Reciprocal effects of reading and mathematics? Beyond the cross-lagged panel model.

Abstract

Prior nonexperimental studies have been used to conclude that children's reading and mathematics achievement bidirectionally influence each other over time, with strong paths from (a) early reading to later mathematics and (b) early mathematics to later reading. In the most influential study on the topic, the early math-to-later-reading path was reported to be stronger than the early reading-to-later-math path (Duncan et al., 2007). Yet prior estimates may be confounded by stable environmental and personal factors influencing both reading and mathematics achievement. We reexamined the bidirectional relations between reading and mathematics achievement using both traditional models and extensions intended to account for unmeasured confounding. Results based on a large nationally representative sample of children from kindergarten to 3rd grade (N ϭ 9,612) indicated that the estimated effects between reading and mathematics achievement differ substantially after accounting for the confounding effects of stable unmeasured factors. In these models, autoregressive and cross-lagged paths were substantially reduced. The finding that early mathematics predicts later reading more strongly than early reading predicts later math disappears and sometimes reverses, suggesting that larger paths from math to reading than from reading to math in previous related analyses are not causally informative. Stability in early mathematics and reading achievement resulted from substantially overlapping time invariant factors that correlate above .90.

Developmental dynamics between reading and math in elementary school

“…From this perspective, patterns of change in math were dependent on reading‐math combinations, rather than on the math construct alone. The unidirectional reading to subsequent math finding presents a point of departure from the results of studies conducted on national datasets which showed bidirectional influences (e.g., Bailey et al., 2020). The simplest explanation for the difference is that those studies examined children across the performance continuum, whereas the present study examined children who might have been academically at‐risk.…”

Rock the MIC: The Matrix of Implied Causation, a Tool for Experimental Design and Model Checking

“…Panel models are very common in the longitudinal literature, but can result in biased causal estimates when various assumptions are violated (Hamaker, Kuiper, & Grasman, 2015;Zyphur et al, 2019). Bailey, Oh, Farkas, Morgan, and Hillemeier (2019) presented a series of closely related variations on cross-lagged panel models (CLPMs) to characterize the development of math and reading achievement across the early school years. We examine the differential predictions of two types of CLPMs for an early intervention targeting children's reading or math skills.…”

“…RI-CLPM Bailey, Oh, Farkas, Morgan, & Hillemeier, 2019). The cross-lagged panel model (CLPM) includes an autoregressive path within each domain, cross-lagged paths from achievement in one area to achievement in the other area the following year, and residual covariation at each wave.…”

“…In the RI-CLPM, the difference between these estimates is small, trending in the opposite direction (0.05 and 0.06). Bailey et al (2019) argued that this latter pattern is more plausible a priori, given the cognitive processes involved in math and reading.…”

A Bayesian Approach to Estimating Reciprocal Effects with the Bivariate STARTS Model using Markov Chain Monte Carlo

“…The RI-CLPM has been introduced as an extension of the traditional cross-lagged panel model (CLPM) that controls stable trait factors. It has received considerable attention in applied methodological literature (Bailey et al, 2020;Berry & Willoughby, 2017;Ehm et al, 2019;Ruzek & Schenke, 2019;Orth et al, 2020) but, at least in its original version (see Mulder & Hamaker, 2020), assumes that the variables are measured without error.…”