[Feature Request]: additional linear regression measures of variable importance

[TarandeepKang]

Description

No response

Purpose

Regression weights cannot be used to draw conclusions about the relative importance of predictors in models

Use-case

Whenever one wishes to draw an inference about the importance of predictors especially in the face of multicollinearity

Is your feature request related to a problem?

Overcoming issues related to multicollinearity and variable importance assessment

Is your feature request related to a JASP module?

Regression

Describe the solution you would like

A number of new metrics described in further detail below

Describe alternatives that you have considered

Variance inflation factors a multicollinearity diagnostics currently available in JASP

Additional context

It would be useful to have a number of additional regression diagnostics available as part of the linear regression module these are: regression weights, zero-order validity coefficients, structure coefficients, Pratt measures, relative importance weights, all-possible-subsets regression, commonality coefficients, and dominance weights

Functions for computing each of these measures are available in the yhat package further computational details are given in the vignette and the papers below: https://cran.r-project.org/web/packages/yhat/index.html

Beaton, A. E. (1973). Commonality. https://eric.ed.gov/?id=ED111829 Kraha, A., Turner, H., Nimon, K., Zientek, L., & Henson, R. (2012). Tools to Support Interpreting Multiple Regression in the Face of Multicollinearity. Frontiers in Psychology, 3. https://doi.org/10.3389/fpsyg.2012.00044 Nimon, K. F., & Oswald, F. L. (2013). Understanding the Results of Multiple Linear Regression: Beyond Standardized Regression Coefficients. Organizational Research Methods, 16(4), 650–674. https://doi.org/10.1177/1094428113493929 Nimon, K., Lewis, M., Kane, R., & Haynes, R. M. (2008). An R package to compute commonality coefficients in the multiple regression case: An introduction to the package and a practical example. Behavior Research Methods, 40(2), 457–466. https://doi.org/10.3758/brm.40.2.457 Thomas, D. R., Zumbo, B. D., Kwan, E., & Schweitzer, L. (2014). On Johnson’s (2000) Relative Weights Method for Assessing Variable Importance: A Reanalysis. Multivariate Behavioral Research, 49(4), 329–338. https://doi.org/10.1080/00273171.2014.905766 Yin, P., & Fan, X. (2001). Estimating R² Shrinkage in Multiple Regression: A Comparison of Different Analytical Methods. The Journal of Experimental Education, 69(2), 203–224. https://doi.org/10.1080/00220970109600656

The functions of:

Lai, J., Zou, Y., Zhang, J., & Peres-Neto, P. R. (2022). Generalizing hierarchical and variation partitioning in multiple regression and canonical analyses using the rdacca.hp R package. Methods in Ecology and Evolution, 13(4), 782–788. https://doi.org/10.1111/2041-210X.13800

Seem to overlap somewhat, so I presume they may also be useful? Though I am much less knowledgeable about what these authors are looking to achieve. Still, may be of interest?

[TarandeepKang]

Hi Team, I'm just wondering what your thoughts are on this?

[treydejong]

At least adding structure coefficients as an optional output would be very useful. I prefer this as an option for dealing with multicollinearity (Henson, 2002) when teaching since my students have less difficulty with the concept than other approaches such as part and partial correlations.

Other software like SPSS do not feature structure coefficients, but they are easily calculated since they are the correlation between each predictor and the prediction scores from the regression model (y-hat). There is unfortunately no way to save predicted scores and therefore calculate structure coefficients in JASP (that I am aware of), so structure coefficients are unavailable in the software.

The structure/pattern matrix is available in JASP for factor analysis, so having structure coefficients available in multiple regression would be appropriate.

[TarandeepKang]

Hi @JohnnyDoorn, sorry to bother you once again, but since you seem to have been busy updating regression recently, I wonder whether you might give this issue a look? I'm sure this would be useful? This time, I'm sure the features aren't already available! :-) In the references above, I would say the Nimon/ Thomas articles are the most important! In terms of improving inferences think it's very much related to #2213

Many Thanks,

Tarandeep