A theoretical analysis of the perceptual span based on SWIFT simulations of the n + 2 boundary paradigm

Figures & data

Figure 1. The SWIFT model. Illustration of components constituting the when- and where-pathways of saccadic control during reading. The model is illustrated at a stage at which lexical activation at the fixated word is increasing and the zoom-lense processing span is decreasing accordingly.

TABLE 1 Summary of parameter values in the present SWIFT model

			Dynamical span modulation
	Parameters	Symbol	M	SE	Range	Schad & Engbert (2012)
Lexical parameters	Frequency, intercept	α	13.1	0.57	1–20	18.7
	Frequency, slope	β	0.07	0.02	0–1	0.71
	Global inhibition	ppf	0.0			0.069
Processing span	Span, constant	δ0	14.5	0.31	1–40	1.64
	Span, dynamic – foveal	δ1	5.04	0.45	0–40	2.15
	Span, asymmetry	δ2	0.27	0.01	0.1–1	–
Visual parameters	Visual preprocessing	pspan	–			15.0
	Word length exponent	η	0.91	0.02	0–1	0.3
	Preprocessing factor	f	0.81			0.814
	Global decay	ω	0.01			0.01
	Transfer across saccades	ι	1.0			0.50
	Eye–mind lag	pcd	30.0			30.0
Saccade timing	Random timing (ms)	tsac	236.5	1.03	150–300	221.2
	Inhibition factor	h	0.48	0.07	0–5	0.549
	Target selection weight	γ	1.0			1.0
Saccade programming	Labile stage (ms)	τlab	100.0			100.0
	Refixation factor	refix	0.7			0.7
	Mislocation factor	misfac	0.75			0.75
	Nonlabile stage (ms)	τnlab	50.0			50.0
	Latency modulation	κ0	2.5			2.5
	Latency modulation	κ1	0.3			0.3
	Saccade execution (ms)	τex	30.0			30.0

Means (M) of all model parameters. For the free parameters (bold), also standard errors (SE) and parameter boundaries (Range) are provided.

Figure 2. Summary of simulation results. Rows correspond to word n, n + 1, and n + 2. Note that for word n + 2, we distinguish between cases when word n + 1 was fixated or skipped. Illustrated is a comparison of simulations with and without saccade cancellation (due to display change) with results from two boundary experiments (Kliegl et al., 2007; Risse & Kliegl, 2011) testing conditions of valid (green) and invalid (red) preview. Vertical lines in left and middle column indicate the experimental means; probability densities are shown for the distribution of simulated fixation durations. The right column shows the likelihood for the experimental preview-benefit effect given the present simulation results. See text for more details.

Figure 3. The three panels in the left column show how varying parameter values for the constant part (top row), δ₀ the dynamic part δ₁ (bottom row), and the asymmetry of the perceptual span δ₂ (top row) affect the shape of the model's processing span at medium foveal activation. In each of these panels, the red curve indicates the processing span with the best-fitting parameter. The second and third columns illustrate how the preview benefit on word n + 2 (difference between valid and invalid preview condition) with word n + 1 being fixated (middle column) or skipped (right column) changes as a function of values for corresponding processing-span parameters. Horizontal dashed lines show the experimental preview benefit and solid lines the simulated preview benefit. Colours code two different fixation duration measures: single fixation durations (SFD; light green) and gaze durations (GD; dark green). Red vertical lines indicate the best-fitting parameter estimates.

Figure A1. Summary statistics of the SWIFT simulations of normal reading with identical preview in the n + 2 boundary paradigm. The upper panels show the simulated (sim) and experimental (exp) data for various fixation duration measures as function of (a) word frequency class and (b) word length class. The lower panels show the comparison for various fixation probability measures for (c) word frequency class and (d) word length class.

TABLE A1 Experimental (exp) and simulated (sim) means for fixation duration and fixation probability measures on word n, n + 1, and n + 2 in the target region

	Word n		Word n + 1		Word n + 2
	exp	sim	exp	sim	exp	sim
1st fixation duration (ms)	187	198	186	216	196	206
2nd fixation duration (ms)	172	174	156	155	176	166
single fixation duration (ms)	207	206	202	204	210	200
total time (ms)	252	257	214	221	264	235
skipping probability (p)	.06	.17	.47	.45	.13	.27
single fixation probability (p)	.81	.60	.52	.50	.74	.59
refixation probability (p)	.13	.23	.01	.06	.13	.14
regression probability (p)	.06	.06	.09	.09	.11	.05

Figure A3. The influence of the display-change assumptions on the simulated preview effects of word n + 2. The upper panels illustrate the variation on n + 2 preview-effect size as a function of the activation reset after the display change. The lower panels show the change in preview effects according to increasing proportion of saccade cancellations in case of word replacements. Panels from left to right summarize the results for fixation durations on word n + 1, on word n + 2 after word n + 1 was fixated, and after it was skipped. The dark green solid lines show the simulated gaze durations, the light green solid lines the simulated single-fixation durations, and dashed lines the respective experimental effect sizes.