Fitting Models for the Iowa Gambling Task Task with R Cognitive - PowerPoint PPT Presentation

IGT models Cheng & Sheu Iowa Gambling Fitting Models for the Iowa Gambling Task Task with R Cognitive Modelling: EV and Other Models A General Chung-Ping Cheng, Ching-Fan Sheu Framework Issues in Random National Chengchi University, National Cheng Kung University Effect Summary 10 July 2009 Cheng & Sheu (NCCU, NCKU) IGT models 10 July 2009 1 / 20

Outline IGT models Cheng & Sheu Iowa Gambling Task 1 Iowa Gambling Task Cognitive Modelling: EV and Other Models Cognitive 2 Modelling: EV and Other Models A General Framework 3 A General Framework Issues in Random Issues in Random Effect 4 Effect Summary Summary 5 Cheng & Sheu (NCCU, NCKU) IGT models 10 July 2009 2 / 20

The Iowa Gambling Task(IGT, Bechara, Damasio, Damasio, & Anderson, 1994) IGT models Cheng & Sheu You Win 100 You Win 100 Iowa Iowa Gambling Task (IGT) also also Gambling You Lose 250 You Lose 250 Task Cognitive Modelling: EV and Other Deck D Deck B Deck C Models A General Framework Issues in $ 2000- $ 2000 -150=1850 150=1850 Random Effect Summary 1 Participant Participant Cheng & Sheu (NCCU, NCKU) IGT models 10 July 2009 3 / 20

The Payoff Distribution IGT models Trial Deck A Deck B Deck C Deck D Cheng & Sheu Iowa 1 100 100 50 50 Gambling Task 2 100 100 50 50 Cognitive Modelling: EV 3 100,-150 100 50,-50 50 and Other 4 100 100 50 50 Models A General 5 100, -300 100 50,-50 50 Framework 6 100 100 50 50 Issues in Random 7 100,-200 100 50,-50 50 Effect 8 100 100 50 50 Summary 9 100,-250 100,-1250 50,-50 50 10 100,-350 100 50,-50 50,-1250 Mean -25 -25 25 25 Cheng & Sheu (NCCU, NCKU) IGT models 10 July 2009 4 / 20

The Expectancy-Valence Model for IGT (Busemeyer & Stout, 2002) IGT models Cheng & Sheu ν t = wW t − ( 1 − w ) L t . (1) Iowa Gambling E ν k , t = ( 1 − a ) E ν k , t − 1 + a ν t , (2) Task if deck k is chosen at trial t ( k = 1 , 2 , 3 , 4 ) . Cognitive Modelling: EV and Other exp ( θ t E ν k , t ) Models = p k , t + 1 , (3) 4 A General � exp ( θ t E ν j , t ) Framework j = 1 Issues in Random where θ t = ( . 1 t ) c . Effect Summary ( p k , t + 1 ∝ E ν k , t ) w denotes attention to gain. a denotes attention to recent outcomes. c denotes response sensitivity to expectancy-valence. Cheng & Sheu (NCCU, NCKU) IGT models 10 July 2009 5 / 20

Yechiam, Busemeyer, Stout & Bechara, 2005 IGT models Cheng & Sheu Iowa Gambling Task Cognitive Modelling: EV and Other Models A General Framework Issues in Random Effect Summary Cheng & Sheu (NCCU, NCKU) IGT models 10 July 2009 6 / 20

Ahn, Busemeyer, Wagenmakers & Stout(2008) IGT models Cheng & Sheu Utility Expectancy ν t = wW t − ( 1 − w ) L t Iowa ν t = ( W t − L t ) α if W t − L t > 0 , Gambling Prospect Task ν t = − ρ | W t − L t | α otherwise. Cognitive Modelling: EV and Other Models Updating A General Delta learning E ν k , t = ( 1 − D k , t a ) E ν k , t − 1 + D k , t a ν k Framework Decay reinforcement E ν k , t = ( 1 − a ) E ν k , t − 1 + D k , t ν k Issues in Random Effect exp ( θ ( t ) E ν k , t ) Summary Choice p k , t + 1 = 4 � exp ( θ ( t ) E ν j , t ) j = 1 θ t = ( . 1 t ) c Trial-dependent θ t = 3 c − 1 Trial-independent Cheng & Sheu (NCCU, NCKU) IGT models 10 July 2009 7 / 20

A General Framework for IGT Models IGT models Cheng & Sheu ν t = ( − ρ ) I ( wW t − lL t < 0 ) | wW t − lL t | α Utility Iowa Gambling Task Expectancy l = 1 − w , α = 1 , ρ = 1 Cognitive Prospect w = 1 , l = 1 Modelling: EV and Other E ν k , t = ( 1 − f β a ) E ν k , t − 1 + D k , t a β ν k Updating Models where f β = ( D k , t + 1 ) β − β A General Framework Delta learning β = 1 Issues in Random Decay reinforcement β = 0 Effect θ t = γ t c Choice Summary γ = . 1 c Trial t-dependent c = 0 Trial t-independent Cheng & Sheu (NCCU, NCKU) IGT models 10 July 2009 8 / 20

The General Framework is a Nonlinear Model. IGT models The General Framework for IGT can be seen as a nonlinear Cheng & Sheu regression model. Iowa Gambling Task t exp (( γ t c D l , k a β ( 1 − f β a ) S ( k , t , l ) ν k , l ) Cognitive � Modelling: EV l = 1 and Other p k , t + 1 = , Models 4 t exp (( γ t c D l , j a β ( 1 − f β a ) S ( j , t , l ) ν j , l ) � � A General Framework j = 1 l = 1 Issues in t l Random Effect � � where S ( k , t , l ) = D m , k − 1 − D m , k , Summary m = 1 m = 1 and ν k , j = ( − ρ ) I ( wW j − lL j < 0 ) | wW j − lL j | α . = f ( W 1 , ..., W t , L 1 , ..., L t , D k , 1 , ..., D k , t ) Cheng & Sheu (NCCU, NCKU) IGT models 10 July 2009 9 / 20

The General Framework is also a Multinomial Logistic Model. IGT models The General Framework for IGT can be also seen as a Cheng & Sheu multinomial logistic model. Iowa Gambling Task Cognitive 1 Modelling: EV p k , t + 1 = and Other t Models 1 + exp ( γ t c D l , k a β ( 1 − f β a ) S ( k , t , l ) ( ν 1 , l − ν k , 1 )) � A General l = 1 Framework t l Issues in � � where S ( k , t , l ) = D m , k − 1 − D m , k , Random Effect m = 1 m = 1 Summary and ν k , j = ( − ρ ) I ( wW j − lL j < 0 ) | wW j − lL j | α . Cheng & Sheu (NCCU, NCKU) IGT models 10 July 2009 10 / 20

Estimated Parameters of Eight Models for a Single Participant IGT models Cheng & Sheu Iowa Step 1. Rearrange the data such that the predictors are Gambling Task outcomes of all previous trials. Cognitive Modelling: EV Step 2. Specify the parameters in the framework such and Other Models that the framework will turn into a special IGT model. A General Step 3. Fitting model to individual data. Framework Issues in Minimize the loglikelihood function by nlm in R. Random Estimate with other functions/packages for multinomial Effect logistic regression(e.g., nnet or vgam in R). Summary Cheng & Sheu (NCCU, NCKU) IGT models 10 July 2009 11 / 20

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Estimated Parameters of Eight Models for a Single Participant - Continued. IGT models Cheng & Sheu Iowa Utility Updating Choice w or α ρ a c or γ Gambling Task Cognitive expec delta dep .743 .172 9.725 Modelling: EV and Other expec decay dep .693 .067 .873 Models expec delta ind .714 .083 9.833 A General Framework expec decay ind .693 .069 .926 Issues in prosp delta dep 1.096 .028 .557 2.987 Random Effect prosp decay dep 1.197 .236 .080 .594 Summary prosp delta ind 1.222 .126 .204 4.082 prosp decay ind 1.164 .255 .076 .654 Cheng & Sheu (NCCU, NCKU) IGT models 10 July 2009 13 / 20

Learning Models IGT models Cheng & Sheu Iowa Some learning models are special cases of framework. Gambling Task The Rescorla-Wagner model (1972) Cognitive Modelling: EV The stochastic learning model of Bush and Mosteller and Other Models (1955) A General Framework The Hullian learning model(Bush and Mosteller, 1959) Issues in A logistic regression model of avoidance learning Random Effect (Gelman, et al., 2002) Summary Cheng & Sheu (NCCU, NCKU) IGT models 10 July 2009 14 / 20