Probabilistic online processing of sentence anomalies

Figures & data

Figure 1. Sample image arrays. A: SVA item (The key to the cabinet(s) literally was/were on the table). Top left = literal subject key; bottom left = non-literal subject keys; right pictures = local noun and a non-literal version of it (cabinet/cabinets). B: Without item (Lulu visited the gym without her hat on/off late yesterday night). Top left = Yes-Accessory agent (the literal interpretation of “without + off”); bottom left = No-Accessory agent (the literal interpretation of “without + on” and non-literal interpretation of “without + off”). Right pictures = location of the verb and a semantic competitor for it.

Figure 2. Subject selection for Experiment 1 SVA trials, split by condition.

Table 1. Results from logistic mixed-effect regression of subject selection (odds of selecting head noun number competitor versus all other items) for Experiment 1 SVA trials.

Fixed effects	$\widehat{\text{β}}$	SE	p(z)
Intercept	−4.76	0.51	<0.001
Local Noun	−1.85	0.58	0.01
Verb	−4.14	0.77	<0.001
Trial Number	−0.95	0.26	<0.001
Local Noun × Verb	−1.85	1.14	0.10
Local Noun × Trial Number	0.17	0.27	0.53
Verb × Trial Number	−1.46	0.51	<0.01
Random effects	Groups		SD
	Item	Intercept	0.49
	Participant	Intercept	1.45

Figure 3. Average proportion of fixations to images in Experiment 1 SVA trials receiving a literal sentence interpretation (KEY selected as the subject), zeroed to reflect verb onset. Vertical lines represent onsets of head nouns, local nouns, and verbs; panels represent sentence conditions. Confidence bands are 95% CIs from a non-parametric bootstrap (1000 iterations) sampled over participants with replacement at 10 msec intervals.

Table 2. Results from linear mixed-effect regression of proportion of fixations to head noun number competitor binned at 500 msec time windows for Experiment 1 SVA trials eliciting a literal-head number interpretation.

Fixed effects	Window 1: Head noun region			Window 2: Local noun region			Window 3: Verb region			Window 4: Post-Verb region
	$\widehat{\text{β}}$	SE	p(χ^2)	$\widehat{\text{β}}$	SE	p(χ^2)	$\widehat{\text{β}}$	SE	p(χ^2)	$\widehat{\text{β}}$	SE	p(χ^2)
Intercept	0.25	0.01	<0.001	0.26	0.02	<0.001	0.20	0.02	<0.001	0.20	0.02	<0.001
Local Noun	0.01	0.02	0.44	0.00	0.02	0.87	−0.05	0.02	0.03	0.03	0.02	0.11
Verb	−0.01	0.02	0.52	−0.02	0.02	0.32	−0.00	0.02	0.94	−0.12	0.02	<0.001
Trial Number	−0.02	0.01	0.09	−0.02	0.01	0.05	−0.04	0.01	<0.001	−0.04	0.01	<0.001
Local Noun × Verb	0.01	0.04	0.78	−0.03	0.04	0.41	0.00	0.03	0.95	−0.01	0.03	0.79
Local Noun × Trial	0.02	0.02	0.21	−0.04	0.02	0.02	0.02	0.02	0.15	−0.01	0.02	0.82
Verb × Trial	0.00	0.02	0.36	−0.03	0.02	0.15	−0.00	0.02	0.78	0.03	0.02	0.07
Local Noun × Verb × Trial	−0.02	0.04	0.61	−0.00	0.04	0.89	−0.04	0.03	0.25	0.06	0.03	0.06
Random effects	Groups		SD	Groups		SD	Groups		SD	Groups		SD
	Item	Intercept	0.04	Item	Intercept	0.04	Item	Intercept	0.03	Item	Intercept	0.04
	Participant	Intercept	0.04	Participant	Intercept	0.06	Participant	Intercept	0.07	Participant	Intercept	0.08
		Verb	0.01		Loc Noun	0.04		Loc Noun	0.07		Loc Noun	0.07
		Trial	0.02		Verb	0.05	Residual		0.30		Residual	0.30
	Residual		0.33		Loc Noun × Verb	0.08
				Residual		0.33

Effects are italicised when they would be significant under a 0.05 alpha level, but not an alpha level corrected for multiple comparisons.

Figure 4. Subject selection for Experiment 1 Without trials, split by condition.

Table 3. Results from logistic mixed-effect regression of subject selection (odds of selecting non-literal subject versus all other items) for Without trials.

Fixed effects	$\widehat{\text{β}}$	SE	p(z)
Intercept	−6.92	1.65	<0.001
Preposition	−9.35	3.29	<0.01
Trial Number	−0.96	0.39	0.01
Preposition × Trial Number	−1.16	0.78	0.14
Random effects	Groups		SD
	Item	Intercept	5.62
		Preposition	11.19
	Participant	Intercept	0.00

Figure 5. Average proportion of fixations to images in of Experiment 1 Without trials, zeroed to reflect preposition onset. Vertical lines represent onsets of without and prepositions; panels represent sentence conditions crossed with sentence interpretation. The non-literal interpretation of “Without-On” (bottom left panel) was not analysed because of an insufficient number of trials but we present it here for completeness. Confidence bands are 95% CIs from a non-parametric bootstrap (1000 iterations) sampled over participants with replacement at 10 msec intervals.

Table 4. Results from linear mixed-effect regression of proportion of fixations to yes-accessory agent binned at 500 msec time windows for Experiment 1 Without trials split by interpretation.

Fixed effects	Window 1: Without region			Window 2 Preposition region			Window 3: Post-Preposition region
	$\widehat{\text{β}}$	SE	p(χ^2)	$\widehat{\text{β}}$	SE	p(χ^2)	$\widehat{\text{β}}$	SE	p(χ^2)
Intercept	0.28	0.02	<0.001	0.25	0.03	<0.001	0.19	0.02	<0.001
Interpretation 1: (Yes- vs. No-Accessory)	0.02	0.06	0.78	−0.10	0.07	0.13	−0.61	0.06	<0.001
Interpretation 2: (No-Accessory Literal vs. Non-Literal)	−0.06	0.07	0.43	−0.13	0.07	0.08	0.08	0.06	0.19
Trial Number	0.04	0.02	0.02	0.00	0.00	0.77	0.00	0.00	0.34
Interpretation 1 (Yes- vs. No-Acc) × Trial	0.08	0.06	0.18	0.00	0.00	0.04	−0.01	0.00	<0.001
Interpretation 2 (Yes-Acc Lit vs. Non-Lit) × Trial	−0.15	0.07	0.03	0.00	0.00	0.40	0.00	0.00	0.28
Random effects	Groups		SD	Groups		SD	Groups		SD
	Item	Intercept	0.03	Item	Intercept	0.06	Item	Intercept	0.03
		Trial	0.02		Interp. 1	0.11	Participant	Intercept	0.06
	Participant	Intercept	0.08	Participant	Intercept	0.09		Interp. 1	0.20
		Interp. 1	0.14		Interp. 1	0.17	Residual		0.31
		Interp. 2	0.11		Interp. 2	0.10
		Trial	0.04	Residual		0.33
	Residual		0.36

Effects are italicised when they would be significant under a 0.05 alpha level, but not an alpha level corrected for multiple comparisons.

Table 5. Response types by category, Experiment 2 SVA trials.

Response type	Loc Plural, Plural Verb	Loc Plural, Singular Verb	Loc Singular, Plural Verb	Loc Singular, Singular Verb
Identical repetition	174	210	216	247
No response	1	1	2	1
Non-literal responses (Inflections changed)
N1 changed	19	4	2	0
N2 changed	27	34	14	8
V changed	42	21	38	9
N1 and N2 changed	9	2	2	0
N1 and V changed	1	0	0	0
N2 and V changed	1	1	3	1
N1, N2, and V changed	1	1	0	0
Other changes (Inflections preserved)
Adverb & verb re-ordered	83	86	81	100
Adverb changed	2	8	3	1
Preposition changed	4	3	6	6
All other changes	20	13	17	11

Grammatical utterances in bold.

Figure 6. Sentence repetition for Experiment 2 SVA trials, split by condition and whether the inflection change led to a grammatical or ungrammatical utterance.

Table 6. Results from logistic mixed-effect regression of responses with number inflection changes, versus identical and other repetitions, for Experiment 2 SVA trials.

Fixed effects	$\widehat{\text{β}}$	SE	p(z)
Intercept	−2.36	0.24	<0.001
Local Noun	−1.12	0.19	<0.001
Verb	−1.27	0.19	<0.001
Trial Number	−0.07	0.09	0.47
Local Noun × Verb	−0.74	0.37	0.05
Local Noun × Trial Number	−0.12	0.18	0.52
Verb × Trial Number	0.77	0.18	<0.001
Local Noun × Verb × Trial Number	0.32	0.36	0.37
Random effects	Groups		SD
	Item	Intercept	0.86
	Participant	Intercept	0.94

Figure 7. Average proportion of fixations to images in the listening phase of SVA trials where all inflections were repeated veridically (identical and other trials), zeroed to reflect verb onset. Vertical lines represent onsets of head nouns, local nouns, and verbs in audio recording; panels represent sentence conditions. Confidence bands are 95% CIs from a non-parametric bootstrap (1000 iterations) sampled over participants with replacement at 10 msec intervals.

Table 7. Results from linear mixed-effect regression of proportion of fixations to head noun number competitor binned at 500 msec time windows for SVA trials where all inflections were repeated correctly (identical and other trials).

Fixed effects	Window 1: Head noun region			Window 2: Local noun region			Window 3: Verb region			Window 4: Post-Verb region
	$\widehat{\text{β}}$	SE	p(χ^2)	$\widehat{\text{β}}$	SE	p(χ^2)	$\widehat{\text{β}}$	SE	p(χ^2)	$\widehat{\text{β}}$	SE	p(χ^2)
Intercept	0.20	0.01	<0.001	0.17	0.01	<0.001	0.20	0.01	<0.001	0.21	0.02	<0.001
Local Noun	−0.00	0.02	0.85	0.01	0.01	0.64	−0.07	0.02	<0.001	−0.00	0.02	0.85
Verb	−0.01	0.02	0.68	0.02	0.01	0.13	−0.01	0.02	0.72	−0.03	0.02	0.11
Trial Number	−0.01	0.01	0.11	−0.00	0.01	0.51	−0.03	0.01	<0.01	−0.02	0.01	0.02
Local Noun × Verb	0.01	0.03	0.97	0.02	0.03	0.54	−0.03	0.03	0.36	−0.01	0.03	0.78
Local Noun × Trial	0.03	0.02	0.08	0.02	0.02	0.19	0.02	0.02	0.30	−0.01	0.02	0.59
Verb × Trial	−0.02	0.02	0.28	−0.03	0.02	0.09	−0.02	0.02	0.30	0.05	0.02	<0.01
Loc Noun × Verb × Trial	0.04	0.03	0.22	0.04	0.03	0.22	0.05	0.03	0.12	−0.04	0.03	0.29
Random effects	Groups		SD	Groups		SD	Groups		SD	Groups		SD
	Item	Intercept	0.03	Item	Intercept	0.04	Item	Intercept	0.04	Item	Intercept	0.06
	Participant	Intercept	0.03	Participant	Intercept	0.04	Participant	Intercept	0.06		Loc Noun	0.03
	Residual		0.27	Residual		0.27		Loc Noun	0.01	Participant	Intercept	0.06
							Residual		0.29		Loc Noun	0.07
											Verb	0.05
											Trial	0.03
											Loc Noun × Verb	0.03
											Residual	0.29

Effects are italicised when they would be significant under a 0.05 alpha level, but not an alpha level corrected for multiple comparisons.

Table 8. Response types by category, Experiment 2 Without trials.

Response type	Without-On	without-Off
Identical repetition	272	220
No response	1	1
Non-literal responses (Without and/or preposition changed)
Preposition changed	7	24
Preposition omitted	4	1
Without -> With	1	5
Without-> With; Preposition changed	1	1
Other changes (Without and preposition maintained)
Time phrase changed	63	87
Name changed	5	8
Verb phrase changed	17	18
Object changed	2	2
Multiple changes	11	17

Referent different than prompt in bold.

Figure 8. Sentence repetition for Experiment 2 Without trials, split by condition.

Table 9. Results from logistic mixed-effect regression of repetitions containing without/preposition changes, versus identical and other repetitions, for Experiment 2 Without trials.

Fixed effects	$\widehat{\text{β}}$	SE	p(z)
Intercept	−3.96	0.47	<0.001
Preposition	−1.20	0.42	<0.001
Trial Number	−0.55	0.20	0.01
Preposition × Trial Number	−0.33	0.40	0.41
Random effects	Groups		SD
	Item	Intercept	0.76
	Participant	Intercept	1.34

Figure 9. Average proportion of fixations to images in the listening phase of Without trials in Experiment 2, zeroed to reflect preposition onset. Vertical lines represent onsets of without and prepositions; panels represent sentence conditions crossed with sentence interpretation. Confidence bands are 95% CIs from a non-parametric bootstrap (1000 iterations) sampled over participants with replacement at 10 msec intervals. Only literal interpretations (identical and other repetitions) were submitted to analyses due to the sparse number of non-literal repetitions (involving changes to without and/or preposition).

Table 10. Results from linear mixed-effect regression of proportion of fixations to yes-accessory agent binned at 500 msec time windows for literally-interpreted (identical and other repetitions) Experiment 2 Without trials.

Fixed effects	Window 1: Without region			Window 2: Preposition region			Window 3: Post-Preposition region
	$\widehat{\text{β}}$	SE	p(χ^2)	$\widehat{\text{β}}$	SE	p(χ^2)	$\widehat{\text{β}}$	SE	p(χ^2)
Intercept	0.19	0.02	<0.001	0.29	0.02	<0.001	0.23	0.02	<0.001
Preposition	−0.01	0.02	0.76	0.02	0.02	0.45	0.10	0.03	<0.001
Trial Number	0.01	0.01	0.56	0.00	0.00	0.23	0.00	0.00	0.03
Preposition × Trial Number	−0.02	0.02	0.36	0.00	0.00	0.93	−0.00	0.00	0.71
Random effects	Groups		SD	Groups		SD	Groups		SD
	Item	Intercept	0.04	Item	Intercept	0.04	Item	Intercept	0.00
		Preposition	0.03		Trial Num	0.05	Participant	Intercept	0.06
	Participant	Intercept	0.06	Participant	Intercept	0.05		Preposition	0.10
	Residual		0.27		Preposition	0.05	Residual		0.32
					Trial Num	0.00
				Residual		0.31

Effects are italicised when they would be significant under a 0.05 alpha level, but not an alpha level corrected for multiple comparisons.