Background
SIMPLE (Scale Invariant Memory and Perceptual Learning) is described more completely in a variety of papers (e.g., Brown, Neath, & Chater, 2002; Neath & Brown, 2006).
This version implements an account of absolute identification described by Neath, Brown, McCormack, Chater, & Freeman (2006).
A common assumption in cognitive psychology is that items are represented in memory as values in multidimensional space, with the importance of a particular dimension varying with each situation. In Murdock's (1960) formulation, the relevant dimension for most lists of items was position whereas in Neath's (1993) model, the dimension is time. Note that items can also vary along other dimensions, such as frequency, length, and so forth. The major difference between SIMPLE and Neath's (1993) model is that the latter is a global distinctiveness model: the computation of distinctiveness includes all items equally. SIMPLE, on the other hand, is a local distinctiveness model in that closer items affect distinctiveness more than do distant items.
SIMPLE typically assumes that the memory representation is a log transform of the physical item. In this version, however, we use a power function such that the items are raised to the power p.
The similarity, η, between two memory representations, Mi and Mj is given by
The parameter c is the main free parameter in SIMPLE and affects the rate at which similarity reduces with psychological distance. The parameter a affects the similarity-distance function determines, e.g., if a = 1.0 the function relating similarity to distance is exponential whereas it is Gaussian when a = 2.0.
The probability of responding Rj given a stimulus Si is given by:
where n is the number of items in the set, ηi,j is the similarity between items i and j in memory.
Instructions
Click once on the "Run the Program" button. You will see a screen that looks like the following (the version number and date that your copy of the program was compiled may be different):
Simple 1.0 3 April 2004 12:31 EST Enter the number of items [3-20, 9] ?
This shows you that the simulation can have between 3 and 20 items in the list, and the default value is 9. If you choose the default values, you'll replicate the simulation that fit the Isolate condition in Experiment 1 of Neath et al. (in press).
The rest of the parameters are shown below:
Enter c [0-100, 6.0] Enter p [0-1.0, 0.399] Enter a [0-?, 0.5] Enter each item in increasing order WARNING: The program does not check to see if the items really are in increasing order. If they aren't, the output will not be valid. Enter the value of item 1 [0.0 to 10000.0, 350.0] ?
A separate window will appear with the results when the simulation is over. You can copy and paste any information from this window to another application (e.g., a spreadsheet). Sample output looks like the following:
Simple 1.0 14 April 2005 13:55 EST Caution: Simulation is accurate enough for demonstration purposes but is *** NOT *** sufficiently accurate for scientific research. Number of items = 9 c = 6.0 p = 0.399 a = 0.5 The input values: 350.0000 367.5000 385.9000 405.2000 469.0000 543.0000 570.1000 598.6000 628.5000 The proabilities before iterative normalization: 0.4964 0.2696 0.1445 0.0766 0.0106 0.0013 0.0006 0.0003 0.0001 0.2252 0.4147 0.2223 0.1178 0.0163 0.0020 0.0010 0.0005 0.0002 0.1190 0.2191 0.4087 0.2166 0.0300 0.0037 0.0018 0.0008 0.0004 0.0722 0.1329 0.2479 0.4679 0.0647 0.0079 0.0038 0.0018 0.0009 0.0143 0.0263 0.0490 0.0925 0.6689 0.0818 0.0396 0.0188 0.0089 0.0013 0.0024 0.0045 0.0086 0.0618 0.5056 0.2446 0.1165 0.0547 0.0006 0.0010 0.0019 0.0036 0.0262 0.2141 0.4427 0.2108 0.0990 0.0003 0.0005 0.0009 0.0018 0.0127 0.1042 0.2153 0.4520 0.2123 0.0002 0.0003 0.0005 0.0010 0.0073 0.0595 0.1230 0.2583 0.5499 The proabilities after iterative normalization: 0.5279 0.2479 0.1314 0.0773 0.0131 0.0014 0.0006 0.0003 0.0002 0.2479 0.3949 0.2094 0.1232 0.0208 0.0022 0.0009 0.0005 0.0002 0.1315 0.2094 0.3863 0.2273 0.0384 0.0040 0.0017 0.0008 0.0005 0.0774 0.1233 0.2274 0.4766 0.0806 0.0083 0.0036 0.0018 0.0010 0.0132 0.0209 0.0386 0.0810 0.7157 0.0741 0.0324 0.0156 0.0085 0.0014 0.0022 0.0040 0.0084 0.0745 0.5160 0.2254 0.1088 0.0593 0.0006 0.0010 0.0018 0.0037 0.0326 0.2255 0.4209 0.2032 0.1108 0.0003 0.0005 0.0008 0.0018 0.0157 0.1089 0.2033 0.4327 0.2359 0.0002 0.0003 0.0005 0.0010 0.0086 0.0594 0.1109 0.2360 0.5833 The predicted performance: 0.5279 0.3949 0.3863 0.4766 0.7157 0.5160 0.4209 0.4327 0.5833
The values may be slightly different in the third or fourth decimal place from those reported in the paper, as this version does only 20 iterations of normalizing.
Suggested Simulations
What follows are suggestions for simulations to run and how to run them.
Simulation 1
Check that the model produces the results described in Neath et al. (2006). Here is a table with the parameter settings used in each Experiment:
| Parameter | Exp. 1 | Exp. 2 | Exp. 3 | Exp. 4 |
| c | 6.000 | 3.433 | 5.569 | 5.742 |
| p | 0.399 | 0.435 | 0.269 | 0.202 |
| a | 0.500 | 0.660 | 1.013 | 0.971 |
