<Research Paper>The Simple View of Reading and Multiple Regression: Comparing and Compromising Multiplicative and Additive Models

Abstract

Controversies abound regarding the choice between linear regression and the Simple View of Reading (SVR) to describe reading comprehension (R), particularly in relation to decoding (D) and linguistic comprehension (C) (Høien-Tengesdal, 2010; Savage, 2006; Savage & Wolforth, 2007). This is despite the stark qualitative difference between multiplicative SVR and additive linear regression. In this comparative study, I (1) examine the different fit criteria, validity, and merits as well as demerits of each instrument, (2) explain why they are mathematically equivalent with optimal zero-point adjustments for D and C in SVR and the inclusion of D×C in linear regression, and (3) generate simulated datasets to examine the contribution of D×C based on significance levels and effect sizes. The equivalence in (2) means that SVR with optimal zeropoint adjustments can always explain more variance in R than multiple regression with only D and C as the predictors. However, the mathematically optimal adjustments may not always make good linguistic sense. These issues are discussed algebraically followed by an illustrative numerical example. This paper concludes with a set of criteria involving the significance, effect size, nullity adjustments, and commonality analysis to assess the applicability of SVR in a given situation.

読解力(R)の描写においては、decoding (D)とlinguistic comprehension (C)の積で説明しようとするSimple View of Reading (SVR)と、DとCのlinear combinationと定数の和からなる多項式で説明しようとするmultiple linear regressionがあり、その優劣がさかんに論じられている。本稿では両者を比較し、(1) fit基準、有効性、利点 (2) SVRにおけるDやCの最適原点調整とlinear regressionにおける相互作用項D×Cの導入による両者の数学的同値性 (3) 有意水準(significance levels)と効果の大きさ(effect size)のシミュレーション、の3点について論じる。(2) の数学的同値性は、最適原点調整を行えばSVRは常に相互作用項D×Cを含まないmultiple linear regressionより多くの分散(variance)を説明することを意味するが、数学的に得られた最適原点調整が言語学的に受け入れられない場合もある。この問題につき、代数的にまた数値化された具体例を使って説明する。最後に、有意レベル、効果の大きさ、原点調整、共通性分析(commonality analysis)に基づいたSVRの妥当性について論じる。