Swiss Classic Blog Multivariable Linear-Regression Models and Standardized Regression Lines

Multivariable Linear-Regression Models and Standardized Regression Lines


標準化後的回歸直線 models are used to analyze the associations between one quantitative dependent variable and several explanatory variables. The unstandardized regression coefficient (b) estimated from the model is an easy-to-interpret statistic that quantifies the effect of a unit increase in the explanatory variable on the outcome variable. The unstandardized regression coefficient and its standard error (SE) are often reported along with a significance test statistic, p value, in articles reporting the results of multivariable linear regression analyses.

The problem with the unstandardized regression coefficient is that differences in the magnitude of underlying relationships between different predictors cannot be distinguished when coefficient estimates are compared between studies and/or across samples. A statistical analysis method that accounts for the effects of standard deviations on regression coefficients can overcome this limitation by transforming the original model into a standardized model.

The Power of Standardization: Understanding Standardized Regression Line

In the standardized model, each observed variable is regressed on a standardized variable that has the same variance as the original variable in the model. The standardized variable is then regressed on the outcome variable, and the regression coefficients are compared using a likelihood ratio (LR) test.

LR tests are typically performed by using a program such as EQS 6.1 for Windows. To illustrate the process, a model is fitted to the Organization for Economic Cooperation and Development’s Programme for International Student Assessment data set (OECD 2009). The aim is to compare the standardized regression coefficients of parental occupational status (g 1 *), child’s home possession (g 2 *) and educational resources at school (g 3 *) on child reading ability (V5).

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