MSc Behavioural and Economic (or Data) Science
PS922: Issues in Psychological Science

Lecture 7c (Memory Models; MATLAB)
Matlab 3:
Models of Human Memory
Plan:
• Models of LTM and categorisation
• A unitary mathematical model of memory (“SIMPLE”)
• Can we account for data taken as evidence for
separate STM and LTM?
•Part 3 of MATLAB assignment
Assignment Part 3
Implement SIMPLE model of memory and explore its behaviour and
limitations
Calculate a serial position curve for a 10-item list: Assume items take 1 s to present,
and recall occurs 1 s after the last item – i.e., if dist contains the temporal distances
of each item at the time of retrieval: dist=[10:-1:1]
What happens to the curve if you add a retention interval?
E.g.: retint = 20; dist=[10:-1:1]+retint
What happens to the curve if you add a temporal gap around one item?
dist=[12:-1:8 6 4:-1:1]
What happens if you change the list length? What happens if you change the c
parameter? Illustrate the effects of both.
Reading
(if needed or useful; won’t be included in class tests
beyond lecture slides)
Nosofsky, R. M. (1992). Similarity scaling and cognitive
process models. Annual Review of Psychology, 43, 25-53.
Brown, G. D. A., Neath, I., & Chater, N. (2007). A temporal
ratio model of memory. Psychological Review, 114, 539-576.
Models of Categorisation and Memory
Exemplar and other models of categorisation
(models of long-term memory)
The SIMPLE model of memory
(apply same machinery to short-term memory)
Categorisation
Categorisation based on properties of objects
Given the colour and shape of a fruit, is it an apple or a banana?
Given the age and income of a US citizen, how likely is the person
to be Republican or Democrat?
Various possibilities:
Rules (if round and red, -> apple)
Prototypes (how similar to typical apple?)
Exemplar models (to be described)
Representational Assumptions 1
Items can be represented in terms of their values along dimensions
• For example, assume that for a US voter we know both age
and income:
Thus it is assumed that items can be
located in terms of their position within a
multidimensional psychological space.
Here we just assume the structure of the
space. But it can be obtained
independently by MDS (multidimensional
scaling) — constructing a space in which
confusable items have closer locations
(see reading)
(Notion of psychological space is crucial)
Representational Assumptions 2
We can then represent knowledge about the political
affiliation of previously encountered exemplars (voters):
Note that knowledge of political affiliation is represented as a
memory of previously encountered exemplars, not as rules or as
prototypes (i.e., the age and income of a “typical” Republican is not
explicitly represented)
Categorising a New Item
Suppose you know the age and income of a “new” person
but not their political affiliation. Will you place them in the
Democrat or Republican category?
Categorising a New Item
Suppose you know the age and income of a “new” person
but not their political affiliation. Will you place them in the
Democrat or Republican category?
Intuitively:
The new item is similar to Democrats (close in psychological space)
The new item is less similar to Republicans
Psychological Space and MDS
Here we are just assuming the structure of the
“psychological space”
But for more realistic applications people have used
multidimensional scaling (MDS) to construct a space in
which the distances between objects reflects their
psychological similarities (as obtained from, e.g., a
similarity-judgement task)
Similarity and Distance
We want items that are close in psychological space to be more similar
So we first need a measure of the distance (di,j) between any pair of items
(items i and j)
Euclidean
The distance between i and j is just
the Euclidean distance between
them in psychological space: di,j = 5
City Block
The distance between i and j is the sum
of the distance between them on
different dimensions: di,j = 7
Distance in Psychological Space
Here we will just use the city block metric
• City block metric generally works best when stimulus dimensions are
“separable” (can be analysed separately, e.g., the length and angle of a
line)
• Euclidean metric works better when stimulus dimensions are
“integral” (e.g., the brightness and saturation of a colour)
Weighting different dimensions
• It is often useful for a participant to pay more attention to a particular
dimension (e.g. income rather than age)
• This is like stretching out the space along one dimension and shrinking
it along others (although the actual underlying space doesn’t change)
Weighting Different Dimensions
For example:
Suppose we have two dimensions, m and n (e.g., dimension m might be
income, while dimension n is age)
We can then give different weights, wm and wn, to the dimensions
The weights must sum to 1: wm + wn = 1
We then weight the distance between i and j on each dimension so that, if
xi,m is the value of item i on dimension m; xi,n is the value of item i on
dimension n, etc., the distance between i and j becomes
di,j = wm|xi,m - xj,m| + wn |xi,n - xj,n|
(this is using the city block metric still)
Distance and Similarity
Now we have a good way of measuring the distance di,j between the
representations of two exemplars in psychological space
How do we turn this into a measure of the similarity between two locations?
Similarity must reduce as distance increases:
Note:
c is a free parameter that
governs the rate at which
similarity reduces with distance
Similarity and Category Membership
Now we can calculate the similarity of the new item
( ? ) to each previously known exemplar separately
We can calculate:
How similar the new item is to Democrats (summed similarity)
How similar the new item is to Republicans (summed similarity)
The Choice Rule
What is the probability of responding “Republican” (R) to item i ?
(summed similarity to Republican)
divided by
(summed similarity to Republicans plus summed similarity to Democrats)
Empirical Application
Exemplar models have proved very successful at
capturing human categorisation data
Artificial stimuli: angle and size of rectangles
Can predict relations between identification,
categorisation, recognition
Temporal Distinctiveness Models of Memory
Plan:
Describe SIMPLE model of memory
See how to implement it
Straightforward enough to interface with economic
models
Aims of the Model
A model of human memory retrieval: Applied to tasks such as serial
recall, free recall, probed recall
• Currently: Many computational models, but task-specific
• Ideal: Same model for many different memory tasks (cf. Ward,
Tan, Bhatarah)
Explore assumption that STM and LTM phenomena need different
models
• No STM-LTM distinction in model
• Apply to data previously taken as evidence for STM/LTM
distinction
• Some long-standing claims for unitary memory system, but
need models to explore the possibility
Key principles
SIMPLE (Scale-Invariant Memory, Perception,
and Learning)
Memory is temporally organised
Memories organised in terms of their temporal distances
Memory retrieval is like temporal discrimination (old claim)
Same principles of forgetting and retrieval apply over short and long
timescales (seconds to weeks)
No forgetting due to trace decay
All forgetting due to interference
Starting Point: Exemplar Models of LTM
Items are located within a multi-dimensional space
Items close to one another will be more similar
(exponential similarity-distance function)
Similar items: easy to categorise together
Similar items: hard to identify and discriminate
Need to consider closeness/similarity along a
temporal distance dimension as well?
Recency Matters
Distance and Discriminability
Consider two telegraph poles separated by 10 m, with the
nearest being 5 m away: Easily discriminable
| | | | | | | | |
But two telegraph poles separated by 10 m, with the nearest
being 55 m away: Difficult
| | | | | | | | |
Led to ratio-rule / temporal disciminability models of recency
effects in memory (Baddeley; Baddeley & Hitch; Bjork & Whitten;
Crowder; Tan & Ward)
Assumption: The confusability of two items in memory
depends on their relative temporal distances atof recall
The confusability of any two items is a function of the
ratio of their temporal distances: Si,j = (Ti/Tj)c.
For example: two items that occurred 4 and 5 s ago will
be more similar to one another (4/5)c than will two
items that occurred 1 and 2 s ago (1/2)c.
Note: The parameter c marks a difference from earlier
ratio-rule models
Confusability as Temporal Distance Ratios
Implementing similarity/confusability as a temporal
distance ratio effectively instantiates the telegraph
pole analogy:
Assumption: The discriminability of a memory item is
inversely related to that item’s similarity to all other items
In other words, items that are confusable with many others (in
terms of their temporal distances) will be less well recalled.
Assumption:
Serial Position Effects
Performance is best plotted as a function of position of last
rehearsal (e.g. Tan & Ward, 2000):
Unitary ratio model of serial position effects may be possible?
(note: primacy effects in normal population are at least partly
due to rehearsal).
Forgetting over Time
Data from Peterson & Peterson (1959)
Forgetting occurs due to increasing proactive interference from earlier items
No forgetting due to trace decay
Phonological Confusability Effects
After a short time interval, STM is reduced for confusable items
Items can be represented in the model in terms of position along both a
temporal and a “phonological confusability” dimension (should really be multi-
dimensional articulatory space but principle is the same)
(Other dimensions important; not included here)
Overview
Exemplar models provide a good account of human
categorisation behaviour
Addition of a temporal dimension allows exemplar
models to be extended to short-term memory data
Assignment Part 3
Implement SIMPLE and explore its behaviour and limitations
Calculate a serial position curve for a 10-item list: Assume items take 1 s to
present, and recall occurs 1 s after the last item – i.e., if dist contains the temporal
distances of each item at the time of retrieval: dist=[10:-1:1]
What happens to the curve if you add a retention interval?
E.g.: retint = 20; dist=[10:-1:1]+retint
What happens to the curve if you add a temporal gap around one item?
dist=[12:-1:8 6 4:-1:1]
What happens if you change the list length? What happens if you change the c
parameter? Illustrate the effects of both.
1) Create a vector of the temporal distances
2) Log transform the temporal distances
3) Calculate the summed similarity of each item’s temporal
distance to every other item’s temporal distance using:
4) Calculate the resulting discriminability of each item
5) Plot the serial position curve
Implementation Steps / Hints
where di,j is distance between items in log space
and c is a free parameter
clear all; clf
clf
c=5; retint=0;
dist=log([10:-1:1]+retint);


for i=1:length(dist)
eta=exp(-c*abs(dist(i)-dist));
discrim(i)=1/sum(eta);
end
%%Note: this could be vectorized for efficiency

plot(discrim,'-om')
axis([0 length(dist) 0 1])
xlabel('Serial Position','fontsize',14)
ylabel('Discriminability','fontsize',14)
set(gcf, 'color', 'white');
A Basis