A Diffusion Model Analysis of the Effects of Aging on Letter Discrimination

Investigations of age-related differences in cognitive tasks have often revealed a pattern of declining performance with advancing age. The most dominant hypothesis has been the generalized slowing hypothesis, which states that all information processing is similarly affected by age (e.g., Birren, 1965; Brinley, 1965; Cerella, 1985, 1990, 1991, 1994; Fisk & Warr, 1996; Salthouse, 1985, 1996; Salthouse, Kausler, & Saults, 1988). For some researchers, the general slowing hypothesis has been replaced by one that argues that different task domains show different degrees of slowing, for example, verbal versus spatial domains (see Allen, Ashcraft, & Weber, 1992; Allen, Madden, Weber, & Groth, 1993; Cerella, 1985, 1994; Hartley, 1992; Hertzog, 1992; Lima, Hale, & Myerson, 1991; Madden, 1989; Madden, Pierce, & Allen, 1992; Myerson, Ferraro, Hale, & Lima, 1992; Myerson, Wagstaff, & Hale, 1994; Perfect, 1994; Sliwinski & Hall, 1998). Whether general or domain specific, the slowing hypothesis has been favored by many cognitive aging researchers because it provides a relatively simple and intuitively appealing explanation of age-related decrements across a variety of laboratory tasks and everyday behaviors. A major source of support for the slowing hypothesis is the empirical regularity observed in Brinley functions. In a Brinley function, older subjects’ response times are plotted against young subjects’ response times and the result is almost always a straight line with a slope in the range of about 1.5 to 2.5 (Brinley, 1965; Cerella, 1985, 1991, 1994; Faust, Balota, Spieler, & Ferraro, 1999; Fisher & Glaser, 1996; Fisk & Fisher, 1994; Hale & Jansen, 1994; Hale, Myerson, & Wagstaff, 1987; Maylor & Rabbitt, 1994; McDowd & Craik, 1988; Myerson & Hale, 1993; Myerson, Hale, Wagstaff, Poon, & Smith, 1990; Myerson et al., 1994; Nebes & Madden, 1988; Perfect, 1994; Salthouse, 1991, chap. 8; Salthouse & Somberg, 1982; G.A. Smith, Poon, Hale, & Myerson, 1988; Spieler, Balota, & Faust, 1996). The slope is taken to be a multiplicative factor that indicates the amount of slowing for the older adults relative to the young adults. The slowing hypothesis has been challenged, however, on several grounds. First, Fisher and Glaser (1996) have shown that models that distinguish among different components of cognitive processing with different slowing rates can give rise to the regularity of slopes greater than one found in Brinley functions (e.g., Fisher & Glaser, 1996). Second, there has been a new interpretation of what Brinley functions represent. Ratcliff, Spieler, and McKoon (2000) showed that the slope of a Brinley function measures how slow older adults are relative to young adults only under limited types of models. More generally, Brinley functions should be viewed as plots of quantiles against quantiles of the distributions of mean response times across experimental conditions, where the quantiles of a distribution are the points that divide the total frequency in the distribution into parts (e.g., the three quartile points divide the distribution into quarters, the .25, .50, and .75 quantiles). As long as the distributions of mean response times have at least approximately the same shape for the older adults as for the young adults, two results follow: First, the Brinley function is linear, and second, the function’s slope is the ratio of the standard deviations of the older subjects’ and the young subjects’ mean response times. Myerson, Adams, Hale, and Jenkins (2003) claimed that the slope is not the ratio of the standard deviations, rather it is the ratio of the standard deviations multiplied by the correlation coefficient, but this is not correct. The analysis of Brinley functions in terms of quantiles is not a special case of linear regression, as we discuss below. Also, as Ratcliff, Spieler, and McKoon (2003) pointed out, the slope of a Brinley function should not be estimated from linear regression because there is variability (i.e., measurement error) in both the older subjects’ mean response times and the young subjects’ mean response times (see also Draper & Smith, 1998). Another important point made by Ratcliff et al. (2000) is that the data on which Brinley function analyses are based, mean response times for correct responses, are only a small subset of the data that need to be addressed. Developing a theory based only on mean response time guarantees that the theory will be wrong (or at least inadequate) when applied to other aspects of the data. Dealing with all of the aspects of response time data, namely, correct and error response times and their relative speeds, the shapes of response time distributions for both correct and error responses, and accuracy values, requires an explicit, fully specified quantitative model. Moreover, given such a model, the Brinley function regularity in slope can be produced in multiple ways. For Ratcliff’s diffusion model (Ratcliff, 1978, 1981, 1985, 1988; Ratcliff, Gomez, & McKoon, in press; Ratcliff & Rouder, 1998, 2000; Ratcliff, Van Zandt, & McKoon, 1999), for example, Ratcliff et al. (2000) showed that a slope in the range of 1.5 to 2.5 can be due to, among other possibilities, older subjects adopting more conservative response criteria than young subjects, older subjects accumulating stimulus information more slowly than young subjects, or older subjects having slower response execution processes than young subjects. Crucially, within the framework of the diffusion model (and almost certainly other sequential sampling models, see Ratcliff & Smith, in press), the effects of aging on response times do not map onto standard slowing hypotheses. Ratcliff’s diffusion model is attractive because it has been successful in accounting for the data from a variety of two-choice response time tasks and because it allows response time data to be analyzed in terms of the components of processing required by a cognitive task. In the aging research domain, Ratcliff, Thapar, and McKoon (2001) applied the model to two visual signal detection tasks, a numerosity judgment task and a distance judgment task. In the numerosity judgment task, subjects viewed an array of asterisks on a computer screen and were asked to decide whether the number of asterisks presented in the display was high or low. In the distance judgment task, subjects viewed two dots and were asked to decide whether the distance between the two dots was large or small. In both tasks, the measures of interest were accuracy, response times for correct and error responses, and the shapes of the response time distributions. For all of these measures, the model gave a good account. The main components of processing into which the model divides the decision process are the quality of the information from a stimulus that drives the decision process, the variability in the quality of the information, the criterial boundaries on the amount of information that must be accumulated in order for a decision to be made, and the nondecisional (encoding and response execution) parts of response time. Applying the model to the numerosity and distance judgment tasks, Ratcliff et al. (2001) identified three main components of comparison between older adults and young adults. First, the older adults set more conservative criteria than the young adults, accumulating more information before making a response. Second, the nondecisional components of processing were slower for the older adults. Third, and most important, the quality of the information driving the decision process was never poorer for the older subjects than the young subjects, and it was sometimes better. This third finding shows that there was no general decrement across all of the components of processing for the older subjects, as the slowing hypothesis predicts there should be. In the tasks used by Ratcliff et al. (2001), the stimuli were displayed until a response was made, so there was no limit on the time available to encode the stimuli, that is, there was no limit on the availability of perceptual information. The aim of the experiment we report in this article was to extend the diffusion model’s analysis of the components of processing to two-choice decisions for which perceptual information is limited by masking and for which there is good evidence that aging affects the acquisition of stimulus information. On each trial of the experiment, one of two letters was displayed, then masked, and the subject’s task was to indicate which of the two letters had been presented. Earlier research on visual information processing and backward masking with older adults has suggested performance deficits for older adults in whole versus partial report procedures (Coyne, Burger, Berry, & Botwinick, 1987; Walsh & Prasse, 1980), in visual persistence (; Kline & Nestor, 1977; Kline & Orme-Rogers, 1978; but see Walsh & Thompson, 1978), and in backward masking (Till & Franklin, 1981; Walsh, 1976). Two relatively recent chapters that provide more general reviews of visual deficits in aging are those by Fozard (1990) and Spear (1993). For letter identification specifically, older adults require more time to view a stimulus before it is masked than do young adults in order to reach a criterion level of accuracy in identification (Cramer, Kietzman, & Van Laer, 1982; Hertzog, Williams, & Walsh, 1976; Schlapfer, Groner, Lavoyer, & Fisch, 1991; Till & Franklin, 1981; Walsh, 1976; Walsh, Till, & Williams, 1978; Walsh, Williams, & Hertzog, 1979). The question for the experiment we present was which of the processing components identified by the diffusion model is responsible for the decrement in performance.