Scientific works

• Published papers

1. de Castro, M. O.; Azevedo, C. L. N.; Nobre, J. S. (2024) A Robust Quantile Regression for Bounded Variables, Statistics & Computing. Subject: Quantile regression for bounded variables.

2. De Freitas, J. V. B. ; Azevedo, C. L. N. ; Nobre, J. S. (2023). A stochastic approximation ECME algorithm to semi-parametric scale mixtures of centred skew normal regression models, Statistics and Computing, 33, 51. Subject: Longitudinal data modelling.

3. Luis Bazán, J.; Flores A., Sandra E.; Azevedo, Caio L. N. ; Dey, D. K. (2023). Revisiting the Samejima-Bolfarine-Bazán IRT models: New features and extensions, Brazilian Journal of Probability and Statistics, 37, 1-25. Subject: Item response modelling.

4. Silva, A. R. S.; Azevedo, C. L. N. ; Bazán, J.  L. ; Nobre, J. S. (2021). Augmented-limited regression models with an application to the study of the risk perceived using continuous scales, Journal of Applied Statistics, 48, 1998-2021. Subject: Bounded data modelling.

5. Silva dos Santos, J. R., Azevedo, C. L. N., Fox, J.-P. (2021). Bayesian Longitudinal Item Response Modeling With Multivariate Asymmetric Serial Dependencies, Journal of Statistical Computation and Simulation, 92, 488-523. Subject: Latent Variable Modeling (Item Response Theory).      

6.  Ribeiro, V. S. O,  J. S. Nobre, J. R. S. Santos, Azevedo, C. L. N. (2021) Beta-rectangular regression models to longitudinal data, Brazilian Journal of Probability and Statistics. Subject: Bounded data modeling (Longitudinal data + zero/one augmented beta distribution).  

7. Silva, A. R. S., N. L., Azevedo, C. L. N., Bazan, J. L., Nobre, J. S. (2019). Augmented-limited regression models with an application to the study of the risk perceived using continuous scales, Journal of Applied Statistics. Subject: Bounded data modeling (zero/one augmented rectangular beta distribution).     

8. Silva, A. R. S., N. L., Azevedo, C. L. N., Bazan, J. L., Nobre, J. S. (2019). Bayesian inference for zero-and/or-one augmented rectangular beta regression model, Brazilian journal of probability and Statistics. Subject: Bounded data modeling (zero/one augmented rectangular beta distribution).

9. Velho, R. M., Merian, A. M., Azevedo, C. L. N. (2020). Communicating science with YouTube videos: how nine factors relate to and affect video views, Frontiers in Communication, 5, 1-14, Subject: Application of Count Regression Models.

10. Nogarotto, D. C., Azevedo, C. L. N., Bazan, J. L. (2020). Bayesian Estimation, residual analysis and prior sensitivity study for zero-one augmented beta regression models with an application to psychometric data, Brazilian Journal of Probability and Statistics, 34, 2, 304-322. (link) Subject: Bounded data modeling (zero/one augmented beta distribution).

11. Chaves, N. L., Azevedo, C. L. N., Vilca-Labra, F. and Nobre, J. S. (2020). A log Birnbaum-Saunders regression model based on the skew-normal distribution under the centred parameterization, Statistics and Its Interface, 13, 3, 335-346. (link) Subject: Non-guassian data modeling (Birnbaum-Saunders distribution).

12. Chaves, N. L., Azevedo, C. L. N., Vilca-Labra, F. and Nobre, J. S. (2019). A new Birnbaum-Saunders type distribution based on the skew-normal model under a centered parameterization, Chilean Journal of Statistics, 10, 1, 55-76. (link)  Subject: Non-guassian data modeling (Birnbaum-Saunders distribution).

13. Padilla, J. L. ; Azevedo, C. L. N. ; Lachos, V. H. (2018). Multidimensional multiple group IRT models with skew normal latent trait distributions, Journal of Multivariate Analysis, 167, 250-268. (link) Subject: Latent Variable Modeling (Item Response Theory).

14. Gonçalves, D. S., Azevedo, C. L. N., Lavor, C. C., Gomes-Ruggiero, M. A. (2018). Bayesian inference for Quantum State Tomography, Journal of Applied Statistics, 45, 10, 1846-1871. (link)  Subject: Bayesian Inference & Quantum Physics.

15. Vilca, F. ; Azevedo, C. L. N. ; Balakrishnan, N. (2016) . Bayesian inference for sinh-normal/independent nonlinear regression models, Journal of Applied Statistics, 44, 11, 2052-2074. (link) Subject: Non-guassian data modeling (Birnbaum-Saunders distribution).

16. Azevedo, C. L. N. ; Fox, Jean-Paul ; Andrade, Dalton F. (2016) . Bayesian longitudinal item response modeling with restricted covariance pattern structures, Statistics and Computing, 26, 443-460. (link) Subject:  Latent Variable Modeling (Item Response Theory).  

17. Ferreira, E. V. ; Azevedo, C. L. N. (2016) Contributions to the study of the Generalized Partial Credit Model (In Portuguese: Contribuições ao estudo do Modelo de Crédito Parcial Generalizado), Estudos em Avaliação Educacional, 28, 67, 236-254. (link)Subject: Latent Variable Modeling (Item Response Theory).

18. Azevedo, C. L. N., Fox, J.-P., and Andrade, D. F. (2015). Longitudinal Multiple-Group IRT Modeling: Covariance pattern selection using MCMC and RJMCMC,  "Special Issue on Bayesian Statistics in Psychometrics", International Journal of Quantitative Research in Education, 2, 3-4 213-243. (link) Subject: Latent Variable Modeling (Item Response Theory).

19. Borgatto, A. F. ; Azevedo, C. L. N. ; Pinheiro, A. S. ; Andrade, D. F. (2015). Comparison of Ability Estimation Methods Using IRT for Tests with Different Degrees of Difficulty, Communications in Statistics. Simulation and Computation, 44, 2, 474-488. (link) Subject: Latent Variable Modeling (Item Response Theory).

20. Lachos, V. H. ; Chen, Ming-Hui ; ABANTO-VALLE, C. A. ; Azevedo, Caio L. N. (2015). Quantile Regression for Censored Mixed-Effects Models with Applications to HIV studies, Statistics and its Interface, 8, 2, 203-215. (link) Subject: Quantile regression and censored data.

21. Costa, D. R. ; Lachos, V. H. ; Bazan, J. L. ; Azevedo, C. L. N. (2014). Estimation methods for multivariate Tobit confirmatory factor analysis, Computational Statistics & Data Analysis, 79, 248-260. (link) Subject: Latent Variable Modeling (Factor Analysis).

22. Ferreira, E. V. ; Azevdo, C. L. N . (2014). Inferential aspects of Generalized Partial Credit Model (In Portuguese: Aspectos inferenciais no Modelo de Crédito Parcial Generalizado da Teoria da Resposta ao Item), Sigmae, 3, 2, 1-15. (link) Subject: Latent Variable Modeling (Item Response Theory).

23. Azevedo, C. L. N. and Andrade, D. F. (2013). CADEM: a conditional augmented data EM algorithm for fitting one parameter probit models, Brazilian Journal of Probability and Statistics, 27, 2, 245-262. (link) Subject: Latent Variable Modeling (Item Response Theory).

24. Santos, J. R. S., Azevedo, C. L. N. and Bolfarine, H. (2013). A multiple group Item Response Theory model with centred skew normal latent trait distributions under a Bayesian framework, Journal of Applied Statistics, 40, 10, 2129-2149. (link) Subject: Latent Variable Modeling (Item Response Theory).

25. Azevedo, Caio L. N. ; Andrade, Dalton F. ; Fox, Jean-Paul (2012). A Bayesian generalized multiple group IRT model with model-fit assessment tools, Computational Statistics & Data Analysis, 56, 12, 4399-4412. (link) Subject:  Latent Variable Modeling (Item Response Theory).

26. Azevedo, C. L. N., Bolfarine, H. and Andrade, D. F. (2011). Bayesian inference for a skew-normal IRT model under the centred parameterization, Computational Statistics & Data Analysis, 55, 1, 353-365. (link) Subject: Latent Variable Modeling (Item Response Theory).

27. Azevedo, Caio L. N. Bolfarine, Heleno and Andrade, Dalton F. (2011). Parameter recovery for a skew-normal IRT model under a Bayesian approach: hierarchical framework, prior and kernel sensitivity and sample size, Journal of Statistical Computation and Simulation, 82, 11, 1679-1699. (link) Subject: Latent Variable Modeling (Item Response Theory).

28. Gonçalves, Flávia ; Azevedo, Caio L. N. ; Ferracane, Jack L. ; Braga, Roberto R. (2011) . BisGMA/TEGDMA ratio and filler content effects on shrinkage stress, Dental Materials, 27, 6, 520-526. (link) Subject: Dental Material.

29. Azevedo, C. L. N. and Andrade, D. F. (2010). An estimation method for the latent traits and population parameter for the nominal response model, Brazilian Journal of Probability and Statistics, 24, 3, 415-433. (link)  Subject: Latent Variable Modeling (Item Response Theory).

30. Azevedo, C. L. N. (2009). Some observations on the identification and interpretation of the 3PL IRT model, Measurement: Interdisciplinary Research & Perspectives, 7, 2, 89-91. (link) Subject: Latent Variable Modeling (Item Response Theory). 

31. Braga, R. R. ; Boaro, L. ; Kuroe, T. ; Azevedo, C. L. N. ; Singer, J. M.  (2006). Influence of cavity dimensions and their derivates (volume and ' C' factor) on shrinkage stress development and microleakage of composite restorations. Dental Materials, 22, 9, 818-82. (link) Subject: Dental Material.

32. Nobre, J. S. and Azevedo, C. L. N. (2006). O princípio da equivariância: conceito e aplicações. Revista Colombiana de Estadística, 29, 2, 195-220. (link) Subject: Fundamentals of Statistics.

33. Reis, A. ; Loguercio, A. D. ; Azevedo, C. L. N. ; Singer, J. M. ; Carvalho, R. M. ; Grande, R. H. M. (2003). Moisture Spectrum of Demineralized Dentin for Adhesive Systems with Different Solvent Bases. Journal of Adhesive Dentistry, 5,  3, 183-192. (link) Subject: Dental Material.

34. Witzel, M. ; Braga, R. R. ; Singer, J. M. ; Azevedo, C. L. N. (2002). Bond strength between polymer resin-based cement and porcelain/dentin surfaces: influence of polymerization mode and early cyclic loading. International Journal Of Prosthodontic, 16, 2, 145-149. (link) Subject: Dental Material.

 

• Accepted Papers

1.  Freias, J. V. B. ; Nobre, J. S. ; Azevedo, C. L. N. (2024). Flexible quasi-beta prime regression models for dependent continuous positive data. Statistics and Its Interface. Subject: Longidutinal modelling for positive data.

• Arxiv

1.      Medeiros, E. S., Lira, J., Silva, R., Azevedo, C. L. N., (2020). Visualizing and Understanding Large-Scale Assessments in Mathematics through Dimensionality Reduction, ArXiv (link). Subject: Latent Variable Modeling (Factor models and Item Response Theory).

• Technical (research) reports

1.      Nathalia L. Chaves, Caio L. N. Azevedo, Filidor Vilca-Labra, Juvêncio S. Nobre. (2018) A log Birnbaum-Saunders regression model based on the skew-normal distribution under the centred parameterization (link).

2.      Nathalia L. Chaves, Caio L. N. Azevedo, Filidor Vilca-Labra, Juvêncio S. Nobre. (2018) A new Birnbaum-Saunders model based on the skew-normal distribution under the centred parameterization (link).

3.      Ana R.S. Santos Caio L. N. Azevedo Jorge L. Bazan Juvêncio S. Nobre (2017). Bayesian Inference for Zero-and/or-one Augmented Rectangular Beta Regression Models (link).

4.      Juan L. Padilla Caio L. N. Azevedo Victor H. Lachos (2017) Multidimensional Multiple Group IRT Models with Skew Normal Latent Trait Distributions (link) 

5.       Put more technical (research) reports

• Submitted/Under review

1. de Freitas, J. V. B. ; Azevedo, C. L. N. ; Nobre, J. S. (2024). GEE inference to semi-parametric additive models for skewed and/or heavy-tailed longitudinal data, submitted to Sankhya B. Subject: Longitudinal data modelling.

2. Galindo, A. F. L.; Azevedo, C. L. N.; Nobre, J. S. (2024) Semi-parametric additive models for bounded data, submitted to Stat. Subject: Regression modelling for bounded data.

3. Medeiros, E. S., Azevedo, C. L. N., Lira, J., Silva, R.,(2023). Identifying Relevant Abilities for Performance Improvement in Large-Scale Mathematics Assessments: A Logistic PCA Approach, submmited to Large-scale Assessments in Education. Subject: Latent Variable Modeling (Factor models and Item Response Theory).

4. Mendes, A. M., Azevedo, C. L. N., Demétrio, C. G. B., Nobre, J. S. (2022). Generalized mixed Poisson distributions, (under review) to International Statistical Review, Subject: Modelling count data.       

5. Mendes, A. M., Azevedo, C. L. N., Demétrio, C. G. B., Nobre, J. S. (2024). Generalized mixed Poisson distributions, submitted to Statistics and Computing, Subject: Modelling count data.       

6. Padilla, J. L. P., Azevedo, C. L.N., Lachos, V. H. (2022) Parameter recovery for skew multidimensional item response models: a comparison of MCMC algorithms and assessment of effects of interest, (under review) Journal of Statistical Computation and Simulation. Subject: Multidimensional IRT data.

7. Bazan, J. L., Prates, M. O.,  Lachos, V. H., Azevedo, C. L. N. (2021)   A new class of binary regression models for unbalance data with applications in medical data, To be submmited XXXXXX. Binary Regression Modeling.

8. Azevedo, C. L. N., Lobos, Vilca, F. V., Villegas, C. (2019). Birnbaum-Saunders Linear Mixed-Effects Models with Censored Data: Bayesian MCMC Inference, rejected with encouragement to be resubmitted, first round, Journal of Statistical Computation and Simulation, to be submmited to another journal(?). Subject: Non-guassian data modeling (Mixed Models - Longitudinal and Censored Data + Birnbaum-Saunders distribution).

• ·Ongoing works

1. Mendes, A. M. F., Azevedo, C. L. N., Chen, M.-H. (2023). Generalized gamma quantile regression models,  to se submitted Subject: Non-guassian data modeling (Quantile regression for positive data).

2. Mendes, A. M. F. Chen, M.-H.,  Azevedo, C. L. N., (2023). Power exponential quantile regression models,  to se submitted Subject: Non-guassian data modeling (Quantile regression for positive data).

3. Mendes, A. M. F., Azevedo, C. L. N., Chen, M.-H. (2023). Centred skew scale-mixture Birnbaum-Saunders quantile regression model,  to se submitted Subject: Non-guassian data modeling (Quantile regression for positive data).

4. de Freitas, J. V. B., Bondon, P., Azevedo, C. L. N., Reisen, V. A., Nobre, J. S. (2023). Scale mixtures of multivariate centered skew-normal distributions, to se submitted to Journal of Multivariate Analysis, Subject: Non-guassian data modeling.

5. de Freitas, J. V. B., Bondon, P., Azevedo, C. L. N., Reisen, V. A., Nobre, J. S. (2023). Scale mixtures of multivariate centered skew-normal distributions, to se submitted to Journal of the Royal Statistical, Series C , Subject: Non-guassian data modeling.

6. Meza, R. O., Tavares, H. R., Azevedo, C. L. N. (2023). Performance of Methods $\omega$, $GBT$, $K$, $K_1$, $K_2$, $S_1$, $S_2$ and the New Approach $T_R$, to se submitted, Subject: Test fraud detection.

7. Meza, R. O., Tavares, H. R., Azevedo, C. L. N. (2023). New Approaches Based on Similarity Analysis Statistics ($\omega$, $GBT$, $K$ and Variants, to se submitted, Subject: Test fraud detection.

8. Meza, R. O., Tavares, H. R., Azevedo, C. L. N. (2023). Use of Machine Learning Methods to Detect Test Fraud, to se submitted, Subject: Test fraud detection.

9. XXXXXX, Azevedo, C. L. N., Vilca-Labra, F. and Nobre, J. S. (2023). Estimating the parameters for a log Birnbaum-Saunders regression model based on the skew-normal distribution under the centred parameterization using the No-U-Turn Sampler, to se submitted Subject: Non-guassian data modeling (Birnbaum-Saunders distribution).

10. (XXXXXXX), Ferreira, E. V., Azevedo, C. L. N., Bazan, J. L. (2023). A General Bayesian Framework for Multiple Group Polytomous IRT Models with Asymmetric Latent Traits distributions, to be submitted. Subject: Latent Variable Modeling (Item Response Theory).

11. XXXXXXX, Azevedo, C. L. N. (2023). Likelihood inference for a new family of the Birnbaum-Saunders models based on the centred skew scale-mixture of normal distributions, to be submitted. (positive data modelling)

12. XXXXXXX, Azevedo, C. L. N. (2023). Likelihood inference for a new family of the Zero Augmented Birnbaum-Saunders models based on the centred skew scale-mixture of normal distributions, to be submitted. (positive data modelling)

13. XXXXXXX, Azevedo, C. L. N. (2023). Birnbaum-Saunders models based on the centred skew scale-mixture of normal distributions: a likelihood based approach, to be submitted. (positive data modelling)

14. XXXXXXX, Azevedo, C. L. N. (2023). Zero Augmented Birnbaum-Saunders models based on the centred skew scale-mixture of normal distributions: a likelihood based approach, to be submitted. (positive data modelling)

15. XXXXXXX, Azevedo, C. L. N. (2023). Birnbaum-Saunders mixed models based on the centred skew scale-mixture of normal distributions, to be submitted. (positive data modelling)

16. XXXXXXX, Azevedo, C. L. N. (2023). Zero augmented Birnbaum-Saunders mixed models based on the centred skew scale-mixture of normal distributions, to be submitted. (positive data modelling)

17. Castro, M. O., A. R. S., Azevedo, C. L. N., Tuerlinckx, F. (2024) A general beta item response model for continuous-limited responses under a Bayesian approach, to be submitted. (IRT modelling for bounded response)

18. Castro, M. O., A. R. S., Azevedo, C. L. N., Tuerlinckx, F. (2024) A general beta rectangular item response model for continuous-limited responses under a Bayesian approach, to be submitted. (IRT modelling for bounded response)

19. Castro, M. O., A. R. S., Azevedo, C. L. N., Tuerlinckx, F. (2024) A general beta rectangular item response model for continuous-limited responses under a Bayesian approach, to be submitted. (IRT modelling for bounded response)

20. Castro, M. O., A. R. S., Azevedo, C. L. N., Tuerlinckx, F. (2024) Bayesian inference for a zero and/or one augmented general beta rectangular item response model for continuous-limited responses, to be submitted. (IRT modelling for bounded response)

21. Galindo, A. F. L., Azevedo, C. L. N.,  Nobre, J. S (2023) Semi-parametric Additive Models for independent and limited augmented data, to be submmited. (augmented limited data modeling)

22. Galindo, A. F. L.,  Nobre, J. S, Azevedo, C. L. N., (2023) Semi-parametric additive models for dependent and limited data , to be submmited. (longitudinal limited data modeling)

23. Galindo, A. F. L.  Nobre, J. S, Azevedo, C. L. N., (2023) Semi-parametric additive models for dependent and limited augmented data, to be submmited. (longitudinal augmented limited data modeling)

24. Mendes, A. M. F., Azevedo, C. L. N.,  Demétrio, C. G. B., Nobre, J. S. (2020) Generalized mixed Poisson regression models for overdispersed count data , to be submmited to Computational Statistics & Data Analysis. (Count data modeling - Overdispersion)

25. Mendes, A. M. F., Azevedo, C. L. N.,  Demétrio, C. G. B., Nobre, J. S. (2020) Bayesian inference for general mixed Poisson regression models with varying dispersion, to be submmited to Statistics & Computing. (Count data modeling - Overdispersion)

26. Santos, J. R. S., Azevedo, C. L. N., Fox, J.-P. (2020). A multiple group growth curve IRT longitudinal model with skewed latent traits distributions, to be submitted to Statistics and Computing. Latent Variable Modeling (Item Response Theory).

27. Santos, J. R. S., Azevedo, C. L. N., Fox, J.-P. (2020). A copula-based modeling for IRT longitudinal data, to be submitted to Journal of Multivariate Analysis. Latent Variable Modeling (Item Response Theory).

28. Gomez, J. L. P, Azevedo, C. L. N., Lachos, V. H. (2020). A family of asymmetric t-distributions: linear and binary regression models under a Bayesian framework, to be submitted to Statistics. Non-guassian data modeling (centered skew scale mixture of  distributions)

29. Gomez, J. L. P, Azevedo, C. L. N., Corinne, A. Lachos, V. H. (2020). IRT Models With Centered Skewed heavy-tailed Distributions For The Latent Traits And Centered Skewed Link Functions, to be submiited to Journal of Statistical Planning and Inference. Latent Variable Modeling (Item Response Theory).  

30. Gomez, J. L. P, Azevedo, C. L. N., Corinne, A. and Lachos, V. H. (2020). Multidimensional Item Response Theory models with asymmetric-heavy tailed item response function and latent trait distributions under a Bayesian framework, to be submitted to Journal of Multivariate Analysis. Latent Variable Modeling (Item Response Theory).

31. Gomez, J. L. P, Azevedo, C. L. N., Corinne, A. and Lachos, V. H. (2020). Bayesian inference for multivariate Item Response Theory models with asymmetric-heavy tailed item response function and latent trait distributions, to be submitted to Statistica Sinica. Latent Variable Modeling (Item Response Theory).

32. Gomez, J. L. P, Azevedo, C. L. N., Corinne, A. Lachos, V. H. (2020). Centered skewed heavy-tailed item response models with collateral information, to be submiited to Journal of Educational and Behavorial Statistics. Latent Variable Modeling (Item Response Theory).  

33. Gomez, J. L. P, Azevedo, C. L. N., Corinne, A. and Lachos, V. H. (2020). Multidimensional centered skewed heavy-tail item response models with collateral information, to be submitted to Psychometrika. Latent Variable Modeling (Item Response Theory).

34. Gomez, J. L. P,  Corinne, A., Azevedo, C. L. N.(2020) Contributions to dimensionality evaluation for dichotomous Item Response data, to be submmited to British Journal of Mathematical and Statistical Psychology. Latent Variable Modeling (Item Response Theory).

35. Gomez, J. L. P, Azevedo, C. L. N., Corinne, A. and Lachos, V. H. (2020). Model fit assessment tools for unidimensional and multidimensional Item Response Theory models, to be submmited to British Journal of Mathematical and Statistical Psychology. Latent Variable Modeling (Item Response Theory).

36.  Azevedo, C. L. N. Fox, J.-P. and Andrade, D. F. (2020). A multilevel modeling for longitidunal item response theory, to be submitted to Bayesian Analysis. Latent Variable Modeling (Item Response Theory).

37. Freitas, J. V. B., Maioli, M. C., Azevedo, C. L. N. (2020) Bayesian Inference for linear regression models based on centered skew scale mixture of normal distributions, to be submitted to Canandian Journal of Statistics. Non-guassian data modeling (centered skew normal scale mixture distributions)

38. Freitas, J. V. B., Maioli, M. C., Bazan, J. L., Lachos, V. H., Azevedo, C. L. N. (2020). A general skew scale mixed based regression model for binary responses, to be submitted to Journal of Statistical Planning and Inference. Binary data modeling (link function + centered skew normal scale mixture distributions)

39. Freitas, J. V. B., Maioli, M., Azevedo, C. L. N. (2020) Bivariate regression models for continuous and binary bivariate data based on centered skew scale mixture of normal distributions, to be submitted to Statistical Modeling. Bivariate Non-guassian data modeling (continuous + binary responses + centered skew normal scale mixture distributions)

40. (XXXXXX) Silva, D. A., Curi, M., Gonzalez, L. F. P., Azevedo, C. L. N. (2020). Bayesian Poisson IRT models for counting response, to be submitted to Biometrical Journal/Bayesian Analysis. Latent Variable Modeling (Item Response Theory).

41. (XXXXXX) Silva, D. A., Curi, M., T., Gonzalez, L. F. P., Azevedo, C. L. N. (2020). IRT models for overdispersed counting response,  to be submitted to Psychometrika. Latent Variable Modeling (Item Response Theory).

42. (XXXXXX) Silva, D. A., Curi, M., T., Gonzalez, L. F. P., Azevedo, C. L. N. (2020). Zero inflanted item response modeling for counting data, to be submitted to Statistics and Computing. Latent Variable Modeling (Item Response Theory).

43. Borgatto, A. F., Azevedo, C. L. N., Andrade, D. F and Pinheiro, A. S. (2020). Estimation of Extreme Proficiency Levels by Multiple Groups. Latent Variable Modeling (Item Response Theory).