QUANTITATIVE MODELS OF MEMORY The value of explicit models –Precision of thinking –Explanatory power –Interval- or ratio-scale predictions –The macho factor Mathematical models of memory –Assumptions about representation What are the stimulus “attributes”? Are traces separate or integrated? Nature of item, order, associative info Local or distributed representation –Assumptions about process How is context utilized? Familiarity match or search? How does the cue “contact” memory?

Implementation of models –Encoding and retrieval mechanisms modeled as equations & flow charts –Model parameters (factors in the equations) can be fixed, or data-based –“solving” equations through simulations can produce predictions Evaluation of models –Elegance: assumptions should be psychologically plausible and direct –Goodness-of-Fit: the match between predicted and observed data –Efficiency: the model predicting the most phenomena with the fewest parameters wins –Distinctiveness: No other models would make that prediction A functional law, though an equation, is not a model! Power law of practice Hick’s law of uncertainty and RT

CAPSULE HISTORY OF MEMORY MODELS –Mathematical Learning Theory models specific tasks (e.g., paired-associate learning) Estes’ (58) Stimulus Sampling Theory –Comprehensive models emerge The Modal Model (Atkinson & Shiffrin, 68); short-term and long-term episodic HAM (Anderson & Bower, 72); list learning and sentence memory –“Global” models appear Wider range of tasks and processes All list items and associations are relevant at retrieval –Distributed-network models of association developed The PDP revolution

Search of Associative Memory (Raaihmakers & Shiffrin, 1981) Designed for recall and recognition of word lists and associations Representation and encoding –Episodic study increases memory trace strength (image) of association between the studied item and.. the “list context” (a) (encoding specificity) Other items in the rehearsal set (b) (relational processing) Itself as a potential cue (c) (item distinctiveness) –Parameters (a,b,c) determine mean rate of increase in strength for item W i with rehearsal time t among n other items S(C,W i ) = at i /n S(W i W h ) = bt ih /n S(W i W i ) = ct i /n

SAM (Cont’d) Retrieval: recognition task –Given item W i as cue, calculate global familiarity –For each item in memory W k : F(C,W k ) = S(C,W k ) x S(W i,W k ) –Sum over all list items (k=1 to N)

Recognition in SAM (cont’d) –If summed familiarity exceeds criterion, item is recognized as old Associative recognition –AB pairs strengthen A,B images as above –At test, pair familiarity obtained by: F(A) x F(B) Recall –Context serves as cue to sample item(s): Ps(W i |C) = S(C,W i )_ Σ[S(C,W k )] then, if strength allows “recovery”, item can serve as part of the cue: Ps(W i |C,W h ) = _S(C,W i ) x S(W h,W i )__ Σ[S(C,W k ) x S(W h,W k )]

SAM and Performance Effects of encoding parameters on performance: –Context (a) improves recovery, no effect on sampling in recall no effect on recognition. Why? –Interitem associations (b): increases familiarity of targets (how?) but not distractors (why not?), so improves recognition improves recovery, and sampling selectivity, so improves recall –Self-strength (c): Item familiarity increased, no effect on distractors, so recognition improves Increases “self-sampling” and so recall (may be?) impaired (cf. part-list cues)

SAM and Performance (cont’d) Effects of “classic” variables: –Study time: Associative and item strengths increased, so recall and recognition improve –Retention interval: Memory images are permanent, so all forgetting is retrieval failure through context changes –Serial position effects: Smaller rehearsal set for first items, so stronger strengths (see encoding) and primacy effect Recency? –Word Frequency: HF words with higher pre-existing associations (d) and easier list associations (b):

Troubles for SAM The “mirror effect” –In mixed-frequency lists, LF words show both higher hits and lower FA’s –Why is this a problem? –How does REM solve the problem? The “list strength” effect –In mixed-study-time lists, recall of short- study items should be worse compared to pure-study-time lists. –Why should this happen in SAM? –Well, it doesn’t –How does REM solve the problem? In Summary: –Models are powerful, but not unfalsifiable –Mix of plausible, less plausible assumptions about representation & process –Sometimes “transparent,” sometimes opaque –Remains relatively unconnected with broader field of memory and cognition