变量相对重要性评估的方法选择及应用

doi:10.3724/SP.J.1042.2023.00145

摘要/Abstract

摘要：

高维数据爆发的背景下, 心理学研究目前急需变量相对重要性评估的有效方法。相对重要性评估的关键是选择合适的评估指标和统计推断方法。相对重要性的评估指标种类繁多, 优势分析和相对权重是重点推荐的相对重要性评估指标。相对重要性的统计推断方法适用情境不同, Bootstrap抽样是推断单变量重要性和两变量重要性差异的常用方法, 而贝叶斯检验是评估多变量重要性次序的新方法。线性回归模型之外, 相对重要性研究已拓展到Logistic回归模型、结构方程模型、多水平模型等, 但适用数据类型仍较为有限。相对重要性评估已广泛应用于心理学实证研究, 但存在不恰当的指标解释和方法选择问题。为此, 结合具体例子说明变量相对重要性的评估过程。

关键词: 相对重要性, 优势分析, 相对权重, Bootstrap, 贝叶斯因子

Abstract:

Psychological researches are more concerned with high-dimensional data than ever. The evaluation of predictors’ relative importance can explore or test the ordering of predictors’ importance, which promotes the effective use of variables with limited resources. This article reviews many aspects of relative importance, including its measures, inference, models, and empirical studies, in order to help researchers select appropriate measures and inference methods and provide directional suggestions for the relative importance studies.

Previous studies proposed various measures of relative importance with different interpretations and calculations. The traditional measure, standardized regression coefficient, considers only the unique effect of a predictor after controlling other predictors but ignores the independent effect of the predictor on the outcome variable. By contrast, the dominance analysis and relative weight measures take into account both the independent and unique contributions of a predictor on the outcome variable. These two measures are recommended because they decompose the R squared such that the contribution to the variation of the outcome variable is attributed to each predictor. Specifically, dominance analysis can be used when the research concerns different importance patterns, whereas relative weight is recommended when evaluating a large number of predictors. After estimating the importance measures, researchers can use the bootstrap sampling or Bayesian testing approach for the inference of the importance of predictors and their orderings. Bootstrap sampling is commonly used to infer the importance of a single predictor or the difference between the importance of two predictors. When comparing the importance of three or more predictors, the Bayesian approach can be used to test the importance orderings.

Besides linear regression models, relative importance analysis has been extended to logistic regression models, multivariate multiple regression models, and multilevel models but not to structural equation models and generalized linear mixed models. Furthermore, the robustness of relative importance has not been analyzed when categorical data is involved in these models. Relative importance analysis can be implemented in many statistical software, such as SPSS, R and Python. However, an integrated software incorporating different measures and inference methods is still absent. Although relative importance analysis has been widely used in psychological studies, researchers may select inappropriate measures and inference methods in different models. Therefore, a real data example is used to illustrate how the relative importance can be evaluated. Finally, we propose that further researches could focus on the applications of relative importance analysis in different models and various types of data together with the software development.

Key words: relative importance, dominance analysis, relative weight, Bootstrap, Bayes factor

中图分类号:

B841

朱训, 顾昕. (2023). 变量相对重要性评估的方法选择及应用. 心理科学进展 , 31(1), 145-158.

ZHU Xun, GU Xin. (2023). Evaluation of predictors’ relative importance: Methods and applications. Advances in Psychological Science, 31(1), 145-158.

图/表 13

图1 回归模型例

表1 变量的相关系数矩阵

变量	考试成绩	学科能力	复习时长	焦虑程度
考试成绩	1.00
学科能力	0.80	1.00
复习时长	0.40	0.50	1.00
焦虑程度	0.00	0.20	0.10	1.00

图2 自变量加入模型的不同次序

图3 自变量可进入的子集

表2 优势分析结果

子集	$R 2 ?$	$R 2$ 增量
子集	$R 2 ?$	$X 1$	$X 2$	$X 3$
$k = 0$ 平均	0	0.64	0.16	0.00
$X 1$	0.64		0.00	0.03
$X 2$	0.16	0.48		0.00
$X 3$	0.00	0.67	0.16
$k = 1$ 平均		0.57	0.08	0.01
$X 1 X 2$	0.64			0.03
$X 1 X 3$	0.67		0.00
$X 2 X 3$	0.16	0.51
$k = 2$ 平均		0.51	0.00	0.03
总平均		0.57	0.08	0.01

表2 优势分析结果

子集	$R 2 ?$	$R 2$ 增量
子集	$R 2 ?$	$X 1$	$X 2$	$X 3$
$k = 0$ 平均	0	0.64	0.16	0.00
$X 1$	0.64		0.00	0.03
$X 2$	0.16	0.48		0.00
$X 3$	0.00	0.67	0.16
$k = 1$ 平均		0.57	0.08	0.01
$X 1 X 2$	0.64			0.03
$X 1 X 3$	0.67		0.00
$X 2 X 3$	0.16	0.51
$k = 2$ 平均		0.51	0.00	0.03
总平均		0.57	0.08	0.01

图4 共性分析

表3 共性分析结果

效应	自变量	CC	百分比(% R²)
独特效应	学科能力	0.51	76
	复习时长	0.00	0
	焦虑程度	0.03	4
共同效应	学科能力-复习时长	0.16	24
	学科能力-焦虑程度	-0.03	-4
	复习时长-焦虑程度	0.00	0
	学科能力-复习时长-焦虑程度	0.00	0
总		0.67	100

表3 共性分析结果

效应	自变量	CC	百分比(% R²)
独特效应	学科能力	0.51	76
	复习时长	0.00	0
	焦虑程度	0.03	4
共同效应	学科能力-复习时长	0.16	24
	学科能力-焦虑程度	-0.03	-4
	复习时长-焦虑程度	0.00	0
	学科能力-复习时长-焦虑程度	0.00	0
总		0.67	100

表4 相对重要性指标对比

指标	非负	方差解释	$R 2$ 的分解	比较变量组
$r j 2$	√	×	×	×
$β ? j 2$	√	×	×	×
$r j β ? j$	×	×	√	×
$Δ R 2 (X j)$	√	√	×	√
$C C$	×	√	√	√
$Δ R 2 ˉ (X j)$	√	√	√	√
$S (X j)$	√	√	√	√
$d (X j)$	√	√	√	√
$w j$	√	√	√	√

表4 相对重要性指标对比

指标	非负	方差解释	$R 2$ 的分解	比较变量组
$r j 2$	√	×	×	×
$β ? j 2$	√	×	×	×
$r j β ? j$	×	×	√	×
$Δ R 2 (X j)$	√	√	×	√
$C C$	×	√	√	√
$Δ R 2 ˉ (X j)$	√	√	√	√
$S (X j)$	√	√	√	√
$d (X j)$	√	√	√	√
$w j$	√	√	√	√

图5 一般优势指标的bootstrap抽样分布

表5 贝叶斯因子标准

$BF$	支持假设的证据
1~3	不明显
3~20	积极的
20~150	强
>150	非常强

表5 贝叶斯因子标准

$BF$	支持假设的证据
1~3	不明显
3~20	积极的
20~150	强
>150	非常强

表6 相关系数与标准化回归系数估计值

变量	$P o s t n u m b$	$P r e n u m b$	$A g e$	$P e a b o d y$	$β^j$
$P o s t n u m b$	1.00
$P r e n u m b$	0.68	1.00			0.57
$A g e$	0.30	0.36	1.00		0.06
$P e a b o d y$	0.50	0.59	0.24	1.00	0.15

表6 相关系数与标准化回归系数估计值

变量	$P o s t n u m b$	$P r e n u m b$	$A g e$	$P e a b o d y$	$β^j$
$P o s t n u m b$	1.00
$P r e n u m b$	0.68	1.00			0.57
$A g e$	0.30	0.36	1.00		0.06
$P e a b o d y$	0.50	0.59	0.24	1.00	0.15

表7 一般优势指标、标准误、置信区间和Wald检验

变量	估计值	标准误	百分位置信区间	BCa置信区间	Wald统计量	$P$ 值
$P r e n u m b$	0.32	0.05	[0.23,0.40]	[0.23,0.40]	7.10	0.000
$A g e$	0.04	0.02	[0.01,0.08]	[0.01,0.08]	2.13	0.017
$P e a b o d y$	0.12	0.03	[0.07,0.18]	[0.07,0.18]	4.27	0.000

表7 一般优势指标、标准误、置信区间和Wald检验

变量	估计值	标准误	百分位置信区间	BCa置信区间	Wald统计量	$P$ 值
$P r e n u m b$	0.32	0.05	[0.23,0.40]	[0.23,0.40]	7.10	0.000
$A g e$	0.04	0.02	[0.01,0.08]	[0.01,0.08]	2.13	0.017
$P e a b o d y$	0.12	0.03	[0.07,0.18]	[0.07,0.18]	4.27	0.000

表8 贝叶斯统计推断

	$H 1$	$H 2$	$H 3$	$H 4$	$H 5$	$H 6$
$B F i u (β ? j 2)$	0.44	5.77	0.00	0.00	0.00	0.00
$B F i u (d j)$	0.01	5.54	0.00	0.00	0.00	0.00

表8 贝叶斯统计推断

	$H 1$	$H 2$	$H 3$	$H 4$	$H 5$	$H 6$
$B F i u (β ? j 2)$	0.44	5.77	0.00	0.00	0.00	0.00
$B F i u (d j)$	0.01	5.54	0.00	0.00	0.00	0.00

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