A clarification of self-terminating versus exhaustive variances in serial and parallel models

Townsend, J. T. (2001). A clarification of self-terminating versus exhaustive variances in serial and parallel models. Perception & Psychophysics, 63(6), 1101-1106.

Abstract:
Comments on the original article by N. Donnelly et al (see record 1999-05611-008) which employs response times variances (in the form of standard deviations) in addition to mean response times. Variances can contribute greatly to model testing. However, there is a danger of perpetuating the kinds of logical and methodological errors that have long attended research employing mean response times alone. This commentary clarifies the theoretical and methodological issues, points out some new results concerning variability in search processes, and indicates how to resolve the global and specific challenges associated with identifying psychological mechanisms.

Note:
This paper discussed whether the measure of variance of RT can be used as an indicator to classify the processing architecture (parallel/ serial) and stopping rule (self-terminating/ exhaustive).

Stemberg (1966) proposed a serial exhaustive search in memory in which the RT increases as the number of to0be0remembered items increases. A rule-of-thumb criterion for serially mean RT slope of greater than 10 ms has been seriously problematic (Wolfe, 1998).

Donnelly, Found, and Muller(1999) used the standard deviation of RT to discriminate serial versus parallel processing. A serial self-terminating may predict a faster increasing variance of RT for target present trails than that for target absent trials. A limited parallel model may predict equally increasing of TRT variance in both conditions. However, Townsend did not agree with this argument.

He gives some examples showing that the var (ST) may be equal to var(EXH), and the var (RT could be keep constant, And Even in a unlimited capacity parallel model, the car(RT) decreases as a function of the load (set-size, n).

Though, the var(RT) could be a useful tool to diagnose the processing architecture, stopping rule, and capacity.

The mathematical computation is little difficult for me, especially for the equation 3 and 4. I should take a close look on these equations.

Parallel versus serial processing in visual search: Further evidence from subadditive effects of visual quality

Egeth, H., & Dagenbach, D. (1991). Parallel versus serial processing in visual search: Further evidence from subadditive effects of visual quality. Journal of Experimental Psychology: Human Perception and Performance, 17(2), 551-560.

Abstract:
The authors propose a diagnostic for distinguishing between serial and parallel processing in visual search; it is based on testing for subadditive effects of a within-trial visual quality manipulation on target-absent trials. It was evaluated in 2 experiments wherein parallel and serial processing might be expected on the basis of previous work and was then applied to a more uncertain situation in a 3rd experiment. The diagnostic indicates parallel processing of stimuli that differ from each other on a featural basis (Xs and Os) and canonical letters that differ in line arrangement (Ts and Ls) but serial processing when Ts and Ls are randomly rotated. These results form a coherent pattern that is understandable in terms of the literature on visual search, and thus they suggest that the diagnostic may be a useful addition to the methodology used to distinguish between serial and parallel processes.

Note:
This paper discussed the issue of parallel/ serial processing in visual search. Traditionally, researchers used the set size effect to define the processing architecture (e.g., the search time increases as a function of the number of distractors, showing a serial processing; a flat slope indicates the parallel processing). For the serial search processing, the ratio between the slope of target-absence and target-presence condition should be approximately 2: 1. Also, both parallel/ serial search occur in visual search at different stage. In the pre-attentive stage, visual search was processed in parallel to gain the simple features. Then, serial search is required for more details.
However, this measurement may be wrong at some time. Searching conjunction features can be parallel with limited capacity. A limited-capacity parallel model can also show the set-size effect (Townsend,1974).
In this paper, they manipulated the visual quality of letters and asked participants to search X among Os (Exp 1), rotated T among Ls (Exp 2), and canonical T among Ls (Exp 3). The manipulation allows different predictions for parallel and serial models in visual search with the target-absence (Table 1) and target0precsence (Appendix). For the target-absence trial, the sub-additive effect indicates the parallel processing. But, the violation of the sub-additive did not necessarily mean the serial processing.
Results showed the sub- additivity in Exp 1and 3 (suggesting parallel processing), and additivity in Exp 2 (suggesting serial processing). More interesting, findings from Exp 3 implied that searching conjunction features can be parallel according to target-distractor similarity, distractor homogeneity, and set-size.
The computation of the additivity by manipulating the information load, and visual quality is a direct test for parallel/ serial processing. The authors also mentioned a possibility of individual differences in visual search.

Wenger, M. J., & Gibson, B. S. (2004). Using Hazard Functions to Assess Changes in Processing Capacity in an Attentional Cuing Paradigm. Journal of Experimental Psychology: Human Perception and Performance, 30(4), 708-719.

Abstract:
Processing capacity-defined as the relative ability to perform mental work in a unit of time-is a critical construct in cognitive psychology and is central to theories of visual attention. The unambiguous use of the construct, experimentally and theoretically, has been hindered by both conceptual confusions and the use of measures that are at best only coarsely mapped to the construct. However, more than 25 years ago, J. T. Townsend and F. G. Ashby (1978) suggested that the hazard function on the response time (RT) distribution offered a number of conceptual advantages as a measure of capacity. The present study suggests that a set of statistical techniques, well-known outside the cognitive and perceptual literatures, offers the ability to perform hypothesis tests on RT-distribution hazard functions. These techniques are introduced, and their use is illustrated in application to data from the contingent attentional capture paradigm.

Note:
This paper is about the capacity measures by using Townsend’s approach. It is well-written and reviews a lot of details about the measurement.

Capacity is defined as the amount of work the observer is capable of performing within some unit of time.
Capacity may be non-causal (how much a system is capable of doing, or how effectively it can perform a task, in various experimental contextsà an aspect of system functioning that is affected by something else (such as stimulus organization) rather than being responsible for producing some result) or causal (aspect of capacity is affecting system functioning to produce a particular pattern of observable results)

They compared the using of mean RT with the using of overall processing time (they suggested the latter is better).
“Cumulating this instantaneous measure over the range of the RT distribution is thus readily interpretable in terms of how much work the observer was capable of doing in that experimental condition across all sampled responses at or before each value of t. Mean RT, in contrast, does not provide this information, giving only an expectation for how much time overall was required to complete the task. And the CDF gives only the unconditional probability that the task would be completed at or before some particular time.”
The hazard function may well describe the capacity. “It expresses a conditional probability—the likelihood of an observer completing the task in the next instant, given that the observer has not yet completed the task.”

They introduced the issue of ordering (complete/ partial ordering) in RT literature which is also related to the capacity measurement.
To examine if the RT from different conditions is ordered, two approaches are introduced. The fist one is graphic. To plot the ln{-ln[s(t)]} against the time (t) to see if there is any cross between different curves. If not, it is well ordered. The second method is to compute the Schoenfeld residual to see if all values are constant (beata coefficient = 0?). If it is, the distributions are ordered. (They introduced the proportional hazards model to analyze the RT data. It allowed us to compare two more hazard factions at once.)
(I think this part is the very crucial part in this paper!!)

Finally, fixed-effect partial likelihood model was used to test if the effect is significant in different conditions.

A Theory of Interactive Parallel Processing: New Capacity Measures and Predictions for a Response Time Inequality Series

Townsend, J. T., & Wenger, M. J. (2004). A Theory of Interactive Parallel Processing: New Capacity Measures and Predictions for a Response Time Inequality Series. Psychological Review, 111(4), 1003-1035.

Abstract:
The authors present a theory of stochastic interactive parallel processing with special emphasis on channel interactions and their relation to system capacity. The approach is based both on linear systems theory augmented with stochastic elements and decisional operators and on a metatheory of parallel channels' dependencies that incorporates standard independent and coactive parallel models as special cases. The metatheory is applied to OR and AND experimental paradigms, and the authors establish new theorems relating response time performance in these designs to earlier and novel issues. One notable outcome is the remarkable processing efficiency associated with linear parallel-channel systems that include mutually positive interactions. The results may offer insight into perceptual and cognitive configural-holistic processing systems.

Note:
This paper addressed that capacity may be affected by the dependency between the channels (cross-talk), and the decision operator (OR/ AND).

UCIP processing means that channels are independent (zero correlation). The dependency occurs when the channels interact with each other. A positive correlation may lead to a supercapacity processing; a negative correlation may lead to a limited capacity processing.

Decision operators may be OR or AND. The OR process means that observers respond yes when either target is presented (minimum reaction time, self-terminating, first-terminating). The AND process means that observers respond yes when both targets were presented.

The performance with OR operation should be compared with Miller inequality (supercapactiy), and with Grice inequality (limited capacity). Simulated data showed that channels with positive correlation may violate the Miller inequality, and those with negative correlation may violate the Grice inequality.

The performance with AND operation should be compared with Colonius-Vorberg (CV bound). Simulated data showed that channels with positive correlation may violate the upper CV bound, and those with negative correlation may violate the lower CV bound.

The coactivation model is not affected by the correlation between channels. Data in coactivation with positive, negative or zero correlation between channels violates the Miller inequality, but does not violate the Grice inequality.

When we measure the capacity limitation, we should consider the dependency between channels and the decision operator.

Consequences of base time for redundant signals experiments

Townsend, J. T., & Honey, C. J. (2007). Consequences of base time for redundant signals experiments. Journal of Mathematical Psychology, 51(4), 242-265.

Abstract:
We report analytical and computational investigations into the effects of base time on the diagnosticity of two popular theoretical tools in the redundant signals literature: (1) the race model inequality and (2) the capacity coefficient. We show analytically and without distributional assumptions that the presence of base time decreases the sensitivity of both of these measures to model violations. We further use simulations to investigate the statistical power model selection tools based on the race model inequality, both with and without base time. Base time decreases statistical power, and biases the race model test toward conservatism. The magnitude of this biasing effect increases as we increase the proportion of total reaction time variance contributed by base time. We marshal empirical evidence to suggest that the proportion of reaction time variance contributed by base time is relatively small, and that the effects of base time on the diagnosticity of our model-selection tools are therefore likely to be minor. However, uncertainty remains concerning the magnitude and even the definition of base time. Experimentalists should continue to be alert to situations in which base time may contribute a large proportion of the total reaction time variance.


Note:
This paper discussed the consequence of base time in the redundant-signal design (RSD). The reaction time in the redundant-signal condition (RS) is faster than that in the single-target (SS) condition, showing a RS facilitation effect. Jeffery Miller (1982) developed a race model inequality to test the effect.

Assumption:
(1) In separate channels, the evidence is accumulated toward completion. Different channels are processed in parallel.
(2) The rate of processing in each channel is invariant across SS and RS condition (so-called context invariance).
(3) Obeyed the minimum-time stopping rule.
(4) Each channel is processed independently.
1-3 à race model 1-4 a race model with independent channel

The base time is also called the residual time or non-decisional time (see Ratcliff’s diffusion model). The base time includes two components: the time for basic sensory system to transfer information to higher processing centers and the time to execute a motor response.

* The presence of base time serves to decrease the maximum sensitivity of the race model inequality to the detection of the race model inequality.
* The presence of base time should lead the capacity coefficient to underestimate the capacity.

To exclude the base time component in the RT data, the estimation will be more precise.