University of Pennsylvania ScholarlyCommons IRCS Technical Reports Series Institute for Research in Cognitive Science January 2001 Separate modifiability, mental modules, and the use of pure and composite measures to reveal them Saul Sternberg University of Pennsylvania, [email protected] Follow this and additional works at: https://repository.upenn.edu/ircs_reports Sternberg, Saul, "Separate modifiability, mental modules, and the use of pure and composite measures to reveal them" (2001). IRCS Technical Reports Series. 25. https://repository.upenn.edu/ircs_reports/25 University of Pennsylvania Institute for Research in Cognitive Science Technical Report No. IRCS-01-08. This paper is posted at ScholarlyCommons. https://repository.upenn.edu/ircs_reports/25 For more information, please contact [email protected]. Separate modifiability, mental modules, and the use of pure and composite measures to reveal them Abstract How can we divide a complex mental process into meaningful parts? In this paper, I explore an approach in which processes are divided into parts that are modular in the sense of being separately modifiable. Evidence for separate modifiability is provided by an instance of selective influence: two factors F and G (usually experimental manipulations) such that part A is influenced by F but invariant with respect to G, while part B is influenced by G but invariant with respect to F. Such evidence also indicates that the modules are functionally distinct. If we have pure measures MA and MB, each of which reflects only one of the parts, we need to show that MA is influenced by F but not G, while MB is influenced by G but not F. If we have only a composite measure MAB of the entire process, we usually also need to confirm a combination rule for how the parts contribute to MAB. I present a taxonomy of separate-modifiability methods, discuss their inferential logic, and describe several examples in each category. The three categories involve measures that are derived pure (based on different transformations of the same data; example: separation of sensory and decision processes by signal detection theory), direct pure (based on different data; example: selective effects of adaptation on spatial-frequency thresholds), and composite (examples: the multiplicative-factor method for the analysis of response rate; the additive-factor method for the analysis of reaction time). Six of the examples concern behavioral measures and functional processes, while four concern brain measures and neural processes. They have been chosen for their interest and importance; their diversity of measures, species, and combination rules; their illustration of different ways of thinking about data; the questions they suggest about possibilities and limitations of the separate-modifiability approach; and the case they make for the fruitfulness of searching for mental modules. Comments University of Pennsylvania Institute for Research in Cognitive Science Technical Report No. IRCS-01-08. This technical report is available at ScholarlyCommons: https://repository.upenn.edu/ircs_reports/25 Separate modifiability, mental modules, and the use of pure and composite measures to reveal them Saul Sternberg University of Pennsylvania Reprinted from Acta Psychologica, 106, 147-246, 2001, with permission from Elsevier Science. This pdf file contains: Table of Contents: Text (page 143) Table of Contents: Appendices (page 144) List of Examples (page 145) Some Features of the Examples (page 145) Lists of Tables, Figures, and Equations (page 146) The Article (pages 147-246). Note that page numbers for the article in the pdf file (147 - 246) match the page numbers for the article as printed. Separate Modifiability, Mental Modules, and the Use of Pure and Composite Measures to Reveal Them Contents (Par t 1: TEXT) 148 1. Introduction 1.1 Antecedents 1.2 Notation . 1.3 Twofold partition as an initial step in understanding a complex process 1.4 Processes, measures, factors, and selective influence 1.5 Statistical issues 1.6 Process decomposition versus task comparison 1.7 Relevance of brain measurement to process decomposition 1.8 Organization of the paper 155 2. Pure measures: Definitions and inferential logic 2.1 Selective influence of factors on processes and their measures 2.2 Hypothesis, prediction, and inference for pure measures 2.3 Why all four properties are important 158 3. Composite measures: Definitions and inferential logic 3.1 Composite measures based on summation 3.1.1. Illustration: The Additive-Factor Method. 3.2 Composite measures based on multiplication 3.3 Factor ial exper iments 163 4. Introduction to three examples of inference based on derived pure measures 164 5. Isolation of a timing module in the rat (Example 1) 5.1 Two kinds of elaboration of the two-module analysis 5.2 Comments 167 6. Parallel neural modules revealed by the lateralized-readiness potential (Example 2) 6.1 Comments 172 7. Separation of sensory and decision processes by signal detection theory (Example 3) 7.1 Why has SDT failed in this respect? 7.2 An approximation to full modularity of sensory and decision processes when reinforcer ratio is controlled 7.3 Comments 178 8. Introduction to three examples of inference based on direct pure measures 179 9. Evidence for modular spatial-frequency analyz ers from selective adaptation (Example 4) 9.1 Comments 182 10. Evidence from individual neurons for temporally-delimited (serial) neural modules (Example 5) 10.1 Estimation of stage durations 10.2 Relation of these findings to the demonstration of separate modifiability 10.3 Comments 186 11. Evidence from fMRI for modular neural processes implemented by anatomically delimited processors (Example 6) 11.1 Comments 190 12. Introduction to four examples of inference based on composite measures 191 13. Evidence for modular spatial-frequency analyz ers from ‘probability summation’ at threshold (Example 7) 13.1 Justification of a multiplicative combination rule for non-detection probability 13.2 Three tests of the joint hypothesis 13.3 Comments 196 14. Evidence from amplitude of the event-related potential for modular neural processes (Example 8) 14.1 The additive-amplitude method 14.2 Application of the additive-amplitude method to word classification 14.3 Comments 200 15. Multiplicative combination rule for response rate (Example 9) 15.1 A plausible systematic deviation from additivity measured by multiplicative interaction of scaled factor levels 15.2 Comments 206 16. Reaction time as a composite measure: Selective effects of sleep deprivation (Example 10) 16.1 Comments 210 17. General Discussion Separate Modifiability, Mental Modules, and the Use of Pure and Composite Measures to Reveal Them Contents (Par t 2: APPENDICES, GLOSSARY, ACKNOWLEDGEMENTS, REFERENCES) . 213 Appendix A1. Process decomposition versus task comparison A1.1 Introduction A1.2 Qualitative task comparison A1.2.1 Behavioral studies of memory. A1.2.2 Effects of sleep deprivation A1.2.3 Task-specific effects of localized brain lesions. A1.2.4 Task-specific effects on localized brain activation. A1.3 Quantitative task comparison: Subtraction and division methods A1.3.1 Donders’ subtraction method. A1.3.2 Jacoby’s division method. A1.3.3 Derived pure measures from subtraction and division methods. 221 Appendix A2. Considerations in the choice of factors A2.1 Unitary factors and qualitative process invariance A2.2 Manipulated versus selective factors A2.3 Inferential logic when hypotheses about modules specify the factors 223 Appendix A3. Composite measures, combination rules, and stochastic independence A3.1 Measures, combination rules, and plausibility A3.2 Multiplication as combination rule: Implications for data analysis of the zero-correlation requirement A3.3 Stochastic independence of process contributions as further evidence of modularity 226 Appendix A6. Evidence for neural and functional modules that correspond 228 Appendix A7. Details of the analysis of brightness discrimination by pig eons A7.1 Support for the equal-var iance Gaussian detection model A7.2 Evaluation of an alternative measure of the decision process 229 Appendix A9. Factorial experiments and multiple-level factors with pure measures A9.1 Advantages of a factor ial design. A9.2 Advantages of multiple factor levels. 231 Appendix A10. Inferring neural processing stages from single-unit recordings A10.1 Classification of neurons A10.2 Combining activation times over neurons A10.3 Effects of stimulus and response factors on stage durations 233 Appendix A11. fMRI and modular processes: Requirements and statistical issues A11.1 Requirements for a process-decomposition study A11.2 Statistical issues 235 Appendix A13. Fitting and testing one-channel and two-channel models of detection 236 Appendix A15. Numerical scaling of factor levels for multiplicative and hybrid combination rules 237 Appendix A16. Processing stages as modules A16.1 Multiplicative combination rule for the proportion of response omissions A16.2 What is a ‘stage’? A16.3 Additive effects of factors on mean reaction time: Alternative inter pretations 240 ACKNOWLEDGEMENTS 241 GLOSSARY 242 REFERENCES Examples (Examples 11 and 12 are not numbered in the text.) Pa ges Ex.# Example TEXT APPX 1 Isolation of a timing module in the rat 164 — 2 Parallel neural modules revealed by the lateralized-readiness potential 167 — 3 Separation of sensory and decision processes by signal detection theory 172 228 4 Evidence for modular spatial-frequency analyzers from selective adaptation 179 229 5 Evidence from