TODAM2 {JoF}

Modeling Judgments of Frequency with TODAM 2

Description

Modeling Judgments of Frequency with TODAM 2

Usage

TODAM2(x, y, ..., sqc, gamma = 1, alpha = 1)

Arguments

x

input handled by TODAM 2. Normal distributed inputs with mean = 0 and sd = 1 / n are allowed. This representation enables discrimination and similarity between different items. See vignette for details.

y

another input handled by TODAM 2. At least two inputs are needed for the simulation.

...

other inputs handled by TODAM 2.

sqc

sequence of the different objects. Each input gets an ascending number. x gets the value 1, y gets the value 2, ... gets the value 3 and so on. The argument sqc = c(1, 2, 3, 2) means: first input x is processed, second input y is processed followed by processing input number three and fourth, th input y is used again. So sqc contains the frequency information too. In c(1, 2, 3, 2), x and the third input are presented once. The input y is presented twice.

gamma

is the atttention- or learningparameter. Values between 0 and 1 are allowed. 1 represents perfect learning. If gamma iis a vector, each input could be handled differently. So gamma = c(.5, .6, 1) means, the third input is stored correctly and betther than the y better than first input x).

alpha

represents the decay. If alpha = 1, the complete memory vector is used (and no forgetting takes place). If alpha is an numeric Vector e. g. alpha = c(.8, .9, 1), the memory vector is weighted. The memory for the first input is weaker than the second than the third.

Details

In the original publication TODAM 2 is more complex and has more parameters. Especially the design for the input is a concatenation between item and context. The normal distributed input has a mean = 0 and sd = 1/n. A pragmatic solution to make the models input comparable is to use a binary input like in PASS. There is no explicit argument for noise.

Convolution:

F_{i}^{2} = \sum_{i=1} f_{i} * f_{m-i+1} and m = 2n - 1

Memory:

M_{t} = \alpha M_{t-1} + \gamma F_{t}^{2}

Correlation

R_{m} = \sum_{(i;j)\in S(m)} F_{t}^{2} there S(m)(i;j)| -(n-1)/2 \le i,j \le (n-1)/2 and i-j = m

References

Murdock, B. B., Smith, D., & Bai, J. (2001). Judgments of frequency and recency in a distributed memory model. Journal of Mathematical Psychology, 45, 564–602. https://doi.org/10.1006/jmps.2000.1339

Examples

o1 <- c(-0.27, -0.24, -0.24, 0.75)
o2 <- c(-0.06, -0.55,  0.66, -0.06)
o3 <- c(0.04,  0.57, -0.65,  0.04)
o4 <- c(0.73, -0.39, -0.20, -0.14)
TODAM2(o1, o2, o3, o4, gamma = rep(c(0.7, 0.8), 5),
alpha = 0.95, sqc = rep(1:4, 4:1))