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R-Square (U) In Contingency Tables

acunar

Community Trekker

Joined:

Jul 7, 2016

Hey All,

 

I had a question about the R-square uncertainty ratio in Contingecy Tables (placed in same table as DOF and loglikelihood). I am currently doing research where I've found significance in my p-value (alpha=.05), but the R-square value is close to 0. Now, I am aware that in continuous vs continuous, an R-value is used to determine the correlation between the two variables. 

 

My question is: What relevance does the Rsquare value in a contingecy table have on my conclusions? 

 

I was able to reject the null hypothesis via my p-value, but as I previously mentioned, the Rsquare is very close to 0, which makes me unsure if I should proceed with the alternative hypothesis in mind.

 

Thanks in advance!

1 ACCEPTED SOLUTION

Accepted Solutions
markbailey

Staff

Joined:

Jun 23, 2011

Solution

You may interpret the RSquare (U) the same way as you would interpret the RSquare from a linear regression. The RSquare is based on sums of squares: SS(model) / SS(total). RSquare (U) likewise is -L(model) / -L(reduced). It tells you the proportion of the total uncertainty that is accounted for by the model, assuming it is the correct model.

This relationship is easier to see in Logistic Fit than in Contingency because Contingency only reports the -L(model). This is the analysis of age by weight from Big Class sample data table:

Capture.JPG

 

The -L(model) above is labeled Difference here. The -L(total) above is labeled Reduced here. The RSquare (U) is therefore Difference / Reduced = 5.037918 / 67.266350 = 0.0749.

It is common for a statistically significant model of a categorical response to exhibit a very low RSquare (U) as this example demonstrates. Like its continuous model RSquare counterpart, it indicates the performance of the conditional prediction over the marginal prediction.

Learn it once, use it forever!
2 REPLIES
markbailey

Staff

Joined:

Jun 23, 2011

Solution

You may interpret the RSquare (U) the same way as you would interpret the RSquare from a linear regression. The RSquare is based on sums of squares: SS(model) / SS(total). RSquare (U) likewise is -L(model) / -L(reduced). It tells you the proportion of the total uncertainty that is accounted for by the model, assuming it is the correct model.

This relationship is easier to see in Logistic Fit than in Contingency because Contingency only reports the -L(model). This is the analysis of age by weight from Big Class sample data table:

Capture.JPG

 

The -L(model) above is labeled Difference here. The -L(total) above is labeled Reduced here. The RSquare (U) is therefore Difference / Reduced = 5.037918 / 67.266350 = 0.0749.

It is common for a statistically significant model of a categorical response to exhibit a very low RSquare (U) as this example demonstrates. Like its continuous model RSquare counterpart, it indicates the performance of the conditional prediction over the marginal prediction.

Learn it once, use it forever!
acunar

Community Trekker

Joined:

Jul 7, 2016

Awesome,

 

Thank you!