0
$\begingroup$

I conducted an experiment and would like to know if how I treated and coded my treatment variable is permissible. Basically, participants rated targets that vary in terms of how similar they are to each participant. I have 6 levels of SIMILARITY (the treatment variable), going from low to high (an ordinal variable). Our analyses indicate SIMILARITY is almost perfectly step-wise so I am treating SIMILARITY as if continuous in regression analyses to avoid having 5 dummy (or effects coded) variables.

I have coded SIMILARITY as 0, 1, 2, 3, 4, 5, so that zero (and intercept) are meaningful (zero capturing lowest level of SIMILARITY). Doing this allows me to make a statement about other predictors in the regression model for targets that are low in similarity. And then I recode SIMILARITY, for example, by shifting the zero (e.g., -1, 0, 1, 2, 3, 4) so that my intercept and other predictors could be interpreted for the second lowest level of similarity (ordinally, this would be level 2, going from low to high).

Is treating similarity this way (shifting the zero across iterations of the model) problematic? I am conducting multilevel models because my design is repeated measure experimental design, but I am not sure that info is necessary to my inquiry.

Thank you for any thoughts on the matter! Dita

$\endgroup$

1 Answer 1

0
$\begingroup$

Deciding about linearity in terms of your SIMILARITY predictor first depends on your knowledge of the subject matter. In that context, it's not clear exactly what you mean by its being "almost perfectly step-wise."

If you have reason to believe (other than your having already looked at the results) that it's almost perfectly stepwise with respect to its association with outcome then you can try coding it as a linear continuous predictor. If it's almost perfectly stepwise just with respect to having approximately equal number of cases in each category, then it can be risky to do that.

One trick with a small number $k$ of ordinal predictor levels is to model it as linear/continuous but add $k-2$ additional dummies to allow for nonlinearity. That provides a direct test of the linearity assumption.

However you proceed with treating SIMILARITY, there's no need for re-coding and re-running your model. All the information you need for predictions is within the original model, even though statistical software by default (with typical treatment/dummy coding) just shows an intercept for the outcome at reference levels of predictors and coefficients representing differences associated with changes in predictors.

There are post-model software tools designed to give outcome estimates for any combinations of predictor variables while correcting for the multiple comparisons that typically entails (a correction that your separate modeling for each level of SIMILARITY wouldn't do directly). In R, the emmeans package is one popular choice for that post-model analysis, able to handle multiple types of models (including mixed models) from other packages.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.