Standardized regression line

In 標準化後的回歸直線 that use multivariate models with a quantitative dependent variable, the association between this variable and one primary quantitative explanatory variable is often reported as a regression coefficient. However, it is often difficult to compare the magnitudes of these regression coefficients because different variables are measured in different units of measurement and control for various confounding factors differ between studies. Hence, the standardized regression line (b) offers a common effect-size index for such comparisons. However, b and its standard error SE(b) are not always readily available in the evaluated articles, and procedures for their estimation and conversion from the data presented are not universally known.

Going Beyond the R-squared: Evaluating Model Performance with Standardized Regression

Using a simple example of the relationship between parental occupational status, educational level, and child’s reading ability, this article illustrates the methods of comparing standardized regression coefficients using EQS software. The first step is to transform the original model to a standardized model. This is done by fixing the variances of the predictor and outcome variables to 1 nonstochastically. The standardized model, M2 is then compared to the original model, M1 by performing a likelihood ratio (LR) test.

Although the LR test is a robust procedure for comparing standardized regression coefficients, there are still issues associated with interpreting its results. The most obvious problem is that the standardized coefficients do not estimate effects on the original scales of the predictor and outcome variables, but only on their standard deviations. This can lead to misleading inferences when comparing the effects of a predictor on a response if the mean difference between populations is not zero and the variable’s sampling variance differs between the two samples.

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