Logistic regression models¶

Choosing logistic regression models¶

\[logit(p(c_r)) \sim RewardedChoice + UnrewardedChoice\]

\[logit(p(c_r)) \sim RewardedChoice + Choice\]

\[logit(p(c_r)) \sim RewardedChoice + UnrewardedChoice + Choice\]

\[logit(p(c_r)) \sim Choice + Reward + Choice*Reward\]

Ignored trials are removed

choice	reward	Choice	Reward	RewardedChoice	UnrewardedChoice	Choice * Reward
L	yes	-1	1	-1	0	-1
L	no	-1	-1	0	-1	1
R	yes	1	1	1	0	1
L	yes	-1	1	-1	0	-1
R	no	1	-1	0	1	-1
R	yes	1	1	1	0	1
L	no	-1	-1	0	-1	1

Some observations:

	Su 2022	Bari 2019	Hattori 2019	Miller 2021
Equivalent to	RewC + UnrC	RewC + (RewC + UnrC)	RewC + UnrC + (RewC + UnrC)	(RewC + UnrC) + (RewC - UnrC) + Rew
Severity of multicollinea- rity	Not at all	Medium	Severe	Slight
Interpretation	Like a RL model with different learning rates on reward and unreward- ed trials	Like a RL model that only updates on rewarded trials, plus a choice kernel	Like a RL model that has different learning rates on reward and unrewarded trials, plus a choice kernel	Like a RL model that has symmetric learning rates for rewarded and unrewarded trials, plus a choice

The choice of optimizer depends on the penalty term, as listed here.

choice	reward	Choice	Reward	RewardedChoice	UnrewardedChoice	Choice * Reward
L	yes	-1	1	-1	0	-1
L	no	-1	-1	0	-1	1
R	yes	1	1	1	0	1
L	yes	-1	1	-1	0	-1
R	no	1	-1	0	1	-1
R	yes	1	1	1	0	1
L	no	-1	-1	0	-1	1

choice	reward	Choice	Reward	RewardedChoice	UnrewardedChoice	Choice * Reward
L	yes	-1	1	-1	0	-1
L	no	-1	-1	0	-1	1
R	yes	1	1	1	0	1
L	yes	-1	1	-1	0	-1
R	no	1	-1	0	1	-1
R	yes	1	1	1	0	1
L	no	-1	-1	0	-1	1

choice	reward	Choice	Reward	RewardedChoice	UnrewardedChoice	Choice * Reward
L	yes	-1	1	-1	0	-1
L	no	-1	-1	0	-1	1
R	yes	1	1	1	0	1
L	yes	-1	1	-1	0	-1
R	no	1	-1	0	1	-1
R	yes	1	1	1	0	1
L	no	-1	-1	0	-1	1