Bayesian Analyses of the Survivor Interaction Contrast
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1 Wright State University CORE Scholar Psychology Faculty Publications Psychology Bayesian Analyses of the Survivor Interaction Contrast Joseph W. Houpt Wright State University - Main Campus, joseph.houpt@wright.edu Andrew Heathcote Ami Eidels James T. Townsend Follow this and additional works at: Part of the Psychology Commons Repository Citation Houpt, J. W., Heathcote, A., Eidels, A., & Townsend, J. T. (212). Bayesian Analyses of the Survivor Interaction Contrast.. This Presentation is brought to you for free and open access by the Psychology at CORE Scholar. It has been accepted for inclusion in Psychology Faculty Publications by an authorized administrator of CORE Scholar. For more information, please contact corescholar@
2 Bayesian Analyses of the Survivor Interaction Contrast Joseph W. Houpt, Andrew Heathcote, Ami Eidels and James T. Townsend NEWCL P~),) K.>I o.>',:i'-'< l ; mllh;(ins..it-l "i ".>; C.J!o'LJiLiy;: &:i~1x:;,: Pn'!\o:l ~L!I L Society for Mathematical Psychology Annual Meeting Columbus, Ohio July 22, 212 Houpt. et al (SMP 212) Bayemn SIC 1 I 3
3 Outline 8 Introduction f) Parametric Test.. Model.. Simulation 8 Nonparametric Test.. Model.. Simulation Comparisons Among SIC Tests.. Simulation.. Application 8 Conclusion Houpt, et al. (S MP 212) Bayes ~a n SIC 2 I XJ
4 Introd uction Outline 8 Introduction t A ~I Houpt, et al. (SMP 212) Bayes~an SIC 3 I XJ
5 Introduction ~ How do different sources of information combine in mental processing? a Are both sources used concurrently, or do we use one at a time? a How many sources are enough to respond? Houpt, et al. (SMP 212) Bayesian SIC 4 13o
6 Introduction Salience e To test architecture and stopping rule, without conflating them with workload capacity, factorially speed up and slow down the processing of each source of information. Houpt, et al. (SMP 212) Bayesian 5 1 C s I 3
7 Introduction Survivor Interaction Contrast ~ Indicates architecture and stopping rule. Houpt. et al (SMP 212) Bayemn SIC 6 I 3
8 Introduction Survivor Interaction Contrast ~ Indicates architecture and stopping rule. ~ The SIC is interaction between the salience manipulations. a Instead of just using the mean time, we use the survivor function: S(t) = Pr{T > t} = 1- F(t). SIC(t) = [SLL (t)- SLH (t)]- [SHL (t)- SHH (t)] Here, the subscripts indicate the salience of each source of information. Houpt. et al (SMP 212) Bayem n SIC 6 I 3
9 Introduction Survivor Interaction Contrast Serial Coactlve Townsend & Nozawa (1995) Schweickert, Giorgi ni & Dzhafarov (2) Dzhafarov, Schweickert & Sung (24) Houpt & Townsend (211) Houpt, et al (SMP 212) Bayes1an SIC 1 I 'YJ
10 Introduction Null Hypothesis Test Kolmogorov-Smirnov Test SIC Statistic if < "' <!> o = max,(f,(t)- F,(t)) " ~ u iii " "' "' Time Time li m Pr{.;No+ > x} ~ P r{.;no- N--+oo - > x} ~.- 2 X2 1 1 NKs ~ ---,----,-- NsJC ~ ---, ,------,----,- 1/m + 1/n 1/k +1/ i +1/m + 1/n Houpt, et al (SMP 212) Bayem n SIC a I 3
11 Introduction Parallel Serial Mean Model o+ o- Interaction Serial-OR Serial-AND././ Parallel-OR././ Para lie I-AND././ Coactive././././: Reject n u II hypothesis : Fail to reject null hypothesis Houpt, et al (SMP 212) Bayem n SIC 9 I 3
12 Introduction Shortcomings e Tests positive and negative deflections not SIC form.._ Requires two separate tests. e Only can gain evidence against a lack of positive or negative deflection. e Only get a yes/ no answer, not relative evidence. Houpt. et al (SMP 212) Bayem n SIC 1 I 3
13 Parametric Test Outline f) Parametric Test a Model a Simulation T tc; Houpt, et al (SMP 212) Bayes~an SIC 11 /3
14 Parametnc Test Mod el f(t): Density (PDF) F(t): Cumulative Distribution (CDF) Parallel-OR Houpt, et al (SMP 212) Bayem n S IC 12 I 3
15 Pa rametnc Test Mod el f(t): Density (PDF) F(t): Cumulative Distribution (CDF) Parallel-OR Parallel-AND f12(t) = f1(t)[l- F2(t)] + f2(t)[l- F1(t)] f12(t) = f1(t)f2(t) + f2(t)f1(t) Houpt, et al (SMP 212) Bayem n SIC 12 I 3
16 Pa rametnc Test Mod el f(t): Density (PDF) F(t): Cumulative Distribution (CDF) Parallel-OR Parallel-AND Serial-OR f12(t) = f1(t)[l- F2(t)] + f2(t)[l- F1(t)] f12(t) = f1(t)f2(t) + f2(t)f1(t) f12(t) = pf1(t) + (1 - p)f2(t) Houpt, et al (SMP 212) Bayem n SIC 12 I 3
17 Pa rametnc Test Mod el f(t): Density (PDF) F(t): Cumulative Distribution (CDF) Parallel-OR Parallel-AND Serial-OR Serial-AND f12(t) = f1(t)[l- F2(t)] + f2(t)[l- F1(t)] f12(t) = f1(t)f2(t) + f2(t)f1(t) f12(t) = pf1(t) + (1 - p)f2(t) f12(t) = f1(t) * f2(t) Houpt, et al (SMP 212) Bayem n SIC 12 I 3
18 Parametnc Test Mod el Ti;H rviq (v:'a 2 ) TJ rv Exponential(1) Ti;L rv IQ ( ~, a 2 ) VL rv 1(4,.1) a rv 1(4,.1) Houpt, et al (SMP 212) Bayem n S IC 13 I 3
19 Paramet nc Test Model Ti;H rviq ( v:'a ) 2 TJ rv Exponential(1) Ti;L rv IQ ( ~, a 2 ) VL rv 1(4,.1) a rv 1(4,.1) {d2 l-(tvi- a) 2 J qt;vi, a)= y2;t3 exp 2 t jczi (tv- ) l /a2 ( tv ) Fi(t;vi,a)= Vt ~-1 +exp[2a vi] - yt ~+1 [ Houpt, et al (SMP 212) Bayemn S IC 13 I 3
20 Parametric Test Simu lation Simulation Parameters T; = inf { t : X;( t) ;::: a} T; "' 1XJ (~, ~ ) v ; C7 2 a = 3 VH =. 3 (7 2 = 1 VL =. 1 p =.5 Houpt, et al (SMP 212) Bayes~an SIC
21 Parametnc Test Simu lation Simulation Results Serial Serial Parallel Parallel OR AND OR AND Coactive Serial-OR 1. Serial-AND.99.1 Parallel-OR.98.2 Parallel-AND 1. Coactive 1. Ho upt. et al (SMP 212) Bayemn SIC 1s I 3
22 Nonparametric Test Outline 8 Nonparametric Test If Model If Simulation ~I Houpt, et al. (SMP 212) Bayes ~a n SIC
23 Nonparametnc Test Mod el a Approach: Model the response time distributions a (as opposed to the RT generating process). a Assume each RT distribution is an independent sample from a Dirichlet process prior. a Compare the Bayes factor of each SIC form in the posterior relative to encom pass1 ng pnor. Ho upt. et al (SMP 212) Bayemn SIC 11 I 3
24 Nonparametnc Test Mod el a Approach: Model the response time distributions a (as opposed to the RT generating process). a Assume each RT distribution is an independent sample from a Dirichlet process prior. a Compare the Bayes factor of each SIC form in the posterior relative to encom pass1 ng pnor. a, "'DP(f3 ) RT1(i) "' o:,. Ho upt. et al (SMP 212) Bayemn SIC 11 I 3
25 Nonparametnc Test Simulation Simulation a Tested on same models as parametric-bayesian test (but with 1 rounds rather than 1).,. Used region of probabilistic equivalence ±.1 for SIC and ±.3 formic. Ho upt. et al (SMP 212) Bayem n SIC 18 I 3
26 Nonparametnc Test Simulation Simulation a Tested on same models as parametric-bayesian test (but with 1 rounds rather than 1).,. Used region of probabilistic equivalence ±.1 for SIC and ±.3 formic. Serial Serial Parallel Parallel OR AND OR AND Coactive Serial OR 1. Serial AND Parallel OR.93.7 Parallel AND 1. Coactive 1. Ho upt. et al (SMP 212) Bayem n SIC 18 I 3
27 Nonparam et nc Test Simula tion Example SICs Serial AND Parallel OR i5 (ij " i5 (ij "' I I " "' " I <D I Time Time Ho upt, et al (SMP 212) Bayemn SIC 19 I 3
28 Comparisons Among SIC Tests Outline Comparisons Among SIC Tests ct Simulation ct Application Houpt, et al. (SMP 212) BayeSia n SIC 2 I 3
29 Compari sons Among SIC Tests Simulation Serial OR Serial AND Parallel OR Parallel AND Coactive KS DP BUGS KS DP BUGS KS DP BUGS KS DP BUGS KS DP BUGS Serial OR Serial AND Parallel OR Parallel AND Coactive Houpt. et al (SMP 212) Bayem n SIC 21 I 3
30 Compari sons Among SIC Tests Simulation Serial Serial Parallel Parallel OR AND OR AND Coactive Serial OR KS DP Serial AND KS DP Parallel OR KS 1. DP Parallel AND KS 1. DP.4.96 Coactive KS.5.5 DP 1. Houpt. et al (SMP 212) Bayemn SIC 22 I 3
31 Compari sons Among SIC Tests Simula tion KS Test DPTest Serial OR ~+---~ { "' N ;; " I Coactiv ~r-----~~p---~ " ~ ' "' Para ll ~ AND ' ~ ~-+~+-----~----~~~ LO.B Ho upt, et al (SMP 212) Bayemn SIC 23 I 3
32 Compa risons Among SIC Tests App lication KS Test OR Task AND Task Participant VFJ6+ VFJ6 VFJ6+ VFJ *** *** *** *** *** *** *** *** *** *** *** * *** *** *** *** *** Ho upt. et al (SMP 212) Bayem n SIC 24 I 3
33 Compa risons Among SIC Tests App lication Parametric Bayes OR Task Serial Parallel OR AND OR AND Coactive Ho upt, et al (SMP 212) Bayem n SIC 2s I 3
34 Compa risons Among SIC Tests App lication Parametric Bayes AND Task Serial Parallel OR AND OR AND Coactive Ho upt, et al (SMP 212) Bayem n SIC 26 I 3
35 Compa risons Among SIC Tests App lication Non para metric Bayes OR Task Serial Parallel OR AND OR AND Coactive Np Ho upt. et al (SMP 212) Bayem n SIC 21 I 3
36 Compa risons Among SIC Tests App lication Non para metric Bayes AND Task Serial Parallel OR AND OR AND Coactive Np Ho upt. et al (SMP 212) Bayem n SIC 28 I 3
37 Conc lusion Outline ~I 8 Conclusion Houpt, et al. (SMP 212) Bayes ~a n SIC
38 Conclusion Overview e Developed parametric and nonparametic Bayesian tests for architecture and stopping rule. e Tested each of these approaches on both simulated data and experimental data. 11 Both did quite well on simul ated data. 11 Parametric conclusions diverged from NHST and nonparametric tests on human data. Houpt. et al (SMP 212) Bayem n SIC 3 I 3
39 Conclusion Overview e Developed parametric and nonparametic Bayesian tests for architecture and stopping rule. e Tested each of these approaches on both simulated data and experimental data. 11 Both did quite well on simul ated data. 11 Parametric conclusions diverged from NHST and nonparametric tests on human data. e What's next? 11 Parametric: Inclusion of base time and more stringent testing. 11 Nonparametric: Continuous (smooth) distributions in the prior. 11 Hierarchical models. Houpt. et al (SMP 212) Bayem n SIC 3 I 3
40 Conclusion Overview e Developed parametric and nonparametic Bayesian tests for architecture and stopping rule. e Tested each of these approaches on both simulated data and experimental data. 11 Both did quite well on simul ated data. 11 Parametric conclusions diverged from NHST and nonparametric tests on human data. e What's next? 11 Parametric: Inclusion of base time and more stringent testing. 11 Nonparametric: Continuous (smooth) distributions in the prior. 11 Hierarchical models. Thank you. Houpt. et al (SMP 212) Bayem n SIC 3 I 3
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