I have run a hidden markov model with five variables on very different scales. Because of this I normalized the input data beforehand using Carets preprocessing:

# Using preProcess to scale the data
data_mapping <- preProcess(data[, column to normalize], method = c('range'))  # preProcess creates a mapping for the chosen variables
pdata_norm <- predict(data_mapping, data)  # we transform the data using predict() and the mapping

I understand that my data has now been scaled to the interval between zero and one. I am now struggling to understand if I am interpreting the outputs correctly. I have looked at similar posts What is the interpretation of scaled regression coefficients when only the predictors are scaled? But I am not mathematically minded! Could someone please confirm in simple terms how to interpret results that have been normalized. Should I be thinking of this data in standard deviations?

A sample of my output is:

    Re1.(Intercept) Re1.CV1 Re1.CV2 Re1.sd Re2.(Intercept) Re2.CV1 Re2.CV2 Re2.sd
St1           0.076   0.060  -0.064  0.079           0.135   0.123 0.378  0.158
St2           0.052   0.017  -0.051  0.036           0.177   0.081 0.247  0.183 
St3           0.017   0.004   0.001  0.020           0.245  -0.029 0.131  0.174 

(St= state, re= response, CV= covariate).

Re1 was in seconds prior to normalisation and Re2 was in meters.

So, for example, am I correct in interpreting this as response 2 in state 3 is 0.11 standard deviations less than when in state 1 (0.245-0.135=0.11). Or is this incorrect? How can I convert the new coefficients to units of the original data (seconds, meters)? Something like this is what I am after but for the outputs of a HMM e.g.0.076 Normalized regression coefficients - interpretation

Thank you so much!!



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