Final choice models

Author

J Talbot

Below I present the most parsimonious 3 models for choice behaviour (PDon versus PDoff, HC versus PDoff, HC versus PDon). The models have been built down from the maximal model, and show no significant inferiority using type 2 Wald test (R’s anova function, using Chisq) compared to more complex models. Importantly, incorporation of trial number leads to significantly better models than those without. I present the model summaries, and have graphed the emmeans predictions (emmip) alongside the actual data - although we have seen most of these graphs, they represent the ‘core’ findings. Thankfully, models including 5 way interactions did not improve models significantly so we don’t have to contend with them.

PD on versus PD off

Best model is:

Choice ~ Effort + Reward + Recipient + Group + Reward:Group + Reward:Trial.number + Effort:Group:Trial.number + Effort:Recipient:Trial.number + (1 + Effort + Reward + Recipient + Trial.number | ID)

	Choice
Predictors	Log-Odds	CI	p
(Intercept)	4.01	3.11 – 4.91	<0.001
Effort	-1.24	-1.62 – -0.87	<0.001
Reward	1.40	1.00 – 1.81	<0.001
Recipient s2z1	0.72	0.36 – 1.08	<0.001
Group [PD on]	0.17	0.01 – 0.33	0.039
Reward × Group [PD on]	0.21	0.06 – 0.37	0.007
Reward × Trial number r	0.12	0.03 – 0.21	0.010
Effort × GroupPD off × Trial number r	-0.19	-0.30 – -0.08	0.001
Effort × Group [PD on] × Trial number r	-0.33	-0.44 – -0.21	<0.001
Effort × Recipient s2z1 × Trial number r	0.13	0.05 – 0.20	0.001
Random Effects
σ²	3.29
τ₀₀ _ID	7.75
τ₁₁ _{ID.scale(Effort)}	1.14
τ₁₁ _{ID.scale(Reward)}	1.16
τ₁₁ _{ID.Recipient_s2z1}	0.97
τ₁₁ _{ID.scale(Trial.number.r)}	0.17
ρ₀₁	0.09
	0.30
	-0.24
	0.38
ICC	0.77
N _ID	38
Observations	11207
Marginal R² / Conditional R²	0.233 / 0.824

Graphs:

Effort:Trial number:Group (left = predicted, right = actual)

Reward:Group (left = predicted, right = actual)

HC versus PDoff

Best model is:

Choice ~ Effort + Reward + Recipient + Group + Reward:Recipient + Effort:Trial.number + Reward:Trial.number + Reward:Group:Trial.number + (1 + Effort + Reward + Trial.number + Recipient + Reward:Recipient | ID)

(note that although Group is not a main effect, its presence is necessary due to the way emmeans detects nesting structures, with effects on model results).

	Choice
Predictors	Log-Odds	CI	p
(Intercept)	4.59	3.55 – 5.63	<0.001
Effort	-1.48	-1.85 – -1.10	<0.001
Reward	2.15	1.66 – 2.63	<0.001
Group [PD off]	0.64	-0.70 – 1.98	0.347
Recipient s2z1	1.21	0.78 – 1.63	<0.001
Reward × Recipient s2z1	0.50	0.23 – 0.76	<0.001
Effort × Trial number r	-0.25	-0.34 – -0.15	<0.001
Reward × Trial number r	0.45	0.31 – 0.59	<0.001
Reward × Group [PD off] × Trial number r	-0.30	-0.49 – -0.11	0.002
Random Effects
σ²	3.29
τ₀₀ _ID	9.92
τ₁₁ _{ID.scale(Effort)}	2.08
τ₁₁ _{ID.scale(Reward)}	2.91
τ₁₁ _{ID.scale(Trial.number.r)}	0.59
τ₁₁ _{ID.Recipient_s2z1}	1.87
τ₁₁ _{ID.scale(Reward):Recipient_s2z1}	0.30
ρ₀₁	0.22
	0.42
	0.22
	-0.03
	0.19
ICC	0.84
N _ID	80
Observations	11802
Marginal R² / Conditional R²	0.298 / 0.887

Graphs:

Reward:Group:Trial number (left = predicted, right = actual):

HC versus PDon

Best model is:

Choice ~ Effort + Reward + Recipient + Group +Trial.number + Reward:Recipient + Effort:Trial.number + Reward:Trial number + Reward:Group:Trial.number + (1 +Effort + Reward + Recipient + Trial.number + Reward:Recipient | ID)

(again, although group is not a main effect it is retained due to nesting structure).

	Choice
Predictors	Log-Odds	CI	p
(Intercept)	4.60	3.60 – 5.60	<0.001
Effort	-1.52	-1.89 – -1.14	<0.001
Reward	2.15	1.67 – 2.64	<0.001
Recipient s2z1	0.85	0.47 – 1.23	<0.001
Group [PD on]	0.90	-0.44 – 2.24	0.187
Trial number r	0.32	0.07 – 0.58	0.014
Reward × Recipient s2z1	0.30	0.06 – 0.54	0.015
Effort × Trial number r	-0.35	-0.45 – -0.26	<0.001
Reward × Trial number r	0.51	0.36 – 0.65	<0.001
(Reward × Group [PD on]) × Trial number r	-0.39	-0.59 – -0.19	<0.001
Random Effects
σ²	3.29
τ₀₀ _ID	10.54
τ₁₁ _{ID.scale(Effort)}	2.03
τ₁₁ _{ID.scale(Reward)}	3.20
τ₁₁ _{ID.Recipient_s2z1}	1.41
τ₁₁ _{ID.scale(Trial.number.r)}	0.62
τ₁₁ _{ID.scale(Reward):Recipient_s2z1}	0.22
ρ₀₁	0.14
	0.37
	-0.26
	0.53
	0.03
ICC	0.85
N _ID	80
Observations	11869
Marginal R² / Conditional R²	0.279 / 0.888

Graphs: