Stimulus Sampling Theory Assignment:

 

1)   Implement the model on p. 31 of Estes & Burke, 1953 using Equation 5 from that paper. stim_sampling.m should help.

a)    The model should have the following properties.

i)     Assume that there are 2 sets of relevant elements, S1 and S2.

ii)   Assume that there are 100 of each element type, i.e., N1 = N2 = 100.

iii) Assume that the probability of sampling an element from S1 is .3 (q1 = .3, this should read theta subscript 1) and the probability of sampling an element from S2 is .1 (q2 = .1).

iv) Assume 50 trials.

b)   Plot PA(n) against n as in the solid line in the figure below. Note that PA(n) is the probability of an A response AFTER the nth trial.

2)   Implement the same model, but instead of using Equation 5, actually simulate the process.

a)    The process should proceed as follows.

i)     On trial n = 0, all elements should start out associated with not-A.

ii)   On each trial, elements from S1 and S2 are sampled according to q1 and q2.

iii) The probability of Response A is given by the ratio of active elements associated with A to the ratio of all active elements (does this look like the Luce choice rule?).

iv) All active elements then become associated with A.

v)   All elements become inactive.

vi) Go back to b 50 times.

b)   Plot PA(n) against n as in the broken red line in the figure below.

c)    A thought question (donŐt turn this in).

i)     Now set N1 = N2 = 5.  You might be getting errors when you run your program.

ii)   Why?

iii) Does this mean the model is ŇbadÓ?  That is, is the problem in the psychological assumption or in the implementation?

3)   Turn in 1.b and 2.b plotted on top of each other. To plot two graphs on top of each other, type 'hold on' inbetween the two plot commands. Type 'hold off' to clear the figure for the next plot.