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Self-consistent estimation of mislocated fixations during reading.

Engbert R, Nuthmann A - PLoS ONE (2008)

Bottom Line: During reading, we generate saccadic eye movements to move words into the center of the visual field for word processing.Our approach is based on iterative computation of the proportions of several types of oculomotor errors, the underlying probabilities for word-targeting, and corrected distributions of landing positions.These results show that fixation probabilities are strongly affected by oculomotor errors.

View Article: PubMed Central - PubMed

Affiliation: Department of Psychology, University of Potsdam, Potsdam, Germany. Ralf.Engbert@uni-potsdam.de

ABSTRACT
During reading, we generate saccadic eye movements to move words into the center of the visual field for word processing. However, due to systematic and random errors in the oculomotor system, distributions of within-word landing positions are rather broad and show overlapping tails, which suggests that a fraction of fixations is mislocated and falls on words to the left or right of the selected target word. Here we propose a new procedure for the self-consistent estimation of the likelihood of mislocated fixations in normal reading. Our approach is based on iterative computation of the proportions of several types of oculomotor errors, the underlying probabilities for word-targeting, and corrected distributions of landing positions. We found that the average fraction of mislocated fixations ranges from about 10% to more than 30% depending on word length. These results show that fixation probabilities are strongly affected by oculomotor errors.

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Iterative procedure for the estimation of mislocated fixations. Each iteration consists of three steps.(A) Oculomotor simulations are based on the parameters of the landing position distributions for a given launch site. Undershoot and overshoot of the target word generate mislocated fixations. (B) Landing position distributions are corrected by the amount of mislocated fixations as suggested by the simulations. (C) Mislocated fixations induce deviations from experimentally observed probabilities for word skippings (left) and refixations (right), which are adjusted after each iteration.
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pone-0001534-g002: Iterative procedure for the estimation of mislocated fixations. Each iteration consists of three steps.(A) Oculomotor simulations are based on the parameters of the landing position distributions for a given launch site. Undershoot and overshoot of the target word generate mislocated fixations. (B) Landing position distributions are corrected by the amount of mislocated fixations as suggested by the simulations. (C) Mislocated fixations induce deviations from experimentally observed probabilities for word skippings (left) and refixations (right), which are adjusted after each iteration.

Mentions: Here we propose a computational approach to the problem of mislocated fixations based on experimentally observed distributions of landing positions. The fraction of mislocated fixations can be estimated by extrapolation of experimentally observed landing distributions (Fig. 2a). The basic problem for such an approach is that experimental data of within-word fixation locations consist of both well-located (i.e., fixations intended for the realized target word) and mislocated fixations (i.e., fixations intended for adjacent words). The proportions of mislocated fixations as a function of within-word fixation position follows a U-shaped curve (Fig. 2b, red line) with higher probabilities of mislocated fixations near word boundaries [8] due to contributions from overlapping tails of the landing position distributions of adjacent words. We used numerical simulations of an oculomotor model (Fig. 2a) to estimate the proportion of mislocated fixations (see Materials and Methods). Simulations of this model permitted the direct computation of distributions of both mislocated and well-located fixations. Assuming that variance in landing positions is caused by oculomotor errors, we expect that distributions of well-located fixations (Fig. 2b, black line) show less variance than the original distributions of all fixations (green line), because the mislocated fractions near word boundaries are removed. A major complication for the estimation of the proportion of mislocated fixations is that these errors also bias probabilities for word skippings and refixations (Fig. 2c, red lines), such that simulated fixation probabilities deviate from the experimental data. As a solution to this problem, we developed an iterative procedure, where numerical simulations of saccade-targeting (Fig. 2a) were applied (i) to decompose the distributions of landing positions into well- and mislocated fixations (Fig. 2b) and (ii) to simultaneously adjust the probabilities for word-targeting, i.e., word skippings and refixations (Fig. 2c). Such an approach is self-consistent, because landing position distributions and word-targeting probabilities converge to numerical values consistent with self-generated errors.


Self-consistent estimation of mislocated fixations during reading.

Engbert R, Nuthmann A - PLoS ONE (2008)

Iterative procedure for the estimation of mislocated fixations. Each iteration consists of three steps.(A) Oculomotor simulations are based on the parameters of the landing position distributions for a given launch site. Undershoot and overshoot of the target word generate mislocated fixations. (B) Landing position distributions are corrected by the amount of mislocated fixations as suggested by the simulations. (C) Mislocated fixations induce deviations from experimentally observed probabilities for word skippings (left) and refixations (right), which are adjusted after each iteration.
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC2211408&req=5

pone-0001534-g002: Iterative procedure for the estimation of mislocated fixations. Each iteration consists of three steps.(A) Oculomotor simulations are based on the parameters of the landing position distributions for a given launch site. Undershoot and overshoot of the target word generate mislocated fixations. (B) Landing position distributions are corrected by the amount of mislocated fixations as suggested by the simulations. (C) Mislocated fixations induce deviations from experimentally observed probabilities for word skippings (left) and refixations (right), which are adjusted after each iteration.
Mentions: Here we propose a computational approach to the problem of mislocated fixations based on experimentally observed distributions of landing positions. The fraction of mislocated fixations can be estimated by extrapolation of experimentally observed landing distributions (Fig. 2a). The basic problem for such an approach is that experimental data of within-word fixation locations consist of both well-located (i.e., fixations intended for the realized target word) and mislocated fixations (i.e., fixations intended for adjacent words). The proportions of mislocated fixations as a function of within-word fixation position follows a U-shaped curve (Fig. 2b, red line) with higher probabilities of mislocated fixations near word boundaries [8] due to contributions from overlapping tails of the landing position distributions of adjacent words. We used numerical simulations of an oculomotor model (Fig. 2a) to estimate the proportion of mislocated fixations (see Materials and Methods). Simulations of this model permitted the direct computation of distributions of both mislocated and well-located fixations. Assuming that variance in landing positions is caused by oculomotor errors, we expect that distributions of well-located fixations (Fig. 2b, black line) show less variance than the original distributions of all fixations (green line), because the mislocated fractions near word boundaries are removed. A major complication for the estimation of the proportion of mislocated fixations is that these errors also bias probabilities for word skippings and refixations (Fig. 2c, red lines), such that simulated fixation probabilities deviate from the experimental data. As a solution to this problem, we developed an iterative procedure, where numerical simulations of saccade-targeting (Fig. 2a) were applied (i) to decompose the distributions of landing positions into well- and mislocated fixations (Fig. 2b) and (ii) to simultaneously adjust the probabilities for word-targeting, i.e., word skippings and refixations (Fig. 2c). Such an approach is self-consistent, because landing position distributions and word-targeting probabilities converge to numerical values consistent with self-generated errors.

Bottom Line: During reading, we generate saccadic eye movements to move words into the center of the visual field for word processing.Our approach is based on iterative computation of the proportions of several types of oculomotor errors, the underlying probabilities for word-targeting, and corrected distributions of landing positions.These results show that fixation probabilities are strongly affected by oculomotor errors.

View Article: PubMed Central - PubMed

Affiliation: Department of Psychology, University of Potsdam, Potsdam, Germany. Ralf.Engbert@uni-potsdam.de

ABSTRACT
During reading, we generate saccadic eye movements to move words into the center of the visual field for word processing. However, due to systematic and random errors in the oculomotor system, distributions of within-word landing positions are rather broad and show overlapping tails, which suggests that a fraction of fixations is mislocated and falls on words to the left or right of the selected target word. Here we propose a new procedure for the self-consistent estimation of the likelihood of mislocated fixations in normal reading. Our approach is based on iterative computation of the proportions of several types of oculomotor errors, the underlying probabilities for word-targeting, and corrected distributions of landing positions. We found that the average fraction of mislocated fixations ranges from about 10% to more than 30% depending on word length. These results show that fixation probabilities are strongly affected by oculomotor errors.

Show MeSH