DIF analysis is commonly used in large-scale educational tests and survey studies. DIF analysis helps reveal whether the test or survey is fair, or whether it is systematically biased against certain groups of test-takers, such as women or certain underprivileged groups. The Liu-Agresti estimator (Liu and Agresti, 1996, DOI: 10.2307/2532838) is widely used when performance is scored according to the degrees of proficiency, rather then correct or incorrect. The Liu-Agresti method can be implemented by packages DIFAS 5.0, WINSTEPS (DIF statistics), etc.

The BUC method (Mukherjee, Ahn, Liu, Rathouz, and Sanchez, 2008, DOI: 10.1002/sim.3325) is named by Baetschmann et al. (2015). For a longitudinal study, researchers are often concerned about the unobserved heterogeneity. The BUC method provides a simple way to obtain consistent fixed effect estimators for an ordered logit model to control the unobserved heterogeneity. The BUC method was originally proposed for biomedical case-control data. Gunasekara, Carter, Liu, , Richardson, and Blakely (2012) first used the method for a longitudinal data.

A multiple response variable is a categorical variable for which respondents can select any number of outcome categories. Such data arise often in a survey. For example, a question might be ``which of the following learning methods have you used'' and the respondents could tick all items that apply. We (DOI: 10.1111/j.0006-341X.1999.00936.x, DOI: 10.1177/0049124101029004001, DOI: 10.1002/bimj.200710395, DOI: 10.1111/insr.12015) used maximum-likelihood or quasi-likelihood approaches to analyse such data. Some of the methods can be implemented using packages SPSS, R (MRCV), etc.

Research Projects, Funding and Scholarships

• I have been awarded the following research grants (current and past):
  • A data-science driven evolution of aquaculture for building the blue economy (Team: Mengjie Zhang, Ivy Liu, Linley Jesson, Maren Wellenreuther, etc. ) MBIE (Strategic Science Investment Fund). Amount: 13m. March 2020 - Feb 2027.

  • Dimension reduction for mixed type multivariate data (PIs: Ivy Liu and Richard Arnold; AIs: Shirley Pledger and Daniel Fernandez) Marsden Fund March 2017 - March 2021.

  • Feature Clustering for Various Types of Variables (PI: Ivy Liu; AIs: Richard Arnold and Bing Xue ) University Research Fund (URF) Jan - Dec 2016.

  • Cluster analysis for ordinal categorical data (PIs: Richard Arnold and Ivy Liu; AI: Shirley Pledger) Marsden Fund March 2013 - March 2016.

    PhD students: Daniel Fernandez Martinez and Roy Costilla

  • Cluster analysis for ordinal data University Research Fund (URF) Jan - Dec 2011.

  • Longitudinal data analysis for ordinal responses University Research Fund (URF) Jan - Dec 2010.

  • Ordinal data challenges for medical sciences University Research Fund (URF) Jan - Dec 2009.

  • SoFIE Health - look at health data in the SOFIE longitudinal study of Family, Income and Employment. Collaboration with Tony Blakely and others (Wellington School of Medicine). Health Research Council funded project 2004-2010. (with Richard Arnold)

  • Analysis of matched case-control study using ordinal models University Research Fund (URF) 2007-2008.

  • Graphical diagnostic methods for ordinal response models Faculty Research Grant (Science Faculty) May - Dec 2008.

  • Modelling repeated multiple responses data University Research Fund (URF) Jan - Dec 2004.

• PhD Scholarships:
• Visit Victoria PhD scholarship (Closing dates: 1 March, 1 July or 1 November; for both domestic and international students)
• Chinese students are able to apply PhD scholarships through the program between China Scholarship Council and Victoria University of Wellington (Closing dates: 1 July or 1 November)

• My research grants can support several research assistants. Succesful applicants will be paid.
• Applicants are expected to have a B+/A- or above in STAT or MATH papers, and have strong programming skills in R.
• If you want to gain work experience, please contact me.

Research publications

• Liu, I., Morrison, P. S. and Zeng, D. (2024). Wellbeing heterogeneity within and among university students. Applied Research in Quality of Life 19, 215–244. https://doi.org/10.1007/s11482-023-10238-0.
• Li, S., Fan, Z., Liu, I., Morrison, P. S., and Liu, D. (2024). Surrogate method for partial association between mixed data with application to well-being survey analysis. The Annals of Applied Statistics 18(3), 2254-2276. arXiv preprint arXiv:2306.05362.
• Cui, Y., McMillan, L., Liu, I. (2024). Semi-supervised Model-Based Clustering for Ordinal Data. In: Benavides-Prado, D., Erfani, S., Fournier-Viger, P., Boo, Y.L., Koh, Y.S. (eds) Data Science and Machine Learning. AusDM 2023. Communications in Computer and Information Science, vol 1943. Springer, Singapore. https://doi.org/10.1007/978-981-99-8696-5_3.
• Zeng, D., Bi, Y., Liu, I., Xue, B., Vennell, R., and Zhang, M. (2023). A New Genetic Programming-Based Approach to Object Detection in Mussel Farm Images. In 2023 38th International Conference on Image and Vision Computing New Zealand (IVCNZ) (pp. 1-6). IEEE.
• Morrison, P. S., Liu, I. and Zeng, D. (2023). Well-being and ill-being on campus. Journal of Wellbeing, 13(3), p. 64-93, https://doi.org/10.5502/ijw.v13i3.2785.
• Preedalikit, K., Fernandez, D., Liu, I., McMillan, L., Ruscone, M. N., and Costilla, R. (2023). Row mixture-based clustering with covariates for ordinal responses. Computational Statistics, https://doi.org/10.1007/s00180-023-01387-9.
• Zeng, D., Liu, I., Bi., Y., Vennell, R., Briscoe, D., Xue, B., and Zhang, M. (2023). A new multi-object tracking pipeline based on computer vision techniques for mussel farms. Journal of the Royal Society of New Zealand, https://doi.org/10.1080/03036758.2023.2240466.
• Fernandez, D., Liu, I., Preti, A., Haro, M., and Siddi, S. (2023). Launay–Slade Hallucination Scale-Extended: simplifying its interpretation. Psychosis, 15(1), p. 56-65, https://doi.org/10.1080/17522439.2021.1983011.
• Liu, I., Suesse, T., Harvey, S., Gu, P. Y., Fernandez, D. and Randal, J. (2023). Generalized Mantel–Haenszel Estimators for Simultaneous Differential Item Functioning Tests. Educational and Psychological Measurement 83(5), p. 1007-1032. https://doi.org/10.1177/00131644221128341.
• Fernandez, D., McMillan, L., Arnold, R., Spiess, M. and Liu, I. (2022). Goodness-of-Fit and Generalized Estimating Equation Methods for Ordinal Responses based on the Stereotype Model. Stats 5(2), 507-520. https://doi.org/10.3390/stats5020030.
• Fernandez, D., Gine-Vazquez, I., Liu, I. , Yucel, R., Ruscone, M. N., Morena, M., Garcia, V. G., Haro, J. M. Pan, W., Tyrovolas, S. (2021). Are environmental pollution and biodiversity levels associated to the spread and mortality of COVID-19? A four-month global analysis. Environmental Pollution, 271, 116326. https://doi.org/10.1016/j.envpol.2020.116326.
• Liu, I. and Fernandez, D. (2020). Discussion on “Assessing the goodness of fit of logistic regression models in large samples: A modification of the Hosmer‐Lemeshow test” by Giovanni Nattino, Michael L. Pennell, and Stanley Lemeshow. Biometrics, 76(2), 564-568, https://doi.org/10.1111/biom.13251.
• Spiess, M., Fernandez, D., Nguyen, T., and Liu, I. (2020). Generalized estimating equations to estimate the ordered stereotype logit model for panel data. Statistics in Medicine, 39(14), 1919-1940, https://doi.org/10.1002/sim.8520.
• Hirose, Y. and Liu, I. (2020). Statistical Generalized Derivative Applied to the Profile Likelihood Estimation in a Mixture of Semiparametric Models. Entropy, 22(3), https://doi.org/10.3390/e22030278.
• Fernandez, D., Liu, I., Costilla, R., and Gu, P. Y. (2020). Assigning Scores for Ordered Categorical Responses. Journal of Applied Statistics, 47, 1261-1281, https://doi.org/10.1080/02664763.2019.1674790.
• Fernandez, D., Liu, I., Arnold, R., Nguyen, T. and Spiess, M. (2020). Model-based goodness-of-fit tests for the ordered stereotype model. Statistical Methods in Medical Research, 29(6), 1527-1541, https://doi.org/10.1177/0962280219864708.
• Fernandez, D., Liu, I., and Costilla, R. (2019). A Method for Ordinal Outcomes: The Ordered Stereotype Model. International Journal of Methods in Psychiatric Research, 28(4), https://doi.org/10.1002/mpr.1801.
• Costilla, R., Liu, I., Arnold, R., and Fernandez, D. (2019). Bayesian model-based clustering for longitudinal ordinal data. Computational Statistics, 34(3), 1015-1038, https://doi.org/10.1007/s00180-019-00872-4.
• Berman, E., Chen, D. Y., Wang, X., and Liu, I. (2019). Executive entrepreneurship in national departments. Administration & Society, 51, 855-884. https://doi.org/10.1177/0095399717701523.
• Suesse, T. and Liu, I. (2019). Mantel-Haenszel estimators of a common odds ratio for multiple response data. Statistical Methods & Applications, 28, 57-76. https://doi.org/10.1007/s10260-018-0429-z.
• Fernandez, D., Arnold, R., Pledger, S., Liu, I., and Costilla, R. (2019). Finite mixture biclustering of discrete type multivariate data. Advances in Data Analysis and Classification, 13, 117-143. https://doi.org/10.1007/s11634-018-0324-3.
• Fernandez, D. and Liu, I. (2016). A goodness-of-fit test for the ordered stereotype model. Statistics in Medicine, 35(25), 4660-4696, https://doi.org/10.1002/sim.7002.
• Preedalikit, K., Liu, I., Hirose, Y. Sibanda, N. and Fernandez, D. (2016). Joint modeling of survival and longitudinal ordered data using a semiparametric approach. Australian & New Zealand Journal of Statistics 58, 153-172, https://doi.org/10.1111/anzs.12153.
• Matechou, E., Liu, I., Fernandez, D., Farias, M., and Gjelsvik, B. (2016). Biclustering models for two-mode ordinal data, Psychometrika 81, 611-624, https://doi.org/10.1007/s11336-016-9503-3.
• Liu, I. (2016). Analysis of Categorical Data with R by BILDER, C. R. and LOUGHIN, T. M. (Book Reviews). Australian and New Zealand Journal of Statistics, 58, 141-142.
• Xue, B., Lane, M., Liu, I., and Zhang, M. (2016). Dimension Reduction in Classification using Particle Swarm Optimisation and Statistical Variable Grouping Information. IEEE Symposium Series on Computational Intelligence (IEEE SSCI 2016). Athens, Greece, December 6-9, 2016 pp (to appear).
• Nguyen, H. B., Xue, B., Liu, I., Andreae, P., and Zhang, M. (2016). New mechanism for archive maintenance in PSO-based multi-objective feature selection. Soft Computing 20, 3927--3946, https://doi.org/10.1007/s00500-016-2128-8.
• Nguyen, H. B., Xue, B., Liu, I., Andreae, P., and Zhang, M. (2015). Gaussian Transformation based Representation in Particle Swarm Optimisation for Feature Selection. Proceedings of the 18th European Conference on the Applications of Evolutionary Computation (EuroApplications 2015). Lecture Notes in Computer Science. Vol. 9028. Copenhagen, Denmark. 8-10 April 2015. pp. 541-553. (Nominated as Best Paper).
• Nguyen, H. B., Xue, B., Liu, I., and Zhang, M. (2014). PSO and Statistical Clustering for Feature Selection: A New Representation. In Simulated Evolution and Learning (pp. 569-581). Springer International Publishing.
• Arnold, R., Chukova, S., Hayakawa, Y. and Liu, I. (2014). Joint Modelling of Failure Times and Severities Using fuzzy Clustering. Proceedings of the Asia-Pacific International Workshop in Advanced Reliability Modelling, Sapporo, Japan, 21-23 August.
• Nguyen, H. B., Xue, B., Liu, I., and Zhang, M. (2014, July). Filter Based Backward Elimination in Wrapper Based PSO for Feature Selection in Classification. In Evolutionary Computation (CEC), 2014 IEEE Congress on (pp. 3111-3118). IEEE.
• Lane, M. C., Xue, B., Liu, I., and Zhang, M. (2014). Gaussian Based Particle Swarm Optimisation and Statistical Clustering for Feature Selection. In Evolutionary Computation in Combinatorial Optimisation (pp. 133-144). Springer Berlin Heidelberg.
• Lane, M. C., Xue, B., Liu, I., and Zhang, M. (2013). Particle Swarm Optimisation and Statistical Clustering for Feature Selection. In AI 2013: Advances in Artificial Intelligence (pp. 214-220). Springer International Publishing
• Suesse, T. and Liu, I. (2013). Modelling strategies for repeated multiple-response data. International Statistical Review 81, 230-248.
• Suesse, T. and Liu, I. (2012). Modelling strategies for repeated multiple response data. Technical Report, MSOR 12-3 , Victoria University of Wellington.
• Suesse, T. and Liu, I. (2012). Mantel-Haenszel estimators of odds ratios for stratified dependent binomial data. Computational Statistics and Data Analysis 56, 2705-2717.
• Solomon, J., Jacobson, S. and Liu, I. (2012). Fishing for a solution: can collaborative resource management reduce poverty and support conservation? Environmental Conservation 39, 51-61.
• Liu, I. (2011). Analysis of Ordinal Categorical Data by AGRESTI, A. (Book Reviews). Australian and New Zealand Journal of Statistics 53, 124-126.
• Gunasekara, F., Carter, K., Liu, I., Richardson, K., and Blakely, T. (2011). The relationship between income and health using longitudinal data from New Zealand. Journal of Epidemiology and Community Health, online: doi:10.1136/jech.2010.125021.
• Suesse, T. and Liu, I. (2011). Modelling strategies for repeated multiple response data. Presented at the New Zealand Statistical Association 2011 Conference in Auckland, New Zealand, 29 - 31August.
• Matechou, E. Liu, I., Pledger, S., and Arnold, R. (2011). Biclustering models for ordinal data. Presented at the New Zealand Statistical Association 2011 Conference in Auckland, New Zealand, 29 - 31August.
• Liu, I. (2010). Marginal Models for Dependent, Clustered, and Longitudinal Categorical Data by BERGSMA, W., CROON, M., and HAGENAARS, J. A. (Book Reviews). Biometrics 66, 323-323.
• Gunasekara, F., Carter, K., Blakely, T., and Liu, I. (2009). Determining the effect of change in income on self-rated health using regression models - ordered, linear, fixed or random? Working Paper to be presented at the British Household Panel Survey Conference July 9-11th 2009, University of Essex, Colchester. R Code
• Mukherjee, B. and Liu, I.. (2009). A Note on Bias Due to Fitting Prospective Multivariate Generalized Liner Models to Categorical Outcomes Ignoring Retrospective Sampling Schemes. Journal of Multivariate Analysis, 100, 459-472.
• Liu, I., Mukherjee, B., Suesse, T., Sparrow, D., and Park, S. K. (2009). Graphical Diagnostics to Check Model Misspecification for the Proportional Odds Regression Model. Statistics in Medicine, 28, 412-429.
• Suesse, T. and Liu, I. (2008). Diagnostics for Multiple Response Data. The proceedings of PROBASTAT 2006 conference, Tatra Mountains Mathematical Publications, 39, 105-113.
• Mukherjee, B., Ahn, J., Liu, I., Rathouz, P, and Sanchez, B. (2008). Fitting stratified proportional odds models by amalgamating conditional likelihoods. Statistics in Medicine, 27, 4950-4971.
• Liu, I. and Mukherjee, B. (2008). Proportional Odds Models. Encyclopedia of Clinical Trials. (Editor: R. D'Agostino, L. Sullivan, and J. Massaro). Wiley: New York.
• Liu, I. and Suesse, T. (2008). The Analysis of Stratified Multiple Responses. Biometrical Journal, 50, 135-149.
• Liu, I., Suesse, T., and Mukherjee, B. (2007). Graphical Model-Checking Methods for Proportional Odds Models. The Proceedings of the International Statistical Institute 56th Session CD-ROM (828.pdf). Lisbon, Portugal.
• Mukherjee, B., Liu, I., and Sinha, S. (2007). Analysis of Matched Case-Control Data with Multiple Ordered Disease States: Possible Choices and Comparisons. Statistics in Medicine, 26, 3240-3257.
• Liu, I. and Wang, D. (2007). Diagnostics for Stratified Clinical Trials in Proportional Odds Models. Communications in Statistics : Theory and Method, 36, 211-220.
• Liu, I. and Mukherjee, B. (2005). Possible Ways of Analysis of Matched Case-Control Data with Multiple Ordered Disease States. The Proceedings of the 40th Annual Conference of the ORSNZ, (Wellington, New Zealand, December 2005), pp. 316-325.
• Liu, I. and Agresti, A. (2005). The Analysis of Ordered Categorical Data: An Overview and a Survey of Recent Developments. Test, 14, 1-73.
• Liu, I. (2005). Breslow-Day Test. Encyclopedia of Biostatistics 2nd ed. (Editors: P. Armitage and T. Colton). Wiley: London.
• Wang, D., Critchley, F. and Liu, I. (2004). Diagnostics Analysis and Perturbations in a Clustered Sampling Model. Communications in Statistics - Theory and Methods, 33, 2709-2721.
• Liu, I. (2003). Modeling and Describing Multiple Responses Given a Stratification Variable. The Proceedings of the 54th Session of the International Statistical Institute CD-ROM, Berlin, Germany.
• Liu, I. (2003). Describing Ordinal Odds Ratios for Stratified r x c Tables. Biometrical Journal, 45, 730-750.
• Hartzel, J., Liu, I. M. and Agresti, A. (2001). Describing Heterogeneous Effects in Stratified Ordinal Contingency Tables, with Application to Multi-Center Clinical Trials. Computational Statistics and Data Analysis, 35, 429-449.
• Agresti, A. and Liu, I. M. (2001). Strategies for Modeling a Categorical Variable Allowing Multiple Category Choices. Sociological Methods and Research, 29, 403-434.
• Agresti, A. and Liu, I. M. (1999). Modeling a Categorical Variable Allowing Arbitrarily Many Category Choices. Biometrics, 55, 936-943.
• Liu, I. M. (1998). Breslow-Day Test. Encyclopedia of Biostatistics (Editors: P. Armitage and T. Colton). Wiley: London.
• Liu, I. M. and Agresti, A. (1996). Mantel-Haenszel-Type Inference for Cumulative Odds Ratios with a Stratified Ordinal Response. Biometrics, 52, 1223-1234.

R Codes

• An example in "Paricle Swarm Optimisation for Multi-Objective Feature Selection Based on Statistical Clustering":

  R Main Code

  Data

  R Main Function

Teaching

• STAT 393: Linear Models. (Trimester 2)
• STAT 438: Generalised Linear Modelss. (Trimester 2)