Research
"Basically, I'm not interested in doing research and I never have been. I'm interested in understanding, which is quite a different thing." - David Blackwell, 1919 - 2010.
"A belief is like a guillotine, just as heavy, just as light." - Franz Kafka, 1883 - 1924.
I was granted my PhD in May of 2015 from the Department of Mathematics at the University of British Columbia.
I worked under the supervision of Malabika Pramanik throughout my graduate studies.
My current research interests span several fields.
I worked under the supervision of Malabika Pramanik throughout my graduate studies.
My current research interests span several fields.
Statistical MeasurementThe domain of statistics has long recognized the importance of study design, sampling, estimation, inference, and modelling, both mathematically and in the pursuit of scientific knowledge. Over the past few decades, computation and communications (i.e., "data science") have rightfully earned their places alongside these pillars of statistics. However, the concept of measurement remains relatively forgotten. My major theoretical work aims at remedying this neglect by developing a general and useable theory of statistical measurement that can be seamlessly integrated into applied modes of estimation, inference, and modelling. Fixed measurements (i.e. sample measurements that generate deterministic values) are surprisingly uncommon in the social sciences; random-variable-valued measurements are the norm. These more general measurements also commonly appear in the health and natural sciences. A robust mathematical theory is required to correct for potential bias and artificially distorted measures of uncertainty when performing inferences that are otherwise naive to the statistical nature of measurement.
Ecology
I love birds, and actively study the urban ecology of gulls, particularly the Glaucous-winged Gull of southwest BC. Recently, I have extended these studies to other North American gull species and their interactions with the urban environment along the Pacific coast of North America from Mexico to Alaska. I am also interested in wildlife conservation and management practices, especially how hard science informs (or fails to inform) government policy.
Have you seen gulls (or terns) nesting in an urban-location? Check the map! If your location is not yet recorded, please send me a quick message with the approximate location and species (if known) of your sighting. Take a moment to marvel at the majesty of Larus glaucescens. |
Scientific MethodologyEach applied science has its own methodological traditions and “best practices.” While the discipline of statistics often evolves in tandem with developments in some applied fields, there almost always exists a sizeable gap between modern methods in statistics and what are considered modern analytical methods in various applied sciences. One of my major programs of research is investigating how the most advanced statistical methods can and should be employed in the social, health, and natural sciences. This entails working with a variety of collaborators across disciplines, tailoring modern statistical methods to fit particular disciplinary needs, and educating applied practitioners about optimal quantitative procedures. Working together with and learning from experts over a variety of domains is key here, and I am very proud of my collaborations with researchers from all applied fields.
Other FlavoursI am greatly interested in modern statistical methods in spatial and temporal modelling, particularly within the context of Bayesian estimation and mixed effects modelling. While these methods have many obvious and important applications in the field of ecology, they also arise from some quite beautiful and intricate mathematics.
I have always been interested in causal inference from both a theoretical and an applied perspective. I remain highly skeptical of most hard claims of causal inference in purely observational frameworks, usually due to what I find are an untenable edifice of practically untestable assumptions and a dearth of consistent, coherent, and/or useful definitions. Perhaps a function of my applied scientific interests, I care about "small data" problems. Data are usually extremely costly and difficult to obtain, and so asymptotics and well-mixing properties of "big data" analytical techniques are rarely applicable. During my graduate work, I was most occupied with various problems in high-dimensional geometric measure theory, especially those of a Kakeya-Nikodym type. You can find some great background on the classical Kakeya problem in my Master's essay and in Terry Tao's lecture notes. |
Talks
An archive of selected talks I've given:
- A transdisciplinary view of measurement error models and the variations of X = T + E, April 8, 2019, Toronto, ON.
- Navigating the p-value swamp for meta-analysts, March 27, 2019, UBC
- The urban bird: promoting and protecting urban nesters, migrants, and residents, March 3, 2019, Kelowna, BC.
- Navigating the p-value swamp for meta-analysts, March 27, 2019, UBC
- The urban bird: promoting and protecting urban nesters, migrants, and residents, March 3, 2019, Kelowna, BC.
Publications & Preprints
Papers are colour-coded according to subject: Statistics (theoretical & applied), Ecology, Mathematics, Biology/Biochemistry, Psychology, Education, Kinesiology
-(St,Ma) Generalized measurement error: Intrinsic and incidental measurement error (2023). E. Kroc. PLoS ONE, 18(6): e0286680. DOI: 10.1371/journal.pone.0286680.
-(Kn,St) Trust the "process"? When fundamental motor skill scores are reliably unreliable (2023). R.M. Hulteen, L. True, E. Kroc. Measurement in Physical Education and Exercise Science, online first: doi.org/10.1080/1091367X.2023.2199126
-(St) Theoretical considerations when simulating data from the g-and-h family of distributions (2022). O.L.O. Astivia, E. Kroc. British Journal of Mathematical and Statistical Psychology, online first: http://doi.org/10.1111/bmsp.12274
-(Ec) Urban gulls living with humans (2022). de Faria, J.P., Lopes, C.S., Kroc, E., Blight, L.K., Nager, R.G. In Seabird Biodiversity and Human Activities, Ramos, J.A. & Periera, L. (eds.): 90-105. Boca Raton: CRC Press.
-(Ed) A randomized, community-based feasibility trial of modified ESDM for toddlers with suspected autism (2022). P. Mirenda, P. Colozzo, V. Smith, E. Kroc, K. Kalynchuk, S.J. Rogers, W.J. Ungar. Journal of Autism and Developmental Disorders, online first.
-(St) How to think clearly about the Central Limit Theorem (2022). X. Zhang, O.L.O. Astivia, E. Kroc, B.D. Zumbo. Psychological Methods, online first.
-(Ec) Attitudes towards leopards (Panthera pardus kotiya) in Sri Lanka and considerations for human-leopard coexistence (2021). A. Uduman, S. Hagerman, E. Kroc, A. Watson, A. Kittle, C. Burton. Oryx: https://doi.org/10.1017/S0030605321000247
-(St) The importance of thinking multivariately when setting subscale cut-off scores (2021). E. Kroc, O.L.O. Astivia. Educational and Psychological Measurement, 82(3), 517-538.
-(Ps) Characteristics of counselling psychology and counselling psychologists in India: A larger scale replication of a nationwide survey (2021). R.P. Bedi, K. Pradhan, E. Kroc, M. Bhatara. Psychological Studies, 66(1), 1-13.
-(St,Ma) Measurement protocols, random-variable-valued measurements, and response process error: Estimation and inference when sample data are not deterministic (2020). E. Kroc. PLoS ONE, 15(10). (link)
-(St,Ma) A transdisciplinary view of measurement error models and the variations of X = T + E (2020). E. Kroc, B.D. Zumbo. Journal of Mathematical Psychology, 98, 1-9. (link)
-(St) Reconciling conflicting simulation studies through statistical theory: The case of Cronbach's coefficient alpha (2020). O.L.O. Astivia, E. Kroc, B.D. Zumbo. Educational and Psychological Measurement, 1-22. (link)
-(St) A measurement is a choice and Stevens' scales of measurement do not help make it: A response to Chalmers (2019). B.D. Zumbo, E. Kroc. Educational and Psychological Measurement, 79(6), 1184 - 1197. (link)
-(Ec) Evaluating UAV-based techniques to census an urban-nesting gull population on Canada's Pacific coast (2019). L.K. Blight, D.F. Bertram, E. Kroc. Journal of Unmanned Vehicle Systems, 7(4), 312-324. (link)
-(St) Centering in multiple regression does not always reduce multicollinearity: How to tell when your estimates will not benefit from centering (2019). O.L.O. Astivia, E. Kroc. Educational and Psychological Measurement, 79(5), 813-826. (link)
-(Ec) An example of year-round nest fidelity among urban-resident Glaucous-winged Gulls (Larus glaucescens) in Vancouver, BC, Canada (2018). E. Kroc. British Columbia Birds, 28, 28-31. (link)
-(St) Investigating the performance of propensity score approaches for differential item functioning analysis (2019). Y. Liu, C. Kim, A. Wu, P. Gustafson, E. Kroc, B.D. Zumbo. Journal of Modern Applied Statistical Methods, 18(1), 2-26. (link)
-(St) Calibration of measurements (2018). E. Kroc, B.D. Zumbo. Journal of Modern Applied Statistical Methods, 17(2), 2-28. (link)
-(Ec) Reproductive ecology of urban-nesting Glaucous-winged Gulls (Larus glaucescens) in Vancouver, BC, Canada (2018). E. Kroc. Marine Ornithology, 46(2), 155-164. (link)
-(Bi) Changes in cuticular wax coverage and composition on developing Arabidopsis leaves are influenced by wax biosynthesis gene expression levels and trichome density (2017). L. Busta, D. Hegebarth, E. Kroc, R. Jetter. Planta, 245(2), 297-311. (link)
-(St) Investigating causal DIF via propensity score methods: a demonstration with logistic regression (2016). Y. Liu, B.D. Zumbo, P. Gustafson, Y. Huang, E.Kroc, A. Wu. Practical Assessment, Research and Evaluation, 21(13), 1-24. (link)
-(St) Some remarks on Rao and Lovric's "Testing the point null hypothesis of a normal mean and the truth: 21st Century perspective" (2016). B.D. Zumbo, E. Kroc. Journal of Modern Applied Statistical Methods, 15(3), 33-40. (link)
-(Ma) Lacunarity, Kakeya-type sets and directional maximal operators (2015). E. Kroc, M. Pramanik. (on the arXiv)
-(Ma) Directional maximal operators over Cantor sets of directions in $\mathbb{R}^{d+1}$ (2016). E. Kroc, M. Pramanik. Journal of Fourier Analysis and Applications, 22(3), 623-674. (link)
-(Ma) An Introduction to the Kakeya Problem. E. Kroc. Mathematics Newsletter of the Ramanujan Mathematical Society, Part 1: 26(3), 69-90, (2015); Part 2: 27(1), 109-124, (2016); Part 3: 27(2), 141-161 (2016). (adapted from my M.Sc. essay)
-(Kn,St) Trust the "process"? When fundamental motor skill scores are reliably unreliable (2023). R.M. Hulteen, L. True, E. Kroc. Measurement in Physical Education and Exercise Science, online first: doi.org/10.1080/1091367X.2023.2199126
-(St) Theoretical considerations when simulating data from the g-and-h family of distributions (2022). O.L.O. Astivia, E. Kroc. British Journal of Mathematical and Statistical Psychology, online first: http://doi.org/10.1111/bmsp.12274
-(Ec) Urban gulls living with humans (2022). de Faria, J.P., Lopes, C.S., Kroc, E., Blight, L.K., Nager, R.G. In Seabird Biodiversity and Human Activities, Ramos, J.A. & Periera, L. (eds.): 90-105. Boca Raton: CRC Press.
-(Ed) A randomized, community-based feasibility trial of modified ESDM for toddlers with suspected autism (2022). P. Mirenda, P. Colozzo, V. Smith, E. Kroc, K. Kalynchuk, S.J. Rogers, W.J. Ungar. Journal of Autism and Developmental Disorders, online first.
-(St) How to think clearly about the Central Limit Theorem (2022). X. Zhang, O.L.O. Astivia, E. Kroc, B.D. Zumbo. Psychological Methods, online first.
-(Ec) Attitudes towards leopards (Panthera pardus kotiya) in Sri Lanka and considerations for human-leopard coexistence (2021). A. Uduman, S. Hagerman, E. Kroc, A. Watson, A. Kittle, C. Burton. Oryx: https://doi.org/10.1017/S0030605321000247
-(St) The importance of thinking multivariately when setting subscale cut-off scores (2021). E. Kroc, O.L.O. Astivia. Educational and Psychological Measurement, 82(3), 517-538.
-(Ps) Characteristics of counselling psychology and counselling psychologists in India: A larger scale replication of a nationwide survey (2021). R.P. Bedi, K. Pradhan, E. Kroc, M. Bhatara. Psychological Studies, 66(1), 1-13.
-(St,Ma) Measurement protocols, random-variable-valued measurements, and response process error: Estimation and inference when sample data are not deterministic (2020). E. Kroc. PLoS ONE, 15(10). (link)
-(St,Ma) A transdisciplinary view of measurement error models and the variations of X = T + E (2020). E. Kroc, B.D. Zumbo. Journal of Mathematical Psychology, 98, 1-9. (link)
-(St) Reconciling conflicting simulation studies through statistical theory: The case of Cronbach's coefficient alpha (2020). O.L.O. Astivia, E. Kroc, B.D. Zumbo. Educational and Psychological Measurement, 1-22. (link)
-(St) A measurement is a choice and Stevens' scales of measurement do not help make it: A response to Chalmers (2019). B.D. Zumbo, E. Kroc. Educational and Psychological Measurement, 79(6), 1184 - 1197. (link)
-(Ec) Evaluating UAV-based techniques to census an urban-nesting gull population on Canada's Pacific coast (2019). L.K. Blight, D.F. Bertram, E. Kroc. Journal of Unmanned Vehicle Systems, 7(4), 312-324. (link)
-(St) Centering in multiple regression does not always reduce multicollinearity: How to tell when your estimates will not benefit from centering (2019). O.L.O. Astivia, E. Kroc. Educational and Psychological Measurement, 79(5), 813-826. (link)
-(Ec) An example of year-round nest fidelity among urban-resident Glaucous-winged Gulls (Larus glaucescens) in Vancouver, BC, Canada (2018). E. Kroc. British Columbia Birds, 28, 28-31. (link)
-(St) Investigating the performance of propensity score approaches for differential item functioning analysis (2019). Y. Liu, C. Kim, A. Wu, P. Gustafson, E. Kroc, B.D. Zumbo. Journal of Modern Applied Statistical Methods, 18(1), 2-26. (link)
-(St) Calibration of measurements (2018). E. Kroc, B.D. Zumbo. Journal of Modern Applied Statistical Methods, 17(2), 2-28. (link)
-(Ec) Reproductive ecology of urban-nesting Glaucous-winged Gulls (Larus glaucescens) in Vancouver, BC, Canada (2018). E. Kroc. Marine Ornithology, 46(2), 155-164. (link)
-(Bi) Changes in cuticular wax coverage and composition on developing Arabidopsis leaves are influenced by wax biosynthesis gene expression levels and trichome density (2017). L. Busta, D. Hegebarth, E. Kroc, R. Jetter. Planta, 245(2), 297-311. (link)
-(St) Investigating causal DIF via propensity score methods: a demonstration with logistic regression (2016). Y. Liu, B.D. Zumbo, P. Gustafson, Y. Huang, E.Kroc, A. Wu. Practical Assessment, Research and Evaluation, 21(13), 1-24. (link)
-(St) Some remarks on Rao and Lovric's "Testing the point null hypothesis of a normal mean and the truth: 21st Century perspective" (2016). B.D. Zumbo, E. Kroc. Journal of Modern Applied Statistical Methods, 15(3), 33-40. (link)
-(Ma) Lacunarity, Kakeya-type sets and directional maximal operators (2015). E. Kroc, M. Pramanik. (on the arXiv)
-(Ma) Directional maximal operators over Cantor sets of directions in $\mathbb{R}^{d+1}$ (2016). E. Kroc, M. Pramanik. Journal of Fourier Analysis and Applications, 22(3), 623-674. (link)
-(Ma) An Introduction to the Kakeya Problem. E. Kroc. Mathematics Newsletter of the Ramanujan Mathematical Society, Part 1: 26(3), 69-90, (2015); Part 2: 27(1), 109-124, (2016); Part 3: 27(2), 141-161 (2016). (adapted from my M.Sc. essay)
