702 C OHEN ,S ANBORN , AND S HIFFRIN

visual dimension, respectively. The psychological evalua- was nearly perfect agreement between the models cho- tion of A i and V j ,a i and v j , respectively, are assumed to lie sen by PV for both group and individual analysis and the between 0, a definite mismatch, and 1, a definite match. generating models (see Table 2). This agreement lends Whereas the FLMP assumes that the probability of a / da/ more weight to using recovery of the generating model as response is given by a Bayesian combination of a i and v j ,

a measure of model selection accuracy.

p ( / / da | , AV i j ) =

av ij

In summary, the use of both average and individual data

av ij +− ( 1 a i ) ( 1 − v j )

, (3) produces good model selection results, with the following

exceptions. When the zero criterion is used, average data the LIM assumes that these two sources of information should be used for low trials per condition. When the op- are averaged,

timal criterion is used, individual data should be used for low trials per condition and individuals per experiment.

p ( / / da | , AV i j ) =

2 Models of Categorization: Generalized Context Model and Prototype Model

Details of the uninformed and informed parameter sam- In a typical categorization task, an individual is asked to pling methods are given in Appendix B. Again, because classify a series of stimuli that vary along multiple feature

the data of interest when uninformed and informed pa- dimensions. The individual receives corrective feedback rameters were used were very similar, only the results after each trial. Two categorization models are considered using the uninformed parameters are discussed.

here: the generalized context model (GCM; Nosofsky, For individual data, in general, model mimicry is low; 1986) and the prototype model (Reed, 1972). Both mod-

both models favor their own data, and the optimal crite- els assume that the stimuli are represented by points in a rion is well approximated by a zero criterion. The excep- psychological M-dimensional space. Let x im

be the psy- tion to this pattern is at very low trials per condition, chological value of stimulus i on dimension m. Then, the

where much of the LIM data are better accounted for psychological distance between stimulus i and j is by the FLMP. The FLMP advantage in this situation is

due to its greater flexibility in fitting extreme data. For 2

mM ∑ ∈ (

w m x im − x jm , (5) the FLMP, setting either parameter to one or zero pro-

d ij =

duces a response probability of one or zero, but for the where the w s are parameters representing the attention LIM model, both parameters need to be set to extreme

weight given to dimension m. Each w m $ 0 and the w values to produce extreme response probabilities. For

m s sum to 1. The similarity between stimulus i and j is an

all-or-none data with few trials per condition, the FLMP exponentially decreasing function of distance in the space is much better at fitting the resulting data. When average (Shepard, 1987), data are used, the advantage of the FLMP with low trials all but disappears.

s ij = exp −⋅ cd ij , (6) The proportion incorrect summary graphs for unin-

formed parameters are displayed in Figure 3. The left and where c is an overall sensitivity parameter. In a two- right columns of Figure 3 represent the proportion of in-

category experiment, the GCM assumes that the probability correct model selections when the optimal criterion and that stimulus i is classified into Category A is given by the the zero (straightforward log likelihood), respectively, are summed similarity of stimulus i to all stored exemplars of used. The model selection errors generated by the greater Category A divided by the summed similarity of stimulus i complexity of the FLMP when low trials per condition to all stored exemplars from both Categories A and B, are used are reflected in the zero-criterion, individual

s data graph. If a zero criterion is used, model mimicry is

∑ ia

= a ∈ A greatly reduced at low trials per condition by using aver-

a ∑ s age data. Utilizing the optimal cutoff greatly reduces the + A b ∑ s

errors associated with using individual data at low trials per condition and, indeed, produces a slight advantage for The prototype model assumes that category decisions are using individual data at very low trials per condition and based on the relative similarity of the test stimulus to the individuals per experiment (where model selection perfor- single central category prototype from each category. Let

mance is particularly bad). For moderate to high trials per P A and P B be the prototypes (usually the mean category condition and individuals per experiment, however, model member) for Categories A and B, respectively. Then, mimicry is similar (and very low) when either individual

s iP or average data are used.

A + s iP B per individual and 34 subjects. In Table 1, the group analy-

A . (8)

s iP

PV was used only for the case with two observations

To account for the finding that subjects tended to re- sis showed an advantage over the individual analysis in spond more deterministically than is predicted by the GCM predicting new data from the same set of simulated sub- (Ashby & Gott, 1988), Ashby and Maddox (1993) proposed jects, giving more evidence that group analysis is useful

a version of the GCM that allows the model to predict more when there are few trials per condition. In addition, there or less response determinism than is predicted by the base-

702 C OHEN ,S ANBORN , AND S HIFFRIN