What's Next? Sequence Length and Impossible Loops in State Transition Measurement
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Published
Jun 30, 2021
Nigel Bosch
Luc Paquette
https://orcid.org/0000-0003-2736-2899
Abstract
Transition metrics, which quantify the propensity for one event to follow another, are often utilized to study sequential patterns of behaviors, emotions, actions, and other states. However, little is known about the conditions in which application of transition metrics is appropriate. We report on two experiments in which we simulated sequences of states to explore the properties of common transition metrics (conditional probability, D'Mello's L, lag sequential analysis, and Yule's Q) where results should be null (i.e., random sequences). In experiment 1, we found that transition metrics produced statistically significant results with non-null effect sizes (e.g., Q > 0.2) when sequences of states were short. In experiment 2, we explored situations where consecutively repeated states (i.e., loops, or self-transitions) are impossible - e.g., in digital learning environments where actions such as hint requests cannot be made twice in a row. We found that impossible loops affected all transition metrics (e.g., Q = .646). Based on simulations, we recommend sequences of length 50 or more for transition metric analyses. Our software for calculating transition metrics and running simulated experiments is publicly available.
How to Cite
Bosch, N., & Paquette, L. (2021). What’s Next? Sequence Length and Impossible Loops in State Transition Measurement. Journal of Educational Data Mining, 13(1), 1–23. https://doi.org/10.5281/zenodo.5048423
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Keywords
sequential analysis, transition metrics, simulated data
References
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ANDRES, A., OCUMPAUGH, J., BAKER, R. S., SLATER, S., PAQUETTE, L., JIANG, Y., BOSCH, N., MUNSHI, A., MOORE, A. L., & BISWAS, G. (2019). Affect sequences and learning in Betty’s Brain. In C. Brooks, R. Ferguson, & H. U. Hoppe (Eds.), Proceedings of the 9th International Conference on Learning Analytics & Knowledge (LAK19) (pp. 383–390). ACM. https://doi.org/10.1145/3303772.3303807
BAKEMAN, R. (1983). Computing lag sequential statistics: The ELAG program. Behavior Research Methods & Instrumentation, 15(5), 530–535. https://doi.org/10.3758/BF03203700
BAKEMAN, R., & DABBS, J. M. (1976). Social interaction observed: Some approaches to the analysis of behavior streams. Personality and Social Psychology Bulletin, 2(4), 335–345. https://doi.org/10.1177/014616727600200403
BAKEMAN, R., MCARTHUR, D., & QUERA, V. (1996). Detecting group differences in sequential association using sampled permutations: Log odds, kappa, and phi compared. Behavior Research Methods, Instruments, & Computers, 28(3), 446–457. https://doi.org/10.3758/BF03200524
BAKEMAN, R., MCARTHUR, D., QUERA, V., & ROBINSON, B. F. (1997). Detecting sequential patterns and determining their reliability with fallible observers. Psychological Methods, 2(4), 357–370.
BAKEMAN, R., & QUERA, V. (1995). Log-linear approaches to lag-sequential analysis when consecutive codes may and cannot repeat. Psychological Bulletin, 118(2), 272–284. https://doi.org/10.1037/0033-2909.118.2.272
BAKER, R. S., D’MELLO, S. K., RODRIGO, MA. M. T., & GRAESSER, A. (2010). Better to be frustrated than bored: The incidence, persistence, and impact of learners’ cognitive–affective states during interactions with three different computer-based learning environments. International Journal of Human-Computer Studies, 68(4), 223–241. https://doi.org/10.1016/j.ijhcs.2009.12.003
BAKER, R. S., RODRIGO, MA. M. T., & XOLOCOTZIN, U. E. (2007). The dynamics of affective transitions in simulation problem-solving environments. In A. C. R. Paiva, R. Prada, & R. W. Picard (Eds.), Affective Computing and Intelligent Interaction (pp. 666–677). Berlin, Heidelberg: Springer.
BISWAS, G., SEGEDY, J. R., & BUNCHONGCHIT, K. (2016). From design to implementation to practice—A learning by teaching system: Betty’s Brain. International Journal of Artificial Intelligence in Education, 26(1), 350–364. https://doi.org/10.1007/s40593-015-0057-9
BOSCH, N., & D’MELLO, S. K. (2017). The affective experience of novice computer programmers. International Journal of Artificial Intelligence in Education, 27(1), 181–206. https://doi.org/10.1007/s40593-015-0069-5
BOSCH, N., & PAQUETTE, L. (2020). Transition metrics simulation code (1.0.0) [Computer software]. https://doi.org/10.5281/zenodo.3711563
CHEN, B., KNIGHT, S., & WISE, A. F. (2018). Critical issues in designing and implementing temporal analytics. Journal of Learning Analytics, 5(1), 1–9. https://doi.org/10.18608/jla.2018.53.1
CHEN, B., RESENDES, M., CHAI, C. S., & HONG, H.-Y. (2017). Two tales of time: Uncovering the significance of sequential patterns among contribution types in knowledge-building discourse. Interactive Learning Environments, 25(2), 162–175. https://doi.org/10.1080/10494820.2016.1276081
COHEN, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd ed.). Lawrence Erlbaum.
DISHION, T. J., NELSON, S. E., WINTER, C. E., & BULLOCK, B. M. (2004). Adolescent friendship as a dynamic system: Entropy and deviance in the etiology and course of male antisocial behavior. Journal of Abnormal Child Psychology, 32(6), 651–663. https://doi.org/10.1023/B:JACP.0000047213.31812.21
D’MELLO, S. K., & GRAESSER, A. (2012). Dynamics of affective states during complex learning. Learning and Instruction, 22(2), 145–157. https://doi.org/10.1016/j.learninstruc.2011.10.001
DONG, Y., & BISWAS, G. (2017). An extended learner modeling method to assess students’ learning behaviors. In X. Hu, T. Barnes, A. Hershkovitz, & L. Paquette (Eds.), Proceedings of the 10th International Conference on Educational Data Mining (EDM 2017), 302–305.
FARAONE, S. V., & DORFMAN, D. D. (1987). Lag sequential analysis: Robust statistical methods. Psychological Bulletin, 101(2), 312–323. https://doi.org/10.1037/0033-2909.101.2.312
GALYARDT, A., & GOLDIN, I. (2015). Evaluating simplicial mixtures of Markov chains for modeling student metacognitive strategies. In R. E. Millsap, D. M. Bolt, L. A. van der Ark, & W.-C. Wang (Eds.), Quantitative Psychology Research (pp. 377–393). Springer. https://doi.org/10.1007/978-3-319-07503-7_24
GAUME, J., GMEL, G., FAOUZI, M., & DAEPPEN, J.-B. (2008). Counsellor behaviours and patient language during brief motivational interventions: A sequential analysis of speech. Addiction, 103(11), 1793–1800. https://doi.org/10.1111/j.1360-0443.2008.02337.x
GUIA, T. F. G., RODRIGO, MA. M. T., DAGAMI, M. M. C., SUGAY, J. O., MACAM, F. J. P., & MITROVIC, A. (2013). An exploratory study of factors indicative of affective states of students using SQL-Tutor. Research and Practice in Technology Enhanced Learning, 8(3), 411–430.
HAMAKER, E. L., CEULEMANS, E., GRASMAN, R. P. P. P., & TUERLINCKX, F. (2015). Modeling affect dynamics: State of the art and future challenges. Emotion Review, 7(4), 316–322. https://doi.org/10.1177/1754073915590619
JEONG, H., & BISWAS, G. (2008). Mining student behavior models in learning-by-teaching environments. In R. S. Baker, T. Barnes, & J. E. Beck (Eds.), Proceedings of the 1st International Conference on Educational Data Mining (pp. 127–136). International Educational Data Mining Society.
KARUMBAIAH, S., BAKER, R. S., & OCUMPAUGH, J. (2019). The case of self-transitions in affective dynamics. In S. Isotani, E. Millán, A. Ogan, P. Hastings, B. McLaren, & R. Luckin (Eds.), Artificial Intelligence in Education (pp. 172–181). Springer International Publishing. https://doi.org/10.1007/978-3-030-23204-7_15
KNIGHT, S., WISE, A. F., & CHEN, B. (2017). Time for change: Why learning analytics needs temporal analysis. Journal of Learning Analytics, 4(3), 7–17. https://doi.org/10.18608/jla.2017.43.2
LARSON, R., & CSIKSZENTMIHALYI, M. (1983). The experience sampling method. New Directions for Methodology of Social & Behavioral Science, 15, 41–56.
LLOYD, B. P., KENNEDY, C. H., & YODER, P. J. (2013). Quantifying contingent relations from direct observation data: Transitional probability comparisons versus Yule’s Q. Journal of Applied Behavior Analysis, 46(2), 479–497. https://doi.org/10.1002/jaba.45
MARION, S. D., TOUCHETTE, P. E., & SANDMAN, C. A. (2003). Sequential analysis reveals a unique structure for self-injurious behavior. American Journal on Mental Retardation, 108(5), 301–313. https://doi.org/10.1352/0895-8017(2003)108<301:SARAUS>2.0.CO;2
MATAYOSHI, J., & KARUMBAIAH, S. (2020). Adjusting the L statistic when self-transitions are excluded in affect dynamics. Journal of Educational Data Mining, 12(4), 1–23. https://doi.org/10.5281/zenodo.4399681
MCQUIGGAN, S. W., ROBISON, J. L., & LESTER, J. C. (2010). Affective transitions in narrative-centered learning environments. Educational Technology & Society, 13(1), 40–53.
MCQUIGGAN, S. W., ROBISON, J. L., & LESTER, J. C. (2008). Affective transitions in narrative-centered learning environments. In B. P. Woolf, E. Aïmeur, R. Nkambou, & S. Lajoie (Eds.), Proceedings of the 9th International Conference on Intelligent Tutoring Systems (ITS 2008) (pp. 490–499). Springer. https://doi.org/10.1007/978-3-540-69132-7_52
MOLINARI, L., MAMELI, C., & GNISCI, A. (2013). A sequential analysis of classroom discourse in Italian primary schools: The many faces of the IRF pattern. British Journal of Educational Psychology, 83(3), 414–430. https://doi.org/10.1111/j.2044-8279.2012.02071.x
MOYERS, T. B., MARTIN, T., HOUCK, J. M., CHRISTOPHER, P. J., & TONIGAN, J. S. (2009). From in-session behaviors to drinking outcomes: A causal chain for motivational interviewing. Journal of Consulting and Clinical Psychology, 77(6), 1113–1124. https://doi.org/10.1037/a0017189
OCUMPAUGH, J., ANDRES, J. M., BAKER, R. S., DEFALCO, J., PAQUETTE, L., ROWE, J., MOTT, B., LESTER, J., GEORGOULAS, V., BRAWNER, K., & SOTTILARE, R. (2017). Affect dynamics in military trainees using vMedic: From engaged concentration to boredom to confusion. In E. André, R. Baker, X. Hu, Ma. M. T. Rodrigo, & B. du Boulay (Eds.), Artificial Intelligence in Education (pp. 238–249). Springer. https://doi.org/10.1007/978-3-319-61425-0_20
OCUMPAUGH, J., BAKER, R. S., & RODRIGO, MA. M. T. (2015). Baker Rodrigo Ocumpaugh Monitoring Protocol (BROMP) 2.0 technical and training manual. Technical Report. New York, NY: Teachers College, Columbia University. Manila, Philippines: Ateneo Laboratory for the Learning Sciences.
RODRIGO, MA. M. T. (2011). Dynamics of student cognitive-affective transitions during a mathematics game. Simulation & Gaming, 42(1), 85–99. https://doi.org/10.1177/1046878110361513
SACKETT, G. P., HOLM, R., CROWLEY, C., & HENKINS, A. (1979). A FORTRAN program for lag sequential analysis of contingency and cyclicity in behavioral interaction data. Behavior Research Methods & Instrumentation, 11(3), 366–378. https://doi.org/10.3758/BF03205679
TOMPKINS, V., ZUCKER, T. A., JUSTICE, L. M., & BINICI, S. (2013). Inferential talk during teacher–child interactions in small-group play. Early Childhood Research Quarterly, 28(2), 424–436. https://doi.org/10.1016/j.ecresq.2012.11.001
VAHDAT, M., ONETO, L., GHIO, A., DONZELLINI, G., ANGUITA, D., FUNK, M., & RAUTERBERG, M. (2014). A learning analytics methodology to profile students behavior and explore interactions with a digital electronics simulator. In C. Rensing, S. de Freitas, T. Ley, & P. J. Muñoz-Merino (Eds.), Proceedings of the 9th European Conference on Technology Enhanced Learning (EC-TEL) (pp. 596–597). Springer International Publishing. https://doi.org/10.1007/978-3-319-11200-8_87
WALSH, A., & OLLENBURGER, J. (2001). Essential statistics for the social and behavioral sciences: A conceptual approach. Prentice Hall.
WITHERSPOON, A. M., AZEVEDO, R., & D’MELLO, S. K. (2008). The dynamics of self-regulatory processes within self-and externally regulated learning episodes during complex science learning with hypermedia. In B. P. Woolf, E. Aïmeur, R. Nkambou, & S. Lajoie (Eds.), Proceedings of the 9th International Conference on Intelligent Tutoring Systems (ITS 2008) (pp. 260–269). Springer. https://doi.org/10.1007/978-3-540-69132-7_30
WUERKER, A. K., HAAS, G. L., & BELLACK, A. S. (2001). Interpersonal control and expressed emotion in families of persons with schizophrenia: Change over time. Schizophrenia Bulletin, 27(4), 671–686. https://doi.org/10.1093/oxfordjournals.schbul.a006906
YANG, T.-C., CHEN, S. Y., & HWANG, G.-J. (2015). The influences of a two-tier test strategy on student learning: A lag sequential analysis approach. Computers & Education, 82, 366–377. https://doi.org/10.1016/j.compedu.2014.11.021
YULE, G. U. (1900). On the association of attributes in statistics: With illustrations from the material of the childhood society. Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character, 194(252–261), 257–319. https://doi.org/10.1098/rsta.1900.0019
ANDRES, A., OCUMPAUGH, J., BAKER, R. S., SLATER, S., PAQUETTE, L., JIANG, Y., BOSCH, N., MUNSHI, A., MOORE, A. L., & BISWAS, G. (2019). Affect sequences and learning in Betty’s Brain. In C. Brooks, R. Ferguson, & H. U. Hoppe (Eds.), Proceedings of the 9th International Conference on Learning Analytics & Knowledge (LAK19) (pp. 383–390). ACM. https://doi.org/10.1145/3303772.3303807
BAKEMAN, R. (1983). Computing lag sequential statistics: The ELAG program. Behavior Research Methods & Instrumentation, 15(5), 530–535. https://doi.org/10.3758/BF03203700
BAKEMAN, R., & DABBS, J. M. (1976). Social interaction observed: Some approaches to the analysis of behavior streams. Personality and Social Psychology Bulletin, 2(4), 335–345. https://doi.org/10.1177/014616727600200403
BAKEMAN, R., MCARTHUR, D., & QUERA, V. (1996). Detecting group differences in sequential association using sampled permutations: Log odds, kappa, and phi compared. Behavior Research Methods, Instruments, & Computers, 28(3), 446–457. https://doi.org/10.3758/BF03200524
BAKEMAN, R., MCARTHUR, D., QUERA, V., & ROBINSON, B. F. (1997). Detecting sequential patterns and determining their reliability with fallible observers. Psychological Methods, 2(4), 357–370.
BAKEMAN, R., & QUERA, V. (1995). Log-linear approaches to lag-sequential analysis when consecutive codes may and cannot repeat. Psychological Bulletin, 118(2), 272–284. https://doi.org/10.1037/0033-2909.118.2.272
BAKER, R. S., D’MELLO, S. K., RODRIGO, MA. M. T., & GRAESSER, A. (2010). Better to be frustrated than bored: The incidence, persistence, and impact of learners’ cognitive–affective states during interactions with three different computer-based learning environments. International Journal of Human-Computer Studies, 68(4), 223–241. https://doi.org/10.1016/j.ijhcs.2009.12.003
BAKER, R. S., RODRIGO, MA. M. T., & XOLOCOTZIN, U. E. (2007). The dynamics of affective transitions in simulation problem-solving environments. In A. C. R. Paiva, R. Prada, & R. W. Picard (Eds.), Affective Computing and Intelligent Interaction (pp. 666–677). Berlin, Heidelberg: Springer.
BISWAS, G., SEGEDY, J. R., & BUNCHONGCHIT, K. (2016). From design to implementation to practice—A learning by teaching system: Betty’s Brain. International Journal of Artificial Intelligence in Education, 26(1), 350–364. https://doi.org/10.1007/s40593-015-0057-9
BOSCH, N., & D’MELLO, S. K. (2017). The affective experience of novice computer programmers. International Journal of Artificial Intelligence in Education, 27(1), 181–206. https://doi.org/10.1007/s40593-015-0069-5
BOSCH, N., & PAQUETTE, L. (2020). Transition metrics simulation code (1.0.0) [Computer software]. https://doi.org/10.5281/zenodo.3711563
CHEN, B., KNIGHT, S., & WISE, A. F. (2018). Critical issues in designing and implementing temporal analytics. Journal of Learning Analytics, 5(1), 1–9. https://doi.org/10.18608/jla.2018.53.1
CHEN, B., RESENDES, M., CHAI, C. S., & HONG, H.-Y. (2017). Two tales of time: Uncovering the significance of sequential patterns among contribution types in knowledge-building discourse. Interactive Learning Environments, 25(2), 162–175. https://doi.org/10.1080/10494820.2016.1276081
COHEN, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd ed.). Lawrence Erlbaum.
DISHION, T. J., NELSON, S. E., WINTER, C. E., & BULLOCK, B. M. (2004). Adolescent friendship as a dynamic system: Entropy and deviance in the etiology and course of male antisocial behavior. Journal of Abnormal Child Psychology, 32(6), 651–663. https://doi.org/10.1023/B:JACP.0000047213.31812.21
D’MELLO, S. K., & GRAESSER, A. (2012). Dynamics of affective states during complex learning. Learning and Instruction, 22(2), 145–157. https://doi.org/10.1016/j.learninstruc.2011.10.001
DONG, Y., & BISWAS, G. (2017). An extended learner modeling method to assess students’ learning behaviors. In X. Hu, T. Barnes, A. Hershkovitz, & L. Paquette (Eds.), Proceedings of the 10th International Conference on Educational Data Mining (EDM 2017), 302–305.
FARAONE, S. V., & DORFMAN, D. D. (1987). Lag sequential analysis: Robust statistical methods. Psychological Bulletin, 101(2), 312–323. https://doi.org/10.1037/0033-2909.101.2.312
GALYARDT, A., & GOLDIN, I. (2015). Evaluating simplicial mixtures of Markov chains for modeling student metacognitive strategies. In R. E. Millsap, D. M. Bolt, L. A. van der Ark, & W.-C. Wang (Eds.), Quantitative Psychology Research (pp. 377–393). Springer. https://doi.org/10.1007/978-3-319-07503-7_24
GAUME, J., GMEL, G., FAOUZI, M., & DAEPPEN, J.-B. (2008). Counsellor behaviours and patient language during brief motivational interventions: A sequential analysis of speech. Addiction, 103(11), 1793–1800. https://doi.org/10.1111/j.1360-0443.2008.02337.x
GUIA, T. F. G., RODRIGO, MA. M. T., DAGAMI, M. M. C., SUGAY, J. O., MACAM, F. J. P., & MITROVIC, A. (2013). An exploratory study of factors indicative of affective states of students using SQL-Tutor. Research and Practice in Technology Enhanced Learning, 8(3), 411–430.
HAMAKER, E. L., CEULEMANS, E., GRASMAN, R. P. P. P., & TUERLINCKX, F. (2015). Modeling affect dynamics: State of the art and future challenges. Emotion Review, 7(4), 316–322. https://doi.org/10.1177/1754073915590619
JEONG, H., & BISWAS, G. (2008). Mining student behavior models in learning-by-teaching environments. In R. S. Baker, T. Barnes, & J. E. Beck (Eds.), Proceedings of the 1st International Conference on Educational Data Mining (pp. 127–136). International Educational Data Mining Society.
KARUMBAIAH, S., BAKER, R. S., & OCUMPAUGH, J. (2019). The case of self-transitions in affective dynamics. In S. Isotani, E. Millán, A. Ogan, P. Hastings, B. McLaren, & R. Luckin (Eds.), Artificial Intelligence in Education (pp. 172–181). Springer International Publishing. https://doi.org/10.1007/978-3-030-23204-7_15
KNIGHT, S., WISE, A. F., & CHEN, B. (2017). Time for change: Why learning analytics needs temporal analysis. Journal of Learning Analytics, 4(3), 7–17. https://doi.org/10.18608/jla.2017.43.2
LARSON, R., & CSIKSZENTMIHALYI, M. (1983). The experience sampling method. New Directions for Methodology of Social & Behavioral Science, 15, 41–56.
LLOYD, B. P., KENNEDY, C. H., & YODER, P. J. (2013). Quantifying contingent relations from direct observation data: Transitional probability comparisons versus Yule’s Q. Journal of Applied Behavior Analysis, 46(2), 479–497. https://doi.org/10.1002/jaba.45
MARION, S. D., TOUCHETTE, P. E., & SANDMAN, C. A. (2003). Sequential analysis reveals a unique structure for self-injurious behavior. American Journal on Mental Retardation, 108(5), 301–313. https://doi.org/10.1352/0895-8017(2003)108<301:SARAUS>2.0.CO;2
MATAYOSHI, J., & KARUMBAIAH, S. (2020). Adjusting the L statistic when self-transitions are excluded in affect dynamics. Journal of Educational Data Mining, 12(4), 1–23. https://doi.org/10.5281/zenodo.4399681
MCQUIGGAN, S. W., ROBISON, J. L., & LESTER, J. C. (2010). Affective transitions in narrative-centered learning environments. Educational Technology & Society, 13(1), 40–53.
MCQUIGGAN, S. W., ROBISON, J. L., & LESTER, J. C. (2008). Affective transitions in narrative-centered learning environments. In B. P. Woolf, E. Aïmeur, R. Nkambou, & S. Lajoie (Eds.), Proceedings of the 9th International Conference on Intelligent Tutoring Systems (ITS 2008) (pp. 490–499). Springer. https://doi.org/10.1007/978-3-540-69132-7_52
MOLINARI, L., MAMELI, C., & GNISCI, A. (2013). A sequential analysis of classroom discourse in Italian primary schools: The many faces of the IRF pattern. British Journal of Educational Psychology, 83(3), 414–430. https://doi.org/10.1111/j.2044-8279.2012.02071.x
MOYERS, T. B., MARTIN, T., HOUCK, J. M., CHRISTOPHER, P. J., & TONIGAN, J. S. (2009). From in-session behaviors to drinking outcomes: A causal chain for motivational interviewing. Journal of Consulting and Clinical Psychology, 77(6), 1113–1124. https://doi.org/10.1037/a0017189
OCUMPAUGH, J., ANDRES, J. M., BAKER, R. S., DEFALCO, J., PAQUETTE, L., ROWE, J., MOTT, B., LESTER, J., GEORGOULAS, V., BRAWNER, K., & SOTTILARE, R. (2017). Affect dynamics in military trainees using vMedic: From engaged concentration to boredom to confusion. In E. André, R. Baker, X. Hu, Ma. M. T. Rodrigo, & B. du Boulay (Eds.), Artificial Intelligence in Education (pp. 238–249). Springer. https://doi.org/10.1007/978-3-319-61425-0_20
OCUMPAUGH, J., BAKER, R. S., & RODRIGO, MA. M. T. (2015). Baker Rodrigo Ocumpaugh Monitoring Protocol (BROMP) 2.0 technical and training manual. Technical Report. New York, NY: Teachers College, Columbia University. Manila, Philippines: Ateneo Laboratory for the Learning Sciences.
RODRIGO, MA. M. T. (2011). Dynamics of student cognitive-affective transitions during a mathematics game. Simulation & Gaming, 42(1), 85–99. https://doi.org/10.1177/1046878110361513
SACKETT, G. P., HOLM, R., CROWLEY, C., & HENKINS, A. (1979). A FORTRAN program for lag sequential analysis of contingency and cyclicity in behavioral interaction data. Behavior Research Methods & Instrumentation, 11(3), 366–378. https://doi.org/10.3758/BF03205679
TOMPKINS, V., ZUCKER, T. A., JUSTICE, L. M., & BINICI, S. (2013). Inferential talk during teacher–child interactions in small-group play. Early Childhood Research Quarterly, 28(2), 424–436. https://doi.org/10.1016/j.ecresq.2012.11.001
VAHDAT, M., ONETO, L., GHIO, A., DONZELLINI, G., ANGUITA, D., FUNK, M., & RAUTERBERG, M. (2014). A learning analytics methodology to profile students behavior and explore interactions with a digital electronics simulator. In C. Rensing, S. de Freitas, T. Ley, & P. J. Muñoz-Merino (Eds.), Proceedings of the 9th European Conference on Technology Enhanced Learning (EC-TEL) (pp. 596–597). Springer International Publishing. https://doi.org/10.1007/978-3-319-11200-8_87
WALSH, A., & OLLENBURGER, J. (2001). Essential statistics for the social and behavioral sciences: A conceptual approach. Prentice Hall.
WITHERSPOON, A. M., AZEVEDO, R., & D’MELLO, S. K. (2008). The dynamics of self-regulatory processes within self-and externally regulated learning episodes during complex science learning with hypermedia. In B. P. Woolf, E. Aïmeur, R. Nkambou, & S. Lajoie (Eds.), Proceedings of the 9th International Conference on Intelligent Tutoring Systems (ITS 2008) (pp. 260–269). Springer. https://doi.org/10.1007/978-3-540-69132-7_30
WUERKER, A. K., HAAS, G. L., & BELLACK, A. S. (2001). Interpersonal control and expressed emotion in families of persons with schizophrenia: Change over time. Schizophrenia Bulletin, 27(4), 671–686. https://doi.org/10.1093/oxfordjournals.schbul.a006906
YANG, T.-C., CHEN, S. Y., & HWANG, G.-J. (2015). The influences of a two-tier test strategy on student learning: A lag sequential analysis approach. Computers & Education, 82, 366–377. https://doi.org/10.1016/j.compedu.2014.11.021
YULE, G. U. (1900). On the association of attributes in statistics: With illustrations from the material of the childhood society. Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character, 194(252–261), 257–319. https://doi.org/10.1098/rsta.1900.0019
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