.1214/aos/1176344136

Sinharay, S., & Almond, R. G. (2007). Assessing fit of cognitive diagnostic models. Educational and Psychological Measurement, 67(2), 239-257. doi:10.1177/0013164406292025

Sinharay, S., Johnson, M. S., & Stern, H. S. (2006). Posterior predictive assessment of item response theory models. Applied Psychological Measurement, 30(4), 298-321. doi:10.1177/0146621605285517

Thompson, W. J. (2019). Bayesian psychometrics for diagnostic assessments: A proof of concept (Research Report No. 19-01). University of Kansas; Accessible Teaching, Learning, and Assessment Systems. doi:10.35542/osf.io/jzqs8

Vehtari, A., Gelman, A., & Gabry, J. (2017). Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Statistics and Computing, 27(5), 1413-1432. doi:10.1007/s11222-016-9696-4

Watanabe, S. (2010). Asymptotic equivalence of Bayes cross validation and widely applicable information criterion in singular learning theory. Journal of Machine Learning Research, 11(116), 3571-3594. https://jmlr.org/papers/v11/watanabe10a.html

Examples

cmds_mdm_dina <- measr_dcm(
  data = mdm_data, missing = NA, qmatrix = mdm_qmatrix,
  resp_id = "respondent", item_id = "item", type = "dina",
  method = "optim", seed = 63277, backend = "rstan",
  prior = c(prior(beta(5, 17), class = "slip"),
            prior(beta(5, 17), class = "guess"))
)
#> Error: object 'mdm_qmatrix' not found

cmds_mdm_dina <- add_reliability(cmds_mdm_dina)
#> Error: object 'cmds_mdm_dina' not found
cmds_mdm_dina <- add_fit(cmds_mdm_dina, method = "m2")
#> Error: object 'cmds_mdm_dina' not found
cmds_mdm_dina <- add_respondent_estimates(cmds_mdm_dina)
#> Error: object 'cmds_mdm_dina' not found