Econometric Models — Pooled Analysis

1 Overview

This section pools all four games (N = 122) to estimate the individual-level predictors of two key outcomes: signal honesty and belief accuracy.

Model choice rationale

Outcome	Support	Model
Signal honesty	Binary (0 = deceptive, 1 = honest)	Logistic regression
Belief accuracy score	Ordinal (0, 1, 2)	Ordered logistic regression (proportional odds)

Both models are estimated in a base specification (game dummies + CRT + quiz errors) and an extended specification (base + MASC ToM score + IRI Empathic Concern + IRI Perspective Taking). The reference game is BS (Battle of the Sexes).

Standard errors are conventional (not clustered). Given the small sample (N = 122) results should be interpreted as exploratory.

1.1 Outcome distributions

Category	n
Y1 — Signal Honesty
Deceptive (0)	42
Honest (1)	80

Category	n
Y2 — Belief Accuracy Score
Score 0	21
Score 1	55
Score 2	46

2 Model fit summary

Outcome	Model	Type	N	AIC	BIC	McFadden R²
Model fit summary
Signal Honesty	Base	Logit	122	163.6	180.4	0.0349
Signal Honesty	Extended	Logit	122	163.9	189.2	0.0711
Belief Accuracy	Base	Ordered Logit	122	257.0	276.7	0.0327
Belief Accuracy	Extended	Ordered Logit	122	262.6	290.6	0.0345

3 Y1 — Signal Honesty

3.1 Regression table

Results are presented as log-odds (with SEs) and odds ratios (with 95% CI).

Y1 — Signal Honesty: Logistic Regression (log-odds)
	Logit (log-odds · SE · p-value)
	Base model	Extended model
Game: MP (ref = BS)	0.185	0.137
	(0.539)	(0.559)
	p = 0.731	p = 0.807
Game: PD (ref = BS)	-0.283	-0.423
	(0.540)	(0.564)
	p = 0.600	p = 0.454
Game: SH (ref = BS)	0.761	0.671
	(0.566)	(0.581)
	p = 0.178	p = 0.248
CRT score (0–4)	0.237	0.154
	(0.227)	(0.237)
	p = 0.298	p = 0.516
Quiz errors	-0.005	-0.003
	(0.026)	(0.026)
	p = 0.838	p = 0.895
MASC — ToM score		0.095
		(0.063)
		p = 0.129
IRI — Empathic Concern		0.024
		(0.052)
		p = 0.639
IRI — Perspective Taking		0.083
		(0.051)
		p = 0.102
N	122	122
Log-Likelihood	-75.80	-72.96
* p<0.01 p<0.05 * p<0.10. Reference game: BS.
* p < 0.1, p < 0.05, * p < 0.01

Y1 — Signal Honesty: Logistic Regression (Odds Ratios)
	Logit (OR · 95% CI · p-value)
	Base model	Extended model
Game: MP (ref = BS)	1.204	1.146
	[0.419, 3.511]	[0.383, 3.476]
	p = 0.731	p = 0.807
Game: PD (ref = BS)	0.753	0.655
	[0.259, 2.177]	[0.213, 1.976]
	p = 0.600	p = 0.454
Game: SH (ref = BS)	2.140	1.956
	[0.719, 6.760]	[0.636, 6.354]
	p = 0.178	p = 0.248
CRT score (0–4)	1.267	1.167
	[0.812, 1.997]	[0.731, 1.872]
	p = 0.298	p = 0.516
Quiz errors	0.995	0.997
	[0.941, 1.049]	[0.943, 1.053]
	p = 0.838	p = 0.895
MASC — ToM score		1.100
		[0.973, 1.247]
		p = 0.129
IRI — Empathic Concern		1.025
		[0.924, 1.134]
		p = 0.639
IRI — Perspective Taking		1.087
		[0.986, 1.207]
		p = 0.102
N	122	122
Log-Likelihood	-75.80	-72.96
* p<0.01 p<0.05 * p<0.10. Reference game: BS. OR > 1 = increases P(honest).
* p < 0.1, p < 0.05, * p < 0.01

3.2 Coefficient plot

Interpretation

Odds ratios greater than 1 indicate a higher probability of sending an honest signal relative to the reference game (BS). Game dummies capture between-game heterogeneity in honesty norms; CRT score captures reflective reasoning ability; quiz errors proxy for lower comprehension of the game structure.

4 Y2 — Belief Accuracy Score

The ordered logit assumes proportional odds: each predictor shifts the cumulative log-odds of being in a higher accuracy category by a constant amount, regardless of the threshold. The estimated proportional odds ratios (POR) are directly interpretable as the multiplicative change in the odds of achieving a higher belief score.

4.1 Regression table

Y2 — Belief Accuracy Score: Ordered Logistic Regression (log-odds)
	Ordered Logit (log-odds · SE · p-value)
	Base model	Extended model
Game: MP (ref = BS)	-0.434	-0.390
	(0.475)	(0.483)
	p = 0.363	p = 0.421
Game: PD (ref = BS)	-0.223	-0.200
	(0.496)	(0.500)
	p = 0.655	p = 0.690
Game: SH (ref = BS)	0.909*	0.912*
	(0.492)	(0.496)
	p = 0.067	p = 0.068
CRT score (0–4)	0.053	0.036
	(0.208)	(0.215)
	p = 0.797	p = 0.866
Quiz errors	0.014	0.011
	(0.024)	(0.025)
	p = 0.569	p = 0.671
MASC — ToM score		0.013
		(0.055)
		p = 0.817
IRI — Empathic Concern		-0.014
		(0.044)
		p = 0.752
IRI — Perspective Taking		-0.018
		(0.043)
		p = 0.673
N	122	122
* p<0.01 p<0.05 * p<0.10. Reference game: BS. Positive = higher belief accuracy.
* p < 0.1, p < 0.05, * p < 0.01

Y2 — Belief Accuracy Score: Ordered Logistic Regression (Proportional Odds Ratios)
	Ordered Logit (POR · 95% CI · p-value)
	Base model	Extended model
Game: MP (ref = BS)	0.648	0.677
	[0.253, 1.641]	[0.260, 1.744]
	p = 0.363	p = 0.421
Game: PD (ref = BS)	0.800	0.819
	[0.300, 2.117]	[0.305, 2.183]
	p = 0.655	p = 0.690
Game: SH (ref = BS)	2.483*	2.490*
	[0.955, 6.624]	[0.951, 6.695]
	p = 0.067	p = 0.068
CRT score (0–4)	1.055	1.037
	[0.700, 1.586]	[0.678, 1.584]
	p = 0.797	p = 0.866
Quiz errors	1.014	1.011
	[0.965, 1.065]	[0.960, 1.063]
	p = 0.569	p = 0.671
MASC — ToM score		1.013
		[0.908, 1.129]
		p = 0.817
IRI — Empathic Concern		0.986
		[0.903, 1.076]
		p = 0.752
IRI — Perspective Taking		0.982
		[0.902, 1.069]
		p = 0.673
N	122	122
* p<0.01 p<0.05 * p<0.10. Reference game: BS. POR > 1 = higher odds of being in higher accuracy category.
* p < 0.1, p < 0.05, * p < 0.01

4.2 Coefficient plot

Interpretation

PORs greater than 1 indicate a higher probability of being in a higher belief accuracy category (i.e., correctly predicting both the opponent’s choice and the opponent’s belief about one’s own choice). The proportional odds assumption should be assessed with a Brant test if results are used in a final paper.