I have two continuous; one with 16 united, the other 10 units, and one categorical (likert scale) with 5 units. I am interested in combining the three into one variable. Is the combination possible? If so, are there statistical conditions, assumptions and precautions to consider when combining and using this new combined variable in regression?
You can create a latent variable of three variables and extract the latent value of it. Google search dependent mixture model for more information.
First you should find out if they are correlated enough to construct one variable from them. What are your variables, and what is the supposed connection?
It's difficult to say without more information, but there may not be any definitive or methodological way to combine these variables. Rather, that you would have to use your judgement to determine how each should be interpreted and weighted. ... As an example, if I want to have a single rating scale for cupcakes, I might want to combine the variables for taste, presentation, and creativity. Even if they are all on a 1 to 10 scale, I might want to weight taste twice as presentation, and maybe presentation more than creativity. I might say Sal'sCupcakeScale = 0.6 * Taste + 0.3 * Presentation + 0.1 * Creativity. There's no method to this other than that I think that taste is the most important and presentation matters too. You get some bonus points for creativity, but a plain vanilla cupcake that tastes great and looks great is still an A grade for me.
You could fit a single-factor confirmatory factor analysis model to your three variables (ideally with an estimation method that is appropriate for ordinal data such as WLSMV or robust maximum likelihood). A 1-factor model with three indicators and freely estimated loadings is just identified (saturated) so that you could not test the model against the data (it will fit perfectly by definition).
Nonetheless, you can take a look at the standardized factor loadings to see how well the variables reflect a single common factor. If all three standardized loadings are substantial (indicating a strong correlation between each measure and the common factor), then it may make sense to aggregate the three variables to a single score or to use the factor measurement model with the 3 items as part of a larger model. In contrast, if some or all of the loadings are rather small, this makes it questionable whether the indicators can be seen as homogeneous measures of a single common factor.
I can think of 2 ways: (1) Transform the continuous variables into binary values (0 or 1). For example, instead of using heart rate, set a cutoff, label the variable as Tachycardia and then allocate a 0 if the rhythm is below than the cutoff and 1 if it is above. Then do a Chi^2. (2) Much better, do a Logistic Regression where you can mix binary, continuous and even categorical (e.g. race) variables. Run the LR and you should get the outcome as a probability. You can then use that p as a continuous variable combining the input mixture of variables or create a binary outcome by setting a cutoff (typically 0.5) and considering everything above p=0.5 as 1 and everything equal or below p=0.5 as 0. You can do the whole thing easily in Excel using the free Real-Statistics Add-In. Good luck.
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