RT Journal Article T1 Fitting model-based psychometric functions to simultaneity and temporal-order judgment data: MATLAB and R routines A1 Alcalá Quintana, Rocío A1 García Pérez, Miguel Ángel AB Research on temporal-order perception uses temporal-order judgment (TOJ) tasks or synchrony judgment (SJ) tasks in their binary SJ2 or ternary SJ3 variants. In all cases, two stimuli are presented with some temporal delay, and observers judge the order of presentation. Arbitrary psychometric functions are typically fitted to obtain performance measures such as sensitivity or the point of subjective simultaneity, but the parameters of these functions are uninterpretable. We describe routines in MATLAB and R that fit model-based functions whose parameters are interpretable in terms of the processes underlying temporal-order and simultaneity judgments and responses. These functions arise from an independent-channels model assuming arrival latencies with exponential distributions and a trichotomous decision space. Different routines fit data separately for SJ2, SJ3, and TOJ tasks, jointly for any two tasks, or also jointly for the three tasks (for common cases in which two or even the three tasks were used with the same stimuli and participants). Additional routines provide bootstrap p-values and confidence intervals for estimated parameters. A further routine is included that obtains performance measures from the fitted functions. An R package for Windows and source code of the MATLAB and R routines are available as Supplementary Files. PB Springer SN 1554-3528 YR 2013 FD 2013-12 LK https://hdl.handle.net/20.500.14352/35050 UL https://hdl.handle.net/20.500.14352/35050 LA eng NO Collett, D. (2003). Modelling Binary Data (2nd ed.). Boca Raton, FL: CRC Press.Colonius, H., & Diederich, A. (2011). Computing an optimal time window of audiovisual integration in focused attention tasks: Illustrated by studies on effect of age and prior knowledge. Experimental Brain Research, 212, 327–337. doi:10.1007/s00221-011-2732-xDiederich, A., & Colonius, H. (2011). Modeling multisensory processes in saccadic responses: Time-window-of-integration model. In M. M. Murray & M. T. Wallace (Eds.), The Neural Bases of Multisensory Processes (pp. 253–276). Boca Raton, FL: CRC Press.Fujisaki, W., & Nishida, S. (2009). Audio–tactile superiority over visuo–tactile and audio–visual combinations in the temporal resolution of synchrony perception. Experimental Brain Research, 198, 245–259. doi:10.1007/s00221-009-1870-xGarcía-Pérez, M. A. (1994). Parameter estimation and goodness-of-fit testing in multinomial models. British Journal of Mathematical and Statistical Psychology, 47, 247–282. doi:10.1111/j.2044-8317.1994.tb01037.xGarcía-Pérez, M. A. (2000). Optimal setups for forced-choice staircases with fixed step sizes. Spatial Vision, 13, 431–448. doi:10.1163/156856800741306García-Pérez, M. A. (2001). Yes-no staircases with fixed step sizes: Psychometric properties and optimal setup. Optometry and Vision Science, 78, 56–64. doi:10.1097/00006324-200101010-00015García-Pérez, M. A., & Alcalá-Quintana, R. (2005). Sampling plans for fitting the psychometric function. Spanish Journal of Psychology, 8, 256–289. http://www.ucm.es/info/Psi/docs/journal/v8_n2_2005/art256.pdfGarcía-Pérez, M. A., & Alcalá-Quintana, R. (2012a). On the discrepant results in synchrony judgment and temporal-order judgment tasks: A quantitative model. Psychonomic Bulletin & Review, 19, 820–846. doi:10.3758/s13423-012-0278-yGarcía-Pérez, M. A., & Alcalá-Quintana, R. (2012b). Response errors explain the failure of independent-channels models of perception of temporal order. Frontiers in Psychology – Perception Science, 3, 94. doi:10.3389/fpsyg.2012.00094García-Pérez, M. A., & Núñez-Antón, V. (2001). Small-sample comparisons for power-divergence goodness-of-fit statistics for symmetric and skewed simple null hypotheses. Journal of Applied Statistics, 28, 855–874. doi:10.1080/02664760120074942García-Pérez, M. A., & Núñez-Antón, V. (2004). Small-sample comparisons for goodness-of-fit statistics in one-way multinomials with composite hypotheses. Journal of Applied Statistics, 31, 161–181. doi:10.1080/0266476032000148849Heath, R. A. (1984). Response time and temporal order judgement in vision. Australian Journal of Psychology, 36, 21–34. doi:10.1080/00049538408255075Keetels, M., & Vroomen, J. (2008). Temporal recalibration to tactile–visual asynchronous stimuli. Neuroscience Letters, 430, 130–134. doi:10.1016/j.neulet.2007.10.044Lin, L. I.-K. (1989). A concordance correlation coefficient to evaluate reproducibility. Biometrics, 45, 255–268. doi:10.2307/2532051Petrini, K., Holt, S. P., & Pollick, F. (2010). Expertise with multisensory events eliminates the effect of biological motion rotation on audiovisual synchrony perception. Journal of Vision, 10(5):2, 1–14. doi:10.1167/10.5.2Read, T. R. C., & Cressie, N. A. C. (1988). Goodness-of-Fit Statistics for Discrete Multivariate Data. New York: Springer.Schneider, K. A., & Bavelier, D. (2003). Components of visual prior entry. Cognitive Psychology, 47, 333–366. doi:10.1016/S0010-0285(03)00035-5Schwarz, W. (2006). On the relationship between the redundant signals effect and temporal order judgments: Parametric data and a new model. Journal of Experimental Psychology: Human Perception and Performance, 32, 558–573. doi:10.1037/0096-1523.32.3.558Sternberg, S., & Knoll, R. L. (1973). The perception of temporal order: Fundamental issues and a general model. In S. Kornblum (Ed.), Attention and Performance IV (pp. 629–685). New York: Academic Press.van Eijk, R. L. J., Kohlrausch, A., Juola, J. F., & van de Par, S. (2008). Audiovisual synchrony and temporal order judgments: Effects of experimental method and stimulus type. Perception & Psychophysics, 70, 955–968. doi:10.3758/PP.70.6.955van Eijk, R. L. J., Kohlrausch, A., Juola, J. F., & van de Par, S. (2010). Temporal order judgment criteria are affected by synchrony judgment sensitivity. Attention, Perception, & Psychophysics, 72, 2227–2235. doi:10.3758/APP.72.8.2227Vroomen, J., & Stekelenburg, J. J. (2011). Perception of intersensory synchrony in audiovisual speech: Not that special. Cognition, 118, 75–83. doi:10.1016/j.cognition.2010.10.002Yamamoto, S., & Kitazawa, S. (2001). Reversal of subjective temporal order due to arm crossing. Nature Neuroscience, 4, 759–765. doi:10.1038/89559Yarrow, K., Jahn, N., Durant, S., & Arnold, D. H. (2011). Shifts of criteria or neural timing? The assumptions underlying timing perception studies. Consciousness and Cognition, 20, 1518–1531. doi:10.1016/j.concog.2011.07.003Yates, M. J., & Nicholls, M. E. R. (2011). Somatosensory prior entry assessed with temporal order judgments and simultaneity judgments. Attention, Perception, & Psychophysics, 73, 1586–1603. doi:10.3758/s13414-011-0117-7Zampini, M., Guest, S., Shore, D. I., & Spence, C. (2005). Audio–visual simultaneity judgments. Perception & Psychophysics, 67, 531–544. doi:10.3758/BF03193329Zampini, M., Shore, D. I., & Spence, C. (2003). Audiovisual temporal order judgments. Experimental Brain Research, 152, 198–210. doi:10.1007/s00221-003-1536-z NO Ministerio de Ciencia e Innovación (MICINN) DS Docta Complutense RD 3 may 2024