I got 4 variables refering to a specific place or spot (like a climbin-rock). There are 2 Liking ratings, one cheap/expensive rating and one young/dynamic rating. Also participants are asked if this spot is there most favorite Location to do sport at. In addition there are some demographic variables about the participant (like age, gender, income, lives in the city or on the countryside, ....).
There are no latent variables in the modell (for now).
With this information i want to predict the "workout-type" of the participants (which was measured by selfrating - picking the best fitting description from 5 options).
Unfortunately i am struggling a lot when it comes to deciding which predictors are more important and which one not. The Problem is the mix of metric and binary predictor-data especially in combination with the categorical dependent Variable.
Mplus gives different standardised coefficients so i am not sure which one to use (especially because the rank of importance of the different variables changes with the standardisation-method).
So i tried to do the standardisation myself and z-transformed all the metric variables. I was thinking about z-transforming the binary dummies too, but it doesn't feel very intuitive to me, so i decided against it. Still im not happy because now the binarys might have a different scale and therefore might be more/less important.
I am really out of ideas how to make a solid judgment about the order of importancies of my given variables.
My last hope would be to try some sort of permutation or leaf out kind of testing (randomly reasigning one of the predictors or leafing out one of the predictors and checking how this effects the prediction quality of the modell. The variable with the biggest decrease in prediction accuracy when left out/randomly reassigned is taken as the most important one).
But to be honest, i think this is not the greatest approach, so i would be very thankful if you could help me out with some better ideas.
Could it help to add in some latent variables? For example workout-type as a latent variable with the selfrating as its observable measurement? This way i might get rid of the categorial dependent and might assume a metric one instead?
Thanks in advance (and also sorry for the bad english)