Longitudinal evidence linking processing speed to the development of reasoning

Research highlights

Introduction

When children solve arithmetic problems, determine whether two stimuli are similar perceptually, or retrieve an object's name from long-term memory, they respond more rapidly as they develop. Speeds on these and other cognitive tasks typically increase substantially during early and middle childhood but more slowly in later childhood and early adolescence (Kail, 1991).

These age-related increases in speed have been linked to the growth of more complex cognitive processes, both directly and indirectly. Direct links are illustrated by the findings that age-related increases in processing speed are associated with higher scores on intelligence tests, with greater success in solving arithmetic word problems, and greater accuracy in ordering landmarks encountered during a walk (Allen & Ondracek, 1995; Coyle, Pillow, Snyder & Kochunov, 2011; Kail & Hall, 1999). Age-related increases in processing speed have also been linked to cognitive development indirectly, via increases in WM: That is, increases in processing speed are associated with increases in the capacity of WM which, in turn, are associated with improvements in complex cognitive processing (e.g. De Alwis, Hale & Myerson, 2014; Fry & Hale, 1996; Nettelbeck & Burns, 2010; Spanoudis, Demetriou, Kazi, Giorgala & Zenonos, 2015).

Most of the aforementioned evidence comes from cross-sectional work. More compelling evidence for the cognitive consequences of age-related change in speed would come from longitudinal studies. The ideal study would assess speed, WM, and cognitive performance using similar tasks on multiple testing occasions, allowing tests of the direct effects of increased speed (e.g. speed → complex cognition) as well as tests of indirect effects (e.g. speed → WM → complex cognition).

In fact, there are few relevant studies and most fall short of the ideal. Rose, Feldman, Jankowski and Van Rossem (2008) reported that 12-month-olds’ processing speed predicted, concurrently, their recognition memory, which predicted their mental development (as assessed by the Bayley) as 2- and 3-year-olds. Clark et al. (2014) found that 3-year-olds’ processing speed predicted their skill at mathematics as 5-year-olds (Clark, Nelson, Garza, Sheffield, Wiebe et al., 2014); similarly, Rose, Feldman and Jankowski (in press) found that 3-year-olds’ processing speed predicted their lexical proficiency as 13-year-olds. Finally, Kail (2007) showed that for 8- to 13-year-olds, more rapid processing speed was associated concurrently with greater WM, which predicted scores on a measure of fluid intelligence administered one year later. In these studies, processing speed is consistently associated with cognitive development but none was designed to provide a comprehensive evaluation of the direct and indirect effects of age-related increases in processing speed.

The study that comes closest to the ideal was reported by Demetriou, Christou, Spanoudis and Platsidou (2002). They administered measures of processing speed and WM as well as tasks assessing reasoning and problem solving in verbal, quantitative, and spatial domains. The participants, 8- to 14-year-olds, were tested three times over two years. Increases in processing speed were linked directly to greater accuracy on the reasoning and problem solving tasks and indirectly, via increases in WM.

The findings of Demetriou et al. (2002) provide the strongest longitudinal evidence for direct and indirect links between processing speed and reasoning. However, conclusions are limited by the way in which processing speed was assessed: participants named words, digits, or shapes. Speeds on such tasks are correlated with performance on psychometric measures of processing speed, but naming tasks (1) are distinct statistically from psychometric measures of processing speed, (2) are less strongly correlated with age than are psychometric measures of processing speed (Kail, 1997; Kail, Hall & Caskey, 1999), and (3) are thought to tap naming circuits in the left hemisphere that are critical for learning to read (Lervåg & Hulme, 2009). Consequently, measures of processing speed that are more typically included in psychometric instruments would provide more compelling evidence.

The aim of the present study was to assess the direct and indirect effects of processing speed on cognitive processes, using a design similar to that of Demetriou et al. (2002) but with conventional measures of processing speed. Children and adolescents were tested multiple times over 2½ years on tasks assessing processing speed, WM, and reasoning. This design allowed us to determine whether increases in speed are linked with cognitive processes directly (i.e. increased processing speed is associated with greater reasoning), are linked indirectly (i.e. the impact of increased processing speed on reasoning is mediated by increases in WM) or both directly and indirectly.

Method

Results

Descriptive statistics are shown in Table 1 and correlations between measures at all time points are shown in Table 2. The raw correlations, shown above the diagonal, reveal that age at Time 1 was highly correlated with all measures, especially performance on the measures of processing speed. Consequently, all analyses were conducted on variables residualized for age; correlations between these variables are shown below the diagonal. Also, as shown in Table 1, many children did not have complete data for all waves of testing. To determine whether missing data occurred randomly – that is, that missing data on one variable could not be predicted by values from other variables – we ran Little's MCAR test on the age-residualized scores (Little, 1988). The outcome, χ² (136) = 147.70, p = .233, was consistent with the null hypothesis that data were missing completely at random.

Testing hypotheses about developmental relationships between processing speed, WM and reasoning requires data from three time points and the correlations in Table 2 include two overlapping sets of such data: the data from Times 1, 2, and 4 as well as the data from Times 1, 3, and 4. For each set of data, we began with a theoretically neutral full model (Model 0) in which all three constructs were linked to the other two within each time point and each construct predicted the other two at the next time point (see Figures 1 and 2, top panels). A second model (Model 1, shown in the bottom panels of Figures 1 and 2), nested within the neutral model, evaluated the presence of direct and indirect links between processing speed and cognition. This model differed from the neutral model in that (a) processing speed predicted WM and reasoning at the next time point, (b) WM predicted reasoning but not processing speed at the next time point, and (c) reasoning predicted neither WM nor reasoning in the next time point. A third model (Model 2), nested within Model 1, evaluated the hypothesis that processing speed is linked to reasoning indirectly, via WM, but not directly. This model differed from Model 1 in omitting direct links from speed to reasoning.

We evaluated these overlapping models using Mplus version 7.11 (Muthén & Muthén, 1998–2012). Missing data were handled by Full Information Maximum Liklihood, the default in Mplus. We regressed each factor at later time points on the same factor at the preceding time point to control for autoregressive effects. The speed factor reflected variation in children's scores on the Cross Out and the Visual Matching tasks at Times 1, 2, and 3. The WM factor reflected variation on listening span plus reading span at Time 1, backward digit span plus alphabetic span at Time 2 and listening span plus operation span at Time 3. As Raven's matrices was the only measure of reasoning, we estimated the true score variance of this measure based on its reliability.

The data from Times 1, 2, and 4 were fitted to the three models, as were the data from Times 1, 3, and 4. For both sets of data, the fit to the (neutral) Model 0 was good, χ² (27) = 36.392, p < .107 and χ² (27) = 21.949, p < .740, respectively, for the two sets of data; CFI = .989 and 1.00, respectively; TLI = .978 and 1.01, respectively; and RMSEA = .035 and .000, respectively.

Of greater importance are the relative fits of Models 1 and 2. Model 1 fits the data well, χ² (30) = 38.543, p < .136 and χ² (30) = 25.954, p < .678, respectively, CFI = .990 and 1.00, respectively; TLI = .982 and 1.01, respectively; and RMSEA = .032 and .000, respectively. Critically, Model 1 fits the data as well as the neutral Model 0, χ² difference (3) = 2.151. p = .542 and χ² difference (3) = 4.005, p = .261, respectively for the two sets of data.

Model 2 also fits the data relatively well, χ² (32) = 47.264, p < .040 and χ² (32) = 33.179, p < .410, respectively; CFI = .982 and .999, respectively; TLI = .969 and .998, respectively; and RMSEA = .041 and .012, respectively. However, Model 2 fits the data significantly less well than Model 1, χ² difference (2) = 8.721, p = .013 and χ² difference (2) = 7.225. p = 027. In other words, a model that includes only indirect effects of speed on reasoning (via WM) fits the data less well than a model that includes direct and indirect effects of speed on reasoning.

Model 1 is shown in the bottom panels of Figures 1 and 2. For the data from Times 1, 2, and 4 (Figure 1), direct effects of speed include links from speed at T1 to reasoning at T2 as well as from speed at T2 to reasoning at T4. In these data, the indirect link between speed and reasoning (via WM) is not significant: neither the T1 speed → T2 WM path nor the T2 WM → T4 reasoning path is significant. For the data from Times 1, 3, and 4 (Figure 2), speed at T1 was linked to WM at T3 and to reasoning at T2 (already shown in Figure 1) but, surprisingly, neither the T3 speed → T4 reasoning path nor the T3 WM → T4 reasoning path is significant. However deleting these two nonsignificant paths leads to a significant decrease in model fit, χ² difference (2) = 19.815, p < 001, suggesting colinearity between speed and WM at T3. Supporting this, a similar model, where speed and WM at T3 were put on the same scale of measurement and constrained to be equal, showed significant paths to T4 reasoning (β = .20, p < .001) and the fit of this model did not differ from the fit of the same model when the two paths were freely estimated, χ² difference (1) = .108. p = .742.

Discussion

The aim of the work reported here was to evaluate direct and indirect links between age-related changes in processing speed and reasoning. We found strong support for direct links between speed and reasoning, an outcome that replicates findings reported by Demetriou et al. (2002) in which processing speed was estimated from performance on naming tasks. We also found much weaker support for possible indirect links via WM. We first consider evidence for indirect links, then comment on the finding of direct links between speed and reasoning.

There was relatively weak evidence for an indirect path linking speed to WM and then to reasoning (such an effect was absent for the T1, T2, T4 data, but there was some support for it in the T1, T3, T4 data). This outcome might be seen as unexpected given the many demonstrations of these paths in concurrent studies. One explanation focuses on the psychometric properties of the processing speed and WM constructs. At each time, the partial correlations for the two measures of processing speed were substantially greater than those for the two measures of WM. For example, at Time 1, correlations with age partialled out were .628 between Visual Matching and Cross Out but only .316 between listening span and reading span. In addition, processing speed was always estimated from the same two tasks but WM was estimated from different tasks. By this explanation, links involving processing speed were easier to detect than those involving WM because the former construct was estimated more consistently than the latter. Nevertheless, it should be noted that the WM construct was remarkably stable across waves, suggesting that the tasks were measuring a common underlying process. Furthermore, WM at T1 predicted reasoning at T2, consistent with the proposed speed → WM → reasoning pathway.

In contrast, speed was linked directly to reasoning: speed at T1 was linked to reasoning at T2, speed at T2 was linked to reasoning at T4, and at T3 speed and WM both were linked to reasoning but their contributions could not be separated from each other. These findings are consistent with many cross-sectional studies (e.g. Frye & Hale, 1996) and some longitudinal work (e.g. Demetriou et al., 2002; Rose et al., 2008) in showing that greater processing speed is associated with enhanced ‘higher-level’ cognitive processing. In other words, increases in processing speed appear to be one factor that contributes to age-related improvements in reasoning skill.

However, this conclusion comes with two caveats. First, although the present study involved a longitudinal design, the effects here remain purely correlational. Consequently, it is worth noting that in one of the few relevant experimental studies, Mackey, Hill, Stone and Bunge (2011) found that following extensive practice on video games that emphasized rapid processing and responding, 7- to 10-year-olds responded more rapidly on psychometric measures of processing speed. However, performance did not change on measures of reasoning (or WM, for that matter); in other words, although practice led children to respond more rapidly on the Cross Out task used here, it did not increase children's accuracy on matrix problems like those found on the Raven's. The failure to find more accurate reasoning following practice-related increases in speed suggests that it would be premature to conclude that age-related increases in speed necessarily lead to improved reasoning.

Second, the present findings were based on analyses of correlations in which age was partialled out, a procedure that assumes that links between speed and reasoning are invariant throughout the ages included in the sample (6 to 13 years). However, a provocative meta-analysis of cross-sectional studies (Demetriou, Spanoudis, Shayer, van der Ven, Brydges et al., 2014) suggests that links between speed, WM, and reasoning may change with age. In this work, at 6–8 and 11–13 years – when qualitatively more sophisticated representations are said to emerge (e.g. inference-based concepts at about 6) – speed predicted reasoning more accurately than did WM. In contrast, at ages 8–10 and 13–16 – when new representations are aligned and integrated – WM predicted reasoning more accurately than did speed. These cyclical changes in the strength of links between speed, WM, and reasoning could not be evaluated here because the sample was too small to divide into the required narrow age bands. Doing so is a task for future longitudinal studies.

In summary, our findings from a large-scale longitudinal study are consistent with the idea that variations in processing speed may act directly to place constraints on the development of reasoning. Further evidence from training studies is needed to test whether such patterns reflect a causal influence of earlier variations in processing speed on later reasoning skills.