Methodological and epistemological issues on linear regression applied to psychometric variables in problem solving: rethinking variance
Methodological and epistemological issues on linear regression applied to psychometric variables in problem solving: rethinking variance
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在问题解决中应用于心理测量变量的线性回归的方法论和认识论问题：重新思考方差
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发表时间：
2010
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通讯作者：
D. Stamovlasis
中科院分区：
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作者：
D. Stamovlasis
本文件有两个目的。首先，它试图支持一些心理测量学变量，如，M-能力，场依存-独立的程度，逻辑思维和移动性-固定性维度，对学生的化学问题解决的成就的作用，以前的研究结果。其次，本文旨在提出一些方法论和认识论问题的一般线性模型（GLM）在这类研究中的实施。采用多元回归分析的方法对86名高中十年级化学必修课学生的问卷调查数据进行分析。为了支持线性模型，实施了三种不同的技术：添加的变量图，逐步回归和最佳子集回归。还进行了残差分析和共线性诊断，以检验推断统计量的稳健性。GLM解释了39%的方差，并表明只有M能力和逻辑思维是显着的预测因子，即使所有的相关系数与成就的统计学显着。对线性回归程序的广泛分析揭示了它们在统计稳健性方面的优点和局限性。此外，讨论的线性模型的解释能力，并建议重新思考下不同的哲学视角解释的方差。有人认为，GLM在研究复杂的动力学过程，如解决问题的弱点，不仅植根于统计假设不成立，或在被忽略的变量，但实质上它是深刻的认识论。
The aim of the present paper is two-fold. First, it attempts to support previous findings on the role of some psychometric variables, such as, M-capacity, the degree of field dependence-independence, logical thinking and the mobility-fixity dimension, on students’ achievement in chemistry problem solving. Second, the paper aims to raise some methodological and epistemological issues concerning the implementation of the general linear model (GLM) in this type of research. Multiple regression analysis was used to analyze the data, which were taken from students (N =86) in tenth grade of high school taking a compulsory course in chemistry. Three different techniques were implemented in order to support a linear model: The Added Variable Plots, the Stepwise Regression and the Best Subsets Regression. Residual analysis and collinearity diagnosis were also performed in order to test the robustness of inferential statistics. The GLM explained 39% of the variance and suggested that only M-capacity and logical thinking were the significant predictors, even though all the correlation coefficients with achievement were statistically significant. The extensive analysis of the linear regression procedures revealed their advantages and also their limitations in terms of statistical robustness. Moreover, a discussion is initiated concerning the explanatory power of linear models and suggests rethinking variance explained under a different philosophical perspective. It is argued that the weakness of the GLM in studying complex dynamical processes, such as problem solving, is rooted not merely in the statistical assumptions that do not hold, or in the variables that are ignored, but substantially it is deeply epistemological.